Phys. Oceanogr., Vol. 10, No. 1, pp. 61-84 (1999) 9 VSP 1999.
Experimental and Field Research Bottom boundary layer in the Black Sea: basic results and prospects of investigations* V. N. E R E M E E V and V. M. K U S H N I R Abstract - - We discuss the current state of the problem of experimental investigation of the bottom boundary layer of the Black Sea and present the data on a new measuring complex (designed and constructed at the Marine Hydrophysical Institute and called the OLT-D profilometer of the bottom layer) together with some results of its application. On the basis of the analysis of the data on the dis: tributions of geothermal fluxes and parameters of the bottom boundary layer in the deep-water part of the sea, we deduce and justify the relations for the evaluation of the critical thickness of the bottom boundary layer as a function of the intensities of geothermal fluxes. It is shown that the numerical resuits are in good agreement with the data of direct measurements of the thickness of the bottom boundary layer. INTRODUCTION The results of investigations of the bottom boundary layer of the Black Sea are of great practical significance and can be used for the solution of numerous oceanographic, geophysical, and geologic problems. A m o n g these problems, one should especially mention the necessity of the analysis of m the causes of the variability of hydrophysical fields in the bottom zone, including bottom vortices, abrupt changes in the flows (bottom storms), wave oscillations, and flows caused by density gradients; diffusion in the bottom layer determining the processes of heat and mass transfer between the water medium and the bottom surface; - - bottom friction in the shelf zones and its influence on the field of flows; - - bottom thermal convection and its correlation with geothermal fluxes; m the processes of formation of sedimentary deposits and the geomorphology of the bottom; the manifestations of active geologic processes (such as m u d volcanoes and gas release) in the hydrophysical, hydrochemical, and hydrooptical fields. Explorations carried out for the purposes of marine building, laying of various types of mains on the s e a floor, geologic prospecting, mariculture, development of projects in the field of environmental protection, and other ecological problems, as *Translated by Peter V. Malyshev and Dmitry V. Malyshev UDC 551.465
62
V. N. Eremeev and V. M. Kushnir
well as the exploitation and practical use of the marine resources are the main applied aspects of the investigation of the boundary bottom layer. Despite the important role of the investigations of the bottom boundary layer for the solution of numerous fundamental and applied problems, this direction is studied quite poorly. This fact is largely explained by a relatively small amount and incompleteness of the available experimental data on the structure and dynamics of the bottom boundary layer caused by difficulties encountered in measurements performed in the bottom region as well as by the lack and low quality of specialized measuring instruments. At present, we know about the results of several separate series of observations of the bottom boundary layer performed with the help of autonomous and cable bottom stations. The data obtained by these stations are used to determine the time dependences of the characteristics of hydrophysical fields, stress parameters, and the coefficients of bottom friction [1-11]. Another direction of the experimental investigation of the bottom boundary layer is connected with the application of sounding instruments. These instruments are used to determine the basic characteristics of the vertical structure of flows and various hydrological, hydrochemical, and hydrooptical elements [12-19]. We can also mention the methods based on the determination of the vertical distribution of the concentration of radon-222 which comes into the bottom layer in the process of diffusion from sediments and distributes in it, as an inert gas, without chemical reactions. Actually, this means that the vertical distribution of the concentration of radon-222 directly reflects the process of diffusion in the bottom layer [20-23]. The problem of the deep-water bottom layer of the Black Sea was intensely studied in the late 50s and early 60th in connection with the projects of burial of radioactive wastes [24, 25]. In recent years, the attention of researchers to this object is explained by complex oceanographic investigations of the Black Sea carried out within the framework of national and international research programs [26, 27]. Even now, the amount of experimental data accumulated by using contemporary high-resolution sounding instruments is relatively small. These data mainly relate to the hydrologic structure (temperature, salinity, and density) of the deep-water bottom boundary layer. At the same time, the data on the field of flows and optical and hydrochemical characteristics of the bottom layer are practically absent. The interpretation of the results of measurements based on the existing ideas about the convective nature of the bottom boundary layer is also insufficient for the explanation of its basic distinctive features [17, 28]. In the shelf zone of the Black Sea, under variable conditions (the slope of the bottom, its density stratification, and the field of flows in the main thickness of water), one can expect that the difference between the parameters of the bottom boundary layer can be significant. This fact is corroborated by the data of measurements of the bottom boundary layer in three regions, although the established general characteristics [15] do not exhibit any principal difference with similar data accumulated for some other regions of the World Ocean (it should be emphasized that, in all cases, the data of this sort are very poor and fragmentary). Thus, to perform the comprehensive investigation of the bottom boundary layer
Bottom boundary layer in the Black Sea: basic results and prospects
63
in the Black Sea required for the purposes of both fundamental sciences and various applications, it is necessary to solve numerous problems including, first of all, the design and manufacturing of specialized measuring instruments aimed at recording vast amounts of data accumulated as a result of observations performed both in the shelf and deep-water parts of the Black Sea, the development of special methods, mathematical tools, and software for processing the data of measurements of the characteristics of the bottom boundary layer, the analysis, systematization, and interpretation of the available data, and the development and justification of special programs of in situ measurements. Some results obtained in this field at the Marine Hydrophysical Institute of the Ukrainian Academy of Sciences are presented below. C O M P L E X OF MEASURING E Q U I P M E N T FOR THE VERTICAL P R O F I L I N G OF THE BOTTOM BOUNDARY LAYER A special OLT-D profilometer of flows and hydrologic elements aimed at the accumulation of vast amounts of the experimental data on the vertical structure of the bottom boundary layer was designed and constructed at the Marine Hydrophysical Institute. This instrument is based on an OLT probe-profilometer created somewhat earlier (see [29, 30]). It enables one to measure the indicated characteristics both in the main thickness of water and in the bottom layer down to the contact of the sounding instrument with the bottom. To realize the possibility of exact measurements of the distance to the bottom, we equipped the OLT-D profilometer with a bottom echo sounder operating at a frequency of 120kHz and guaranteeing a depth resolution of 10 cm at distances of about 50-55 m. The indications of the bottom echo sounder were displayed in the screen of a personal computer in order to perform the exact monitoring of the distance from the bottom in the process of sounding. In recalculating the indications of the echo sounder to distances from the bottom, we used actual values of the sound velocity. A specially designed high-strength titanium enclosure of transducers was used in the submersible part of the OLT-D profilometer. When the probe touches the bottom, this enclosure guarantees the location of the sensitive elements of the transducers at a distance of 40-50 cm from the surface. Special mathematical tools and software were developed for the computer processing of the data of vertical profiling of the bottom boundary layer. The software package is organized in the form of successive operation of different software modules with intermediate graphic monitoring of the data and specification of the parameters of computations in each stage in the interactive mode. The first software module is used for the preliminary preparation of the experi mental data. Its operation results in the unpacking of the data and determination of the total number of frames and the maximal depth of immersion. Further, the number of rejected frames (from the beginning of the procedure of recording) N O is "specified in the interactive mode. For the remaining array, we compute the values of depth Z, temperature T, salinity S, sound velocity C, projections of the relative
64
V. N. Eremeev and V. M. Kushnir
velocity of the flow on the meridian VN, parallel liE, and vertical Vz, density ~t, and distance from the bottom R. Finally, according to the results of computations, we form the z T S ~ t , zVzRT, and z VNVecr t files and the operator decides whether it is reasonable or not to check the data by using the program of graphic representation. To pass to the ~second software module, it is necessary to determine the exact distance between the transducers of the probe and the bottom according to the formula R D = - Z g + Z + AZp,
(1)
where Zg is a depth of the sea according to the data of the shipbome echo sounder and Azp is a correction to the value of depth specified by measuring the exact distance to the bottom according to the indications of the bottom echo sounder. To exclude possible errors and large deviations, it is necessary to subject the experimental data to median filtering with a given step. After this, we form the R o T S c t and R D Vtl,'ec t files. They can be used for the graphic monitoring of numerical results. The next module is intended for the evaluation and compensation of the velocity of motion of the sounding instrument with respect to the bottom (VcI~ VCE) There are two procedures used for numerical calculations. The first procedure is simpler. It is based on the evaluation of the velocity of motion of the probe by analyzing the increments of the length of the load-carrying cable AL and depth Az for fixed intervals of time A T. For this purpose, we use a sliding regression algorithm of numerical computations with data averaging over layers with a thickness of 30 m for a sinking speed of 1 m/s~ The direction of motion is found by determining the angle between the horizontal projection of the inner end of the load-carrying cable and the plane of magnetic meridian with regard for the current course of the ship. The second procedure is more complicated but quite efficient. It is based on the numerical solution of the equilibrium equation for the load-carrying cable which can be written in the form
= (VF)F,
I~n = I?- q ,
(2)
where G is the weight of a unit length of the load-carrying cable, d is its diameter, p is the density of water, C n and C t are, respectively, the coefficients of normal and tangential hydrodynamic resistance, I7n and 17tt are, respectively, the normal and tangential velocities of the flow of water relative to the moving load-carrying cable, T is a tensile force, ~ is a unit vector tangent to the load-carrying cable, and l is its current length.
Bottom boundary layer in the BlackSea: basic resultsand prospects
65
The boundary conditions for the running end of the load-carrying cable are specified for each segment Al according to the indications of a built-in meter of the angular parameters of spatial orientation of the probe. The value of Cn depends on many factors and is also computed for each segment by using the condition of minimization of the variance of deviations of the actual depth of the probe measured according to the experimental data from the results obtained by using the numerical solution of equation (2) [31]. To complete the operation of this software module, we form the R D VCI~CE and R O Vc~+ VNVcE +VE files, which can be used for the purposes of graphic monitoring and subsequent calculations. The last module of data processing is used for the interpolation of the data to a given regular grid of depths, their smoothing by using a fifth-order Butterworth filter (if necessary), and correction of the data on the velocity of the probe in the bottom region according to the condition that the measured value of the flow velocity must be equal to zero when the submersible device comes into contact with the bottom~ The step of the regular grid of depths, the parameter of the Butterworth filter, and the parameters correcting the velocity of the probe are specified in the interactive mode and can be changed many times. The final results of calculations of the parameters of the bottom boundary layer are formed as the R D VNVE(Yt, R o (~UE(Yt, and RD~(Y t files and can be used for the graphic representation of the results and subsequent calculations connected with the interpretation of the data. Here, V~v and VE are the components of the relative velocity of the flow reduced to the regular grid of depths after filtration and UN and UE are the components of the absolute velocity of the flow also reduced to the regular grid of depths after filtration. In Fig. 1, we present an example of indications of the bottom echo sounder R and the profile of the sound velocity C obtained as a result of a single procedure of sounding in the shelf zone (station 5928, the 32nd cruise of the R/V Professor Kolesnikov). As the distance from the bottom becomes smaller than 60 m, the indications of the bottom echo sounder begin to vary although reliable contact with the bottom is guaranteed for distances from the bottom of about 33 m. For the indicated working parameters, the bottom echo sounder operating together with a depth indicator with a resolution of 25 cm (its error can be as high as 5-7 m) enables one to guarantee the possibility of reliable control over the process of sinking of the probe into the bottom boundary layer down to its contact with the bottom and establish the exact correspondence between the data of measurements and the current distance from the transducers to the bottom. INVESTIGATIONS OF THE BOTTOM BOUNDARY LAYER IN THE SHELF ZONE The first series of measurements in the bottom boundary layer in the shelf zone of the Black Sea was carded out with the help of an OLT probe-profilometer in [15].
66
V. N. Eremeev and V. M. Kushnir
4460.0
146LI.0
!
i
QoO 0.0 - ~'-'-"-
(2,m/s
lq 6~I.0
I
,o..o
I
ao..o
3o..o.
4o..o
!
so,.o
.
60,.0
.
.R, m
~'0.0.
R 40.0 ~0.o
~0.0 10o, o -
.lo..o.o q
1'~0.0
H,m
-~"
H g = 33 m
Figure 1. Typical example of the vertical profiling of the bottom boundary layer in the shelf zone (C is the sound velocity and R are indications of the bottom echo sounder).
According to the results of these measurements, we determined the following generalized parameters of the bottom boundary layer: the friction velocity, the upper and lower boundaries (with regard for the slope of the bottom and the character of density stratification), the Froude numbers characterizing the dynamic stability of the bottom layer, the local inertial period, and the coefficients of vertical transfer (diffusion) of momenta, heat, and salinity. The indicated parameters varied within fairly broad ranges typical of many other regions of the World Ocean. The data of direct measurements of the thickness of the bottom boundary layer were in good agreement with numerical results. In the 32nd cruise of the R/V Professor Kolesnikov, the measurements were carried out by using the OLT-D complex in the shelf zone of the north-west part of the Black Sea and to the south of the Crimea. As in the case of the first series of measurements, the OLT profilometer made it possible to discover a great variety of structural features of the bottom boundary layer in the shelf zone (at depths of 70150 m). Two series of typical profiles of the projections of the flow velocity on the meridian VN and parallel VE, density ~t, temperature T, and salinity S are depicted in Fig. 2. In Fig. 2a, the bottom boundary layer is observed in the form of a 10-meter layer with quasihomogeneous distributions of temperature, density, and salinity. Within this layer, we also observe a sharp decrease in the flow velocity from 8 cm/s to zero at the bottom. In Fig. 2b, we present a typical example of an increase in the temperature, salinity, and density gradients in the bottom layer with a thickness of 12 m. The same layer is also characterized by a decrease in the flow velocity from 3-4 cm/s to zero. As a distinctive feature of density stratification, we can mention the phenomenon of strong interbedding of layers with variable vertical gradients.
Bottom boundary layer in the Black Sea: basic results and prospects
67
.=_ c~
~
I j
i i
~: ~, .~
E
!I.~,
:~/~
N
| 4"
,/" :,,,/.;-
7 ]/I%I 'q j
.J'q
: .24 / f " r../'
F~ '~
~
[J
I
,
.
r
11
~'~~
II 4'
=.
I J i j
I
jl'~# ~'~'~
,t. +"
//
/ / /
I
i
oi[
~
68
V. N. Eremeev and V. M. Kushnir
Note that the profiles of flows are characterized by the formation of intermediate maxima of the flow velocity in layers with lower density gradients (e.g., at distances of 30 and 60 m from the bottom in Fig. 2b). Inlayers characterized by higher density gradients, we observe an increase in the vertical shifts of the components of the horizontal flow velocity. The indicated features of the correspondence between the profiles of flows and density are readily visible in Fig. 2a and other profiles plotted both in the sheff zone at intermediate depths of 500-1000 m and in the deep-water part of the Black Sea. The profiles displayed in Fig. 2 reflect, in a certain sense, limiting situations. In the other profiles of flows and hydrologic characteristics plotted for the shelf zone, we observe various intermediate values of the bottom density gradients and the thickness of the layers characterized by a sharp decrease in the flow velocity varies within the range 3-15 m. The accumulated experimental data corroborate the assumption made above concerning the possibility of a relatively large variety of structures of the bottom boundary layer in the shelf zone. For the evaluation of the generalized parameters of the bottom boundary layer, one can use various models [32], in particular, the model of turbulent boundary layer of a liquid with density stratification over an uneven bottom [19, 33] (as in [15]), the semiempirical model of Nabatov and Ozmidov [34], the model based on the concept of the Richardson flow number [19], etc. For given profiles of the flow velocity and density and the parameters of the slope of the bottom, one can determine the optimal model of the bottom boundary layer and find the proper values of the parameters of this layer. INVESTIGATIONS OF THE BOTTOM BOUNDARY LAYER IN THE DEEP-WATER PART OF THE BLACK SEA According to the existing concepts, the formation of the bottom boundary layer in the deep-water part of the Black Sea is connected with the development of convectional circulation induced by geothermal fluxes. The thickness of the bottom boundary layer attains 400-500 m and its upper boundary is readily visible in the profiles of potential temperature, salinity, and density in the form of 30-80-m layers of locally elevated gradients and sharp transitions to the homogeneous structure [16, 17, 25, 27, 28]. The convectional mechanism of formation of the deep-water bottom boundary layer is qualitatively corroborated by the laboratory investigations of convection in a layer of water stabilized by a positive vertical gradient of salinity [35, 36]. In experiments of this sort, it is possible to reproduce the formation of a bottom region with quasihomogeneous distributions of temperature and salinity separated from the nonperturbed layer of water by a relatively thin gradient layer similar to a frontal zone. It is worth noting that, under laboratory conditions, the process of formation of this stratified structure is nonstationary. In analyzing the structure of the deep-water bottom boundary layer, we used the archival data from the database of the Marine Hydrophysical Institute, namely, the results of deep-water STD-soundings performed by using the ISTOK-7 and OLT in-
Bottom boundary layer in the Black Sea: basic results and prospects
69
struments with a temperature resolution of 0.0004"C. We processed these data to determine the profiles of potential density and salinity and the values of modified potential temperature Om which differ from the values of potential temperature O by the procedure of computations based on the analysis of cooling in the process of adiabatic expansion of a volume of water not on the sea surface but on the upper boundary of the bottom layer, i.e., 0m
=
T - P(T, S, p) + P ( TG, S G, PG) = 0 + P ( TG, S G, Po),
(3)
where P(T, S, p ) is a polynomial used for the evaluation of the degree of adiabatic cooling of a volume of water and TG, SG, and P G are, respectively, the values of temperature, salinity, and hydrostatic pressure on the upper boundary of the bottom layer [37]. As a distinctive feature of the profiles Om (z), one can mention the fact that, in many cases, we observe a temperature drop AOm within the bottom boundary layer equal to 0.0005--0.001~ The analysis of a great number profiles of the hydrologic elements in the bottom boundary layer demonstrates that, in many cases, their structure is quite complicated. Thus, in some profiles, we discover an additional well-pronounced layer with homogeneous distribution of potential temperature whose thickness varies within fairly broad limits. The temperature drop between the upper and lower quasihomogeneous layers is relatively low and equal to 0.0005-0.002~ On the inner boundary, we also observe small drops of salinity and potential density and the vertical gradient of density changes its sign. Due to the absence of data on the vertical structure of flows in the deep-water bottom boundary layer, measurements of this sort are of certain interest. The first measurements of the profiles of flows were carried out by using the OLT-D probe parallel with the measurements of the hydrologic elements in the meridional section to the south of the Crimea during the 32nd cruise of the R/V Professor Kolesnikov in December, 1994. The examples of profiles of the projections of the flow velocity onto the meridian VN and parallel V~ and conditional density ~t are presented in Fig.3. The typical values of the flow velocity in the 200-m bottom layer are as high as 2--4 cm/s. At a distance of about 40 m from the bottom, we observe the appearance of inhomogeneities in the profile of conditional density in the form of stepwise structures. In the same layer, the flow velocity decreases to zero at the bottom. Layers with developed fine structure were recorded at Station 5920 at distances of 90-130 and 200240 m. At the same depths, according to the indications of a high-frequency bottom echo sounder, we recorded layers of false bottom characterized by the stable reflection of high-frequency hydroacoustic signals (Fig. 3). At the neighbouring stations of the meridional section, we also recorded layers of false bottom at the same depths. This phenomenon is of interest for further investigations with the use of special hydrooptical instrumentation and sampling for subsequent hydrochemical analyses.
70
V. N. Eremeev and V. M. Kushnir
S t . 5920, z 0 - 1930 m
llo
#r.~io -ato 9
~4,12 ' '-o.0~"
'
~o
1 09"
-,,;-,,
-
~ ?
2~
'
~
V.. V~mi s
"
~o
o Z,, HI.
o.J'~'
~.ji i ~r '
I./,'
/
:
\ j ' ) 9.o# ~/4~
' |
9
IM '.i~ '
'
.
,
.,
7'.'C
rz.~' ~,,
i
i
S,T.
,,~
\.
~0
#O 4o
~.....,., ~..f.....~..a
\
0
Figure 3. Profdes of the projections of the flow velocity onto the meridian VN and parallel VE , density a t , temperature 7", and salinity S in the deep-water bottom boundary layer. Since the indicated meridional section is located in the zone o f the abyssal Trans-Black-Sea Fault, we can assume that the appearance o f these layers is explained by active geologic processes. The d e g r ~ of inhomogeneity of the flow velocity in the bottom boundary layer can be estimated by using the Hunt formula [38]:
o,, = c~ (q0~) ~/3,
(4)
Bottom boundary layer in the Black Sea: basic results and prospects
71
where qo = c~gQ/PoCp = txgHr is the buoyancy-induced flow, h 0 is the thickness of the bottom boundary layer, c~ is the coefficient of thermal expansion, g = 9.81 m/s 2 is the acceleration of gravity, H T is the heat flux, and C 1 = 1-1.5 is an empirical coefficient. Under the conditions of the deep-water part of the Black Sea, we have t~ = 1.36-10 -4, HT= 1.25-10-Sdeg.m/s (50mW/m2), h 0 = 500m, and Cv = 0.66 cm/s or, with a probability of 0.99, the inhomogeneities of the flow velocity can be as high as + 2 cm/s. These results are in approximate agreement with the degrees of vertical inhomogeneity of the flow velocity in the bottom boundary layer established according to the data of vertical profiling by using the OLT-D probe. The drop of the flow velocity in the gradient layer on the upper boundary of the bottom layer can be evaluated by using the Long relation [39] as follows: cyv2 = CLAbhg,
Ab = g (~AS - t~AT),
(5)
where CL = 0.13-0.5 is an empirical coefficient, hg is the thickness of the gradient zone on the upper boundary of the bottom layer, 13 is the coefficient of salinity-induced compression, and AT and AS are, respectively, the increments of salinity and temperature in the gradient zone of the bottom boundary layer. Under the conditions of the deep-water bottom boundary layer in the Black Sea, the minimal and maximal values of crv are equal to 0.7 and 1.2cm/s, which corresponds to the possibility of appearance of inhomogeneities of the flow velocity in the gradient zone varying from + 2 to + 3.6 cm/s. These values also coincide with the experimental data (see Fig. 3). R E L A T I O N S H I P BETWEEN THE CRITICAL THICKNESS OF T H E B O T T O M BOUNDARY LAYER IN T H E DEEP-WATER PART OF T H E SEA AND G E O T H E R M A L FLUXES The concept of critical thickness h 0 of a mixed homogeneous layer over a heated surface was introduced by Turner on the basis of the results of laboratory investigations of the process of thermal convection in a water layer stabilized by a positive vertical gradient of salinity. The critical thickness of the bottom boundary layer corresponds to the situation where the growth of a homogeneous layer terminates and a convective instability begins to develop in the gradient transitional layer on the upper boundary of the homogeneous layer promoting the formation of the second homogeneous layer. This process leads to the appearance of a set of quasihomogeneous convective layers and, as a final result, to the complete mixing of the liquid. Thus, in laboratory tests, the concept of critical thickness of the bottom boundary layer corresponds to one of the stages of the nonstationary process of thermal convection in a layer of water stabilized by a gradient of salinity and heated from below. The concept of critical thickness of the bottom boundary layer proves to be useful for the interpretation of the data of measurements of the characteristics of convective layers under certain conditions in the World Ocean and lakes.
72
V. N. Eremeev and K M. Kushnir
2~r~
dO"
~2 ~
.1r
.t6 o
.~aR
~ff.
12" E
48"N
46*
/
44*
,--4"! ::
42*
Figure 4. Map of distributions of the geothermal fluxes in the Black Sea (mW/m2 ). Thus, in particular, Newman published the data on the thickness of the bottom convective layer for three regions of the Lake Kivu, which are in good agreement with the results of evaluation of its critical thickness [40]. Fedorov also accumulated the data proving that the thickness of convective layers in the ocean is in satisfactory agreement with the values of critical thickness h o [41]. On the basis of these resuits, he advanced a hypothesis on the possibility of stationary existence of the critical layer under natural conditions in the presence of horizontal advection and diffusion of salts in the bottom boundary layer. In [17], Murray, Top, and Ozsoy made an attempt to compute the critical thickness of the bottom boundary layer for the deep-water part of the Black Sea by using the Turner [35] and Femando [36] formulas and compare it with the actual thickness of the bottom boundary layer. According to the Turner formula, the value of h 0 was somewhat higher than 40 m and the Fernando formula gave the value of about 20 m, whereas the actual thickness of the bottom boundary layer was 300--400 m. We do not want to discuss here the physical grounds for the comparison of the thickness of the bottom boundary layer with its critical value. We only consider the procedure of evaluation of this parameter for the conditions of the deep-water part of the Black Sea taking into account the influence of the Coriolis force on the development of convective instability in the transition gradient layer on the upper boundary of the bottom layer. To analyze the relationship between the critical thickness of the bottom boundary layer and geothermal fluxes, we collected all available data of their direct measurements [42-46]. On the basis of these data, we drew a map of the geothermal
Bottom boundary layer in the Black Sea: basic results and prospects fluxes depicted
i n F i g . 4. D e s p i t e t h e c o m p l e x
character
mal fluxes, one can easily reveal their correlations of the Black-Sea
Basin, in particular, with the main
Kaliakrian,
and Crimean,
also known
that there exists pronounced
the geothermal
with the border
fluxes and anomalies
of inhomogeneities
with the basic geologic
of therstructures
abyssal faults: Trans-Black-Sea,
of the Russian
correlation
73
Platform,
between
of the geomagnetic
etc. [47].
the inhomogeneities
It is of
field [42, 47].1
Table 1. Characteristics o f the bottom boundary layer in the deep-water part o f the Black Sea
Coordinates
Depth, m
Geothermal flux, mW/m
Thickness o f the bottom boundary layer, m
N
E
total
43o29 ,
31o14 ,
1550
23
60
-
44020 ,
33~
1580
20
170
76
43o30 "
32o15 "
2010
20
196
73
43~
32~
"
2030
23
250
83
43o30 "
33~
`
2180
38
365
-
43o48 "
33045 ,
2110
36
323
160
,
internal layer
42o50 "
37o45 ,
2100
40
360
240
43o30 "
32045 "
2016
30
286
-
43o30 ,
37o45 "
2100
27
290
-
43o30 "
35045 "
2200
28
360
-
43030 "
35o14 ,
2200
36
410
-
43o30 ,
34045 ,
2200
36
380
-
43o30 ,
38o15 ,
2090
25
360
275
43o30 "
32o45 ,
2016
31
256
196
43o30 ,
36~
2170
37
355
-
43o30 ,
37o15 "
2160
36
320
-
44~
35o45 ,
1800
30
210
-
43o15 ,
34~
,
2200
36.5
370
-
43o50 "
33045 ,
2054
33
184
-
43o30 ,
31014 ,
1970
25
276
140
43011 ,
34o15 "
2200
36
360
-
43o50 "
35~
2090
30
390
290
"
44~
36o45 ,
1950
30
250
-
43o50 ,
33o15 "
1980
34
310
-
43o30 "
31o45 ,
2100
30
290
-
42030 "
38o45 "
2045
37
345
-
43o11 ,
34o15 "
2212
36.5
362
-
44~
37~
1994
27.5
244
-
I T h e detailed m a p o f the geothermal fluxes and the p r o b l e m s of their description b y the g e o t h e r m a l m o d e l o f the Black Sea Basin are d i s c u s s e d in the work by Prof. R. Kutas et al. prepared for publication in the Geofizicheskii Zhurnal (Institute of G e o p h y s i c s , Ukrainian A c a d e m y o f Sciences).
V. N. Eremeev and V. M. Kushnir
74
,12
I
I
4
I
5
I
43030 ,
32015 ,
2010
22
200
-
43030 ,
32045 ,
2016
31
291
216
43030 "
36015 "
2040
20
225
-
43~
37045 ,
2130
27
340
-
43~
31045 ,
1589
26.5
89
-
44010 ,
32~
1580
31
120
-
43030 ,
31045 ,
1925
28
205
-
43010 ,
31015 ,
1804
24
120
-
42~
30045 "
2100
32
380
-
42~
30~
2097
40
377
-
42030 ,
29015 ,
2000
40
300
-
43030 ,
31045 "
1950
25
130
-
43~
31~
1816
25
66
-
42050 ,
30015 "
2100
40
350
-
42~
30~
2100
40
330
-
43030 ,
31045 "
1950
22
130
-
43~
34015 "
2200
37
440
-
43o30 ,
31045 ,
1950
25
190
-
HnL, 500
400
e
300
9
4 9
9
9 ~
200
e
100
e
W, m W / m 0
1(3
20
30
2
40
F i g u r e 5. D e p e n d e n c e o f t h e t h i c k n e s s o f t h e d e e p - w a t e r b o t t o m b o u n d a r y l a y e r HBB L o n t h e i n t e n sity o f t h e g e o t h e r m a l flux W.
Bottom boundary layer in the Black Sea: basic results and prospects
75
The data on the spatial distribution of inhomogeneities of the geothermal fluxes were related to the values of thickness of the deep-water bottom boundary layer. The main data for the regions of measurements are presented in Table 1. In Fig. 5, we present the plot of the dependence of the thickness of the bottom boundary layer on the intensity of geothermal fluxes. Despite a relatively large spread and ambiguity of the experimental data, we can discover a certain regularity, namely, that the thickness of the bottom boundary layer increases with the intensity of the geothermal flux. It is well known that the intensity of the geothermal flux depends on the critical thickness of the bottom boundary layer as follows [35, 36]: h 0 = (0.25Rak) 0"25(vq03 kt 2 N-8) ~
(6)
r gQ qo =
PoCp'
where Rag is the critical value of the Rayleigh number, N is the Brunt-V~iis~il~i frequency in the transition gradient layer, k t is the coefficient of molecular thermal conductivity, and v is the coefficient of kinematic viscosity. First, we consider the principal factors determining the possibility of application of relation (6) for the in situ conditions of the Black Sea. We have already shown that the structure of the vertical profiles of temperature established under laboratory and in situ conditions are qualitatively similar. Indeed, they are characterized by the presence of a relatively thin gradient layer on the upper boundary of the quasihomogeneous bottom layer observed both in the course of laboratory investigations of the process of thermal convection of a water layer stabilized by a positive vertical gradient of salinity and for the most part of the actual profiles of potential temperature. To establish quantitative criteria of the possibility of application of relation (6) under the in situ conditions, we consider the ratio of the thickness of the gradient layer to the thickness of the quasihomogeneous bottom layer, i.e., the quantity K b = hg/ho. In the well-known work by Turner [35], this quantity was obtained by equating the temperature drop on the upper boundary of the quasihomogeneous bottom layer (specified by the balance relations) to the temperature drop in the gradient layer specified by the solution of the equation of vertical diffusion for this layer. Thus, we perform the transition from the critical thickness of the bottom boundary layer to the thickness of the gradient layer on its upper boundary. According to the Turner formula, for the quantity K b, we can write K o = 2 KTN2 = 7.54318-1012 KTNz , qo Hw
(7)
where H w is the geothermal heat flux (mW/m 2) and K T is the coefficient of ther-
76
V. N. Eremeev and V. M. Kushnir
mal conductivity for the gradient layer characterized by positive temperature and salinity gradients. Under these conditions, Fedorov [48] deduced the following relation for KT: K r = 9.0f(Rp) w,
(8)
where f(Ro) is the ratio of the heat flux through the liquid interface to the heat flux through the solid heat-conducting plate for the same drop of temperature. For this dependence, we know various empirical relations [49]. Their application enables us to reduce (8) to the following formulas: K r = 4.94682.10-SR~ K r = 1 . 3 7 2 -10--6 exp
f
(Turner, 1973), r
11
~4.6exp [-0.54(R0 - 1)] ~, (Marmorino and Caldwell, 1976)
K r = 4.94-10 -7 exp (4.8 Rp-~ ),
(9)
(Kelly, 1990).
Relations (7)--(9) were used to compute the ratio K 0 according to the data of experiments performed by using the ISTOK-7 and OLT-D instruments at 19 hydrologic stations in the deep-water part of the Black Sea. For the same stations, the quantities K 0 were also found according to the results of direct measurements. The numerical results are compared with the experimental data in Fig. 6. Despite a certain spread in the data with respect to the line of equal values, the average deviation is as large as about 5% for the Kelly relation, 15% for the Turner relation, and 18% for the Marmofino--Caldwell relation. In our opinion, these data demonstrate that the well-known Turner model [35] can be used for the analysis of the structure of the bottom boundary layer in the deep-water part of the Black Sea. It is known that the theoretical value of the critical Rayleigh number is equal to 657.5. According to the dntn of different laboratory experiments, it varies from 103 to 104. Newman [40] established the correspondence between the thickness of the critical layer and the actual thickness of the bottom boundary layer on the Lake Kivu for Rat = 2.4.104. The thickness of the gradient layer hg on the upper boundary of the bottom layer in the Black Sea varies within the range 30-80 m. In determining the conditions required for the development of convective instabilities in a layer whose thickness varies within the indicated range, it is necessary to take into account the influence of the Coriolis force. However, in many other cases, this factor may be insignificant. Indeed, under laboratory conditions, the thickness of the gradient layer is, as a rule, equal to several centimeters and the Taylor number (T = fZhgv-2) has, in this case, the order of 10 - 2 , i.e., it is much lower than the critical Rayleigh number.
Bottom boundary layer in the Black Sea: basic results and prospects
o.~
77
h x / h 0 meas.
O ~9
0..~
O
+
9
+
+o 9
a.J
9
+
o
0
.//0
+
9 "" + 0 0 o p / "
0.2
9
o
9 -I- o
4-/*
9
++0 +
~,~ o
.
+
0
"1"*
*
+
4
o 9
+
*
9
9 0 0 0
0
o
Q
--
2
,§247 -,5
0.! hi]h0 calc.
0
l=
o.1
I
0.9
I
I
O.J
0.4~
,
|
a5
I
I
0.6
0.7
Figure 6. Comparisonof the experimentaland theoreticalvalues of the ratio hg/ho performedby using differentempiricalrelationsfor the function Hn = f(Rp): (1) Turner (1973), (2) Marmorino and Caldwell(1976), (3) Kelly(1990). In Newman's measurements, the thickness of the bottom boundary layer did not exceed 1.5 m and the corresponding thickness of the gradient layer was, as a rule, not larger than 0.3-0.5 m. These parameters correspond to Taylor numbers varying within the range 40-300. They are also much lower than Rag and, therefore, the influence of the Coriolis force on the development of convective instabilities is insignificant in this case. However, under the conditions of the bottom boundary layer in the deep-water part of the Black Sea, for hg = 30-80 m, the Taylor numbers vary within the range 3.9. 109-2 9 1011, i.e., are much higher than Rag. Therefore, in this case, the effect of the Coriolis force should necessarily be taken into account. Tareev [50] considered the general statement of a problem of this sort. The system of hydrodynamic equations reduced to the dimensionless form yields the following condition for the development of convective motions: o 2 - c ~ R a + s 2 ( R a + T ) = 0,
(lO)
where c = l 2 + m 2 + s 2 is the sum of squared wave numbers of the convective cells along the horizontal and vertical axes. The condition
78
V. N. Eremeev and V. M. Kushnir
0Ra Ot~ = 3 c c - R a
= 0
determining the minimal critical Rayleigh number Ra k = 3~c2 implies the following cubic equation: (Yc 2
-
-
1.5s2c32 - 0.5sET = 0.
(11)
Note that the lowest real positive roots o f this equation correspond to the minimal vertical wave number s = ~. Equation (11) has the following real solution: oc = 0.5 r~ + ~ + 13, = [0.25/~2 (T + 0.5/~4 ) + 0.25rc2 (T 2 + re4 T)O.5 ]1/3, = [ 0.25rc 2 (T + 0.5r~ 4) - 0.25rc 2 ( r 2 */t4T) 0"5]I/3. For T >> ~4, we obtain t~ c = ( 0 . S r c 2 T ) I/3
and
Rag = 3(0.5~2T) 1/3.
(13)
Substituting the expression for Rak in relation (6), we fred .... 0.75-o.333 -0.o833-1.67 -1- -I--0.5 h = l . z l 4 p o q o 3" v n~ g /x~ ttr t ,
(14)
where A~ t is the increment of potential density in the frontal zone of the convective layer. It is convenient to use the following representation of the buoyancy-induced flow q0 via the intensity of the geothermal flux H w measured in mW/m2: q0 = 2.6514.10-13Hw .
(15)
Under the conditions of the deep-water bottom boundary layer in the Black Sea, w e h a v e po = 1017kg/m3, f = 104rad/s, v = 1.436-1ff6m2/s, kt= 1.35.10-Tm2/s, g = 9.81 m / s 2. As a result, we arrive at the following relation for the critical thickness of the bottom boundary layer: h 0 = 48776.742 qO.75 ng'-I67/x(y t - -1 or
(16)
Bottom boundary layer in the Black Sea: basic results and prospects
nnl,
79
m
400
300
200
9 /
10o
//.
is
Figure 7. Comparison of the experimentally measured values of the thickness of the deep-water bottom boundary layer Hm with its theoretical values ho. ..075-167--
h o = 1.80226.10-5Hf~
n~" ' ~ t
-1
9
(17)
For the values H w = 30 mW/m 2, hg = 50 m, and Ao t = 5.10 4 typical of the Black Sea, we get h 0 = 318 m in good agreement with the actual values of the thickness of the bottom boundary layer. Relation (17) was used to find the critical thickness of the deep-water bottom boundary layer. The results of comparison of the computed values of h 0 with the actual values Hm of the thickness of the bottom boundary layer measured by using sounding instruments are depicted in Fig. 7. In general, we observe a fairly good agreement between the theoretical and experimental data. This means that, just as in the works cited above, the thickness of the bottom boundary layer in the deep-water part of the Black Sea is close to its critical value. This may happen if the bottom boundary layer is "fed" by a flow of salt. However, the physical mechanism of this "feeding" remains unclear. P R O S P E C T S OF T H E EXPERIMENTAL INVESTIGATIONS OF T H E B O T T O M BOUNDARY LAYER In the previous sections, we have briefly described some available results of the investigations of the bottom boundary layer in the Black Sea. For the sake of brevity,
80
v. N. Eremeev and V. M. Kushnir
we do not consider, e.g., the problems of heat fluxes through the frontal zone of the deep-water bottom boundary layer [49], optimization of the procedures of data processing in the course of deep-water sounding aimed at the objective separation of useful signals and determination of the boundaries of the bottom layer, etc. In view of practically complete absence of data of this sort, measurements of the characteristics of the bottom boundary layer in the shelf zones are of interest for the initial accumulation, zoning, and systematization of the data on generalized parameters (such as the friction velocity, the parameter of dynamic stability, and the coefficients of vertical transfer) and their dependences on the characteristics of the bottom pattern, density stratification, and fields of flows. In the regions of economic activity (mariculture, building, laying of mains, etc.), it is reasonable to organize permanent monitoring of the bottom boundary layer in order to guarantee the possibility of prediction of the ecological consequences of these works and develop the optimal programme of environmental protection. In some cases, e.g., in the process of artificial breeding of mussels and oysters, the data of measurements of the parameters of the bottom boundary layer should be included in the technological cycle in order to control the process of feeding of molluscs and optimize the location of collectors at the bottom. The experimental investigations of the bottom boundary layer in the deep-water zone of the Black Sea are of great importance for the study of large-scale convective processes in marine media, monitoring of the general ecological situation in the basin, and complex research into the geophysical and geologic problems of the region. At present, the available data of direct measurements of the characteristics of the deep-water bottom boundary layer are very poor and fragmentary and, therefore, we actually know nothing about the field of flows and distributions of hydr0chemical and hydrooptical characteristics in the bottom region. On the other hand, it is well known that the theoretical solution of the problem of large-scale convection in a rotating layer is connected with serious difficulties [51 ]. For this reason, the accumulation of experimental data on the structure and dynamics of the deep-water bottom boundary layer is necessary for the subsequent progress in the development of the fundamental theory of the indicated natural processes. Due to the absence of noticeable tidal oscillations in the bottom region of the Black Sea, the characteristics of the bottom boundary layer are largely determined by the process of convectional circulation induced by the geothermal fluxes. In their turn, the geothermal fluxes strongly depend on the main geologic structures and geophysical anomalies. These factors enable one to use the deep-water bottom boundary layer as a large-scale natural detector of geophysical and geologic structures in the investigated region and changes in these structures. As compared with the traditional methods of geophysical and geologic investigations, this approach has the following advantages: relative simplicity of measurements and small amounts of time spent by the ship at each station (at most 3-4 h); -
-
- - the possibility of rapid analysis of the situation in the entire basin (for 15-20 days);
Bottom boundary layer in the Black Sea: basic results and prospects
81
the possibility of exclusion of random noises caused by small scales of the tools used for direct measurements of the geothermal fluxes and, as a consequence, by the strong influence of various random inclusions in the thickness of sediments. As far as the nearest plans are concerned, the maximum attention of the researchers should be given to the investigation of the deep-water region in the northwest part of the Black Sea and to the south of the Crimea. This is explained by the fact that the largest abyssal Trans-Black-Sea Fault is located just in this region. This region is also characterized by the presence of anomalies of the geomagnetic field and geothermal fluxes. The east edge of the abyssal Trans-Black-Sea Fault borders the Central Black-Sea Upheaval, which separates the West Black-Sea and East Black-Sea Basins and forms the largest geologic structure stretching from the Crimean continental slope to the Anatolian coast. In this region, mud volcanoes and areas of active gas release were discovered at depths of 2180 and 2210 m [52, 53]. The complex hydrophysical and hydrochemical survey of the bottom boundary layer performed for a grid of stations with a step of 20-30 miles for 12-15 days would enable one to establish, for the first time, the distributions of the basic parameters of the bottom boundary layer and determine the character of their correlations with geologic and geophysical structures. These works would also enable one to study the influence of active geologic processes on the distributions of hydrophysical and hydrochemical characteristics of the bottom boundary layer. In the future, investigations of this sort would probably be carried out within the framework of the programmes of international cooperation. CONCLUSIONS 1. The OLT-D high-resolution shipboard complex for the vertical profiling of flows and hydrologic elements designed and constructed at the Marine Hydrophysical Institute makes it possible to accumulate vast amounts of the experimental data on the characteristics of the vertical structure of the bottom boundary layer both in the shelf zones and deep-water parts of the Black Sea. The data obtained in the course of these measurements are processed by using specially developed procedures, mathematical tools, and software. The in situ testing of the OLT-D complex was carried out during the research cruise of the R/V Professor Kolesnikov in December, 1994, and the fin'st profiles of flows and hydrologic elements in the bottom boundary layer were obtained. 2. Episodic measurements of the characteristics of the bottom boundary layer performed earlier in some regions of the shelf zone of the Black Sea, together with the data obtained by using the OLT-D complex in December, 1994, demonstrate that there exists a great variety of structural features of the bottom boundary layer depending on the bottom pattern, the character of density stratification, and the field of flows. 3. We systematized the data on the structural features of the deep-water bottom boundary layer and the intensities of geothermal fluxes and discovered some new
82
V. N. Eremeev and V. M. Kushnir
structural features of the bottom boundary layer, namely, the formation of several bottom layers with quasihomogeneous distributions of potential temperature. The data on the field of flows in the deep-water bottom boundary layers was obtained and analyzed. 4. We analyzed the relationship between the critical thickness of the deep-water bottom boundary layer and the geothermal fluxes and demonstrate the importance o f taking into account the Coriolis force for the evaluation of the critical value of the Rayleigh number determining the convective stability of the upper boundary o f the bottom layer. We also deduced relations for the evaluation of the critical thickness of the bottom boundary layer as a function of the intensity of geothermal fluxes, the increment of density, and the thickness of the upper boundary of the bottom layer. The comparison of the computed values with the data of direct measurements of the thickness of the bottom boundary layer demonstrates that the agreement between these results is satisfactory. 5. We analyzed the prospects of experimental investigations o f the bottom boundary layer in the Black Sea as an important part of the complex investigation o f this layer and, in particular, the necessity of coordination of these activities with geologic and geophysical investigations of the region.
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Bottom boundary layer in the Black Sea: basic results and prospects
83
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33. Lykosov, V. N. and Gutman, L. N. Turbulent boundary layer over the inclined base course. Izv. Akad. Nauk SSSR, Fiz, Atmosf. Okean. (1972) 8, No. 8, 799-809. 34. Nabatov, V. N. and Ozmidov, R. V. Investigation of the turbulence of the bottom boundary layer in the ocean. Okeanologiya (1987) 27, No. 1, 5-11. 35. Turner, J. S. The behaviour of a stable salinity gradient heated from below. J. Fluid Mech. (1968) 33, 183-200. 36. Femando, H. J. S. The formation of layered structure when a stable salinity gradient is heated from below. J. Fluid Mech. (1987) 182, 525-541. 37. Bryden, H. L. New polynomials for thermal expansion, adiabatic temperature gradient, and potential temperature of the sea water. Deep-Sea Res. (1973) 20, No. 4, 401-408. 38. Hunt, J. C. R. Turbulence structure in the thermal convection and shear-free boundary layers. J. Fluid Mech. (1984)138, 161-184. 39. Long, R. R. A theory of mixing in a stably stratified fluid. J. Fluid Mech. (1978) 84, 113124. 40. Newman, F.C. Temperature steps in Lake Kivu: a bottom heated saline lake. J. Phys. Oceanogr. (1976) 6, 157-163. 41. Fedorov, K. N. Stepwise structure of temperature inversions in the ocean. Izv. Akad. Nauk SSSR, Fiz~ Atmosf. Okean. (1970)6, No. 11, 1178-I 188. 42. Zolotarev, V. G., Sochel'nikov, V. V., and Malovitsky, Ya. P. Results of measurements of the heat flux in the basins of the Black and Mediterranean Seas. Okeanologiya (I 979) 19, Issue 6, 1059--1065. 43. Sysoev, N. N. Heat flows from the bottom of the Black Sea. Dokl. Akad. Nauk SSSR, (1961) 139, 974-975. 44. Lyubimova, E. A., Nikitina, V. N., and Tomara, G. A. Heat Fields in the Internal and Peripheral Seas of the USSR: State of Observations and the Theory of Interpretation of Two-Di9mensional Inhomogeneities. Moscow: Nauka (1976). 45. Zolotarev, V. G. and Kobzar', V. M. New measurements of the heat fluxes in the Black Sea. Okeanologiya (1980) 20, Issue 1,106-110. 46. Duchkov, A. D. and Kazantsev, S. A. Heat flows in the Black Sea Basin. In: Geophysical Fields of the Atlantic OcearL Moscow: Izd. Akad. Nauk SSSR (1988), pp. 121-130. 47. Yankif, P., Malovitskii, K., et aL (Editors) Geology and Hydrology of the West Part of the Black Sea. Sofia: Izd. Bolg. Akad. Nauk (1979). 48. Fedorov, K. N. Thickness of layers and the coefficients of transfer in the process laminar convection in the ocean. In: Selected Works on Physical Oceanology. Leningrad: Gidrometeoizdat (1991), pp. 100-106. 49. Kusimir, V. M. Heat flows and the stability of the upper boundary of the deep-water bottom layer in the Black Sea. Morsk Gidrofiz. Zh. (1996) No. 1, 35-45. 50. Tareev, B. A. To the theory of convectional circulation in deep-water oceanic basins. Izv. Akad. Nauk SSSR, Geofizika (1960) No. 7, 1022-1029. 51. Busse, F. H. Transition to turbulence in the Rayleigh-Bernard convection. In: Hydrodynamic Instabilities and Transition to Turbulence. Moscow: Mir (1984), pp. 124-168. 52. Vol'vovsky, B. S., Vol'vovsky, I. S., and Ismagilov, D. F. Structures of the base of the deepwater Black Sea Basin. Geotektonika (1989) No. 2, 57-66. 53. Ivanov, M. K., Konyukhov, A. I., Kul'titsky, A. M., et aL Mud volcanoes in the deep-water part of the Black Sea. Vesm. Mosk. Univ., Geologiya (1989) No. 3, 48-55.
