J. Marine Sci. Appl. (2010) 9: 340-346 DOI: 10.1007/s11804-010-1018-1

Tidal Energy Fluxes and Bottom Boundary Layer Energy Dissipation in the Bering Sea Pei-liang Li1*, Juan Zhou1, Lei Li1, Wei Zhao1 and Chang-lin Chen2 1. Physical Oceanography Laboratory, Ocean University of China, Qingdao 266003, China 2. State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Hangzhou 310012, China Abstract: The spatial distribution of the energy flux, bottom boundary layer (BBL) energy dissipation, surface elevation amplitude and current magnitude of the major semidiurnal tidal constituents in the Bering Sea are examined in detail. These distributions are obtained from the results of a three-dimensional numerical simulation model (POM). Compared with observation data from seven stations, the root mean square errors of tidal height are 2.6 cm and 1.2 cm for M2 and N2 respectively, and those of phase-lag are 21.8° and 15.8° respectively. The majority of the tidal energy flux off the deep basin is along the shelf edge, although some of this flux crosses the shelf edge, especially in the southeast of the shelf break. The total M2 energy dissipation in the Bering Sea is 30.43 GW, which is about 10 times of that of N2 and S2. The semidiurnal tidal energy enters mainly to the Bering Sea by Samalga Pass, Amukta Pass and Seguam Pass, accounting more than 60% of the total energy entering the Being Sea from the Pacific. Keywords: tidal energy flux; bottom boundary layer (BBL) dissipation; tidal current; the Bering Sea Article ID: 1671-9433(2010)03-0340-08

1 Introduction1 The Bering Sea is the most northern part of the Pacific, connects with the Arctic by the Bering Strait. It is a semi-enclosed high-latitude sea that is bounded on the north by the Bering Strait, on the west by Russia, on the east by Alaska, and on the south by the Aleutian Islands. It is divided almost equally between a deep basin (maximum depth 3 500 m) and the continental shelves (<200 m). Between the deep basin and the continental shelves, a shelf break exists with great depth gradient. The broad (>500 km) shelf in the east contrasts with the narrow (<100 km) shelf in the west. There are three larger gulfs on the shelves: the gulf of Anadyr, the Norton Sound and the Bristol Bay. Many islands distribute in the Bering Sea. The St. Lawrence Island and the Nunivak Island are the largest islands in the northeast Bering Sea. There are many passes in the Aleutian Islands. From east to west, major channels are Unimak Pass, Akutan Pass, Umnak Pass, Samalga Pass, Amukta Pass, Seguam Pass, Atka Pass, Adak Strait, Tanaga Pass, Amchitka Pass, Oglala Pass, Buldir Pass, Near Strait and Kamchatka Strait respectively. Tides provide the most important and continuous driving force in the Bering Sea. The tides and tidal currents on the Bering Sea shelf play an important role in such oceanographic processes as the maintenance of the Received date: 2009-07-21. Foundation item: Supported by the Outstanding Middle-aged and Young Scientist Foundation in Shandong Province under Grant of No. 2008BS06003; National High Technology Research and development Program (863 Program) (No.2007AA06A403), National Nature Science Foundation under Grant of No.40706008. *Corresponding author Email: [email protected] © Harbin Engineering University and Springer-Verlag Berlin Heidelberg 2010

temperature, salinity and density structure. In the stratified ocean, the amount of energy available for mixing controls the oceanic circulation (Huang, 1998). The winds and tides are the only possible source of mechanical energy to drive the interior mixing in the ocean and a surprising conclusion is that the equator-to-pole heat flux of 2 000 TW associated with the meridional overturning circulation would not exist without the comparatively minute mechanical mixing sources (Munk and Wunsch, 1998). The small-scale mixing processes are necessary to resupply the potential energy removed in the interior by the overturning and eddy-generating process. So oceanographers are very interested in the research on the tidal energy flux and dissipation. In order to understand the different spatial distributions between various tidal constituents on the shelf, it is instructive to consider the constituents’ energy flux and spatial distribution of the dissipation one by one. A lot of work had been done on the study of tides in the Bering Sea by measurement or numerical model simulation (Sunderman, 1977; Liu and Leenderste, 1979, 1981, 1982, 1990; Pearson et al., 1981; Mofjeld et al., 1984; Mofjeld, 1984, 1986; Kowalik, 1999). The primary source for the tides in the Bering Sea is the Pacific Ocean, and there is a small contribution from the Arctic Ocean through the Bering Strait (Pearson et al., 1981; Mofjeld, 1984). Observations show that over most of the shelf the tides are primarily semidiurnal. The diurnal tides are dominant, however, in proximity to the M2 amphidromic points, in Norton Sound, at some locations along the shelf break, and near some Aleutian Islands (Kowalik, 1999). Because the Alaska

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Peninsula bordering the southeastern Bering Sea shelf lies to the right of the incident wave direction, diurnal (and semidiurnal) tides can propagate as Kelvin waves along the peninsula and decay seaward (Pearson et al., 1981). Only Foreman et al. discussed the tidal energy flux and dissipation in the Bering Sea. So the results of energy flux and dissipation in our paper will give some light on other people’s research and on other respects of study.

the reference density and ρ is the density at sigma level σ . The second terms in the right-hand side of (2) and (3) are parameterized Reynolds stresses, where K M is the turbulent

In this paper we briefly describe the POM model and the model setting first. Then the distribution of the surface elevation, tidal current, tidal energy fluxes and energy dissipation will be discussed in detail.

(4)

2 Tidal model and model setting The Princeton Ocean Model (POM) is a three-dimensional model that contains an embedded second moment turbulence closure sub-model, which provides vertical mixing coefficients (Mellor, 1998). It uses a sigma coordinate [σ = ( z − η ) /( H + η )] in the vertical, a curvilinear orthogonal coordinate and an “Arakawa C” differencing scheme in the horizontal, where z is the conventional Cartesian coordinate; D = H + η , where

H ( x, y ) is the bottom topography and η is the surface elevation. The model has a free surface and a split time step. The external mode portion of the model is two-dimensional, and uses a short time step based on the CFL condition and the external wave speed. The internal mode is three-dimensional, and uses a long time step based on the CFL condition and the internal wave speed. It has been used to simulate the tide in continental shelf regions (Wan et al., 1998), and in the East China Sea (Li et al., 2005a). It also has been used to calculate the tidal energy (Li et al., 2005b). The nonlinear controlling equations used in the POM model are ∂DU ∂DV ∂ω ∂η + + + =0 (1) ∂x ∂y ∂σ ∂t

∂UD ∂U 2 D ∂DUV ∂U ω ∂η + + + − fVD + gD + ∂t ∂x ∂y ∂σ ∂x gD 2

ρ0

σ ′ ∂D ∂ρ ′ ⎤ ∂ ⎡ K M ∂U ⎤ − dσ ' =Fx + ⎢ ⎥ σ ⎣ ∂x D ∂x ∂σ ' ⎦ ∂σ ⎢⎣ D ∂σ ⎥⎦

∫

0 ⎡ ∂ρ ′

(2)

∂VD ∂UVD ∂V 2 D ∂V ω ∂η + + + + fUD + gD + ∂t ∂x ∂y ∂σ ∂y

(3) ⎡ K M ∂V ⎤ ⎢ D ∂σ ⎥ ρ0 ⎣ ⎦ where U and V are the horizontal velocity components in the x and y directions respectively, ω is the velocity component normal to sigma surface, Fx and Fy are gD 2

σ ′ ∂D ∂ρ ′ ⎤ ∂ − ⎢ ⎥ dσ ' =Fy + σ ⎣ ∂y D ∂y ∂σ ' ⎦ ∂σ

∫

0 ⎡ ∂ρ ′

horizontal viscosity and diffusion terms, t is time, g is the gravitational acceleration, f is the Coriolis parameter, ρ0 is

diffusion coefficient. The POM model also contains the equations of temperature and salinity that are cancelled in the present case. The boundary condition for (2) and (3) is K M ⎛ ∂U ∂U ⎞ , ⎜ ⎟ = −τ a = − ρ aCD U10 U10 ,σ → 0 D ⎝ ∂σ ∂σ ⎠

where ρ a is the air density, CD is the drag coefficient at the air-sea interface, and the U10 is the surface wind speed (10 m above mean sea level), and K M ⎛ ∂U ∂U ⎞ , ⎜ ⎟ = ρ C z U C U C ,σ → −1 D ⎝ ∂σ ∂σ ⎠

(5)

where C z is the drag coefficient in the ocean bottom boundary layer, U C the bottom current vector and ρ is water density. CZ is taken as 0.002 5. The lateral boundary condition is the zero flow normal to solid boundary and a radiation condition is applied on the open boundary. Along the open boundaries the heights of the water surface are given as

ζ =

∑f

C HC

cos[ωC t + (V0 + u )C − gC ]

(6)

where H and g are harmonic constants for the amplitude and phase-lag respectively, the subscript C stands for either one of the constituents: M2, S2 and N2, ω is the angular speed of the tidal constituents, f is the nodal factor, u is the nodal angle, V0 is the initial phase angle of the equilibrium tide. Along the open boundaries, amplitudes and phase-lags for every tidal constituent are specified according to the results of FES95.2, with little adjustment. Because the spatial resolution in our model is higher than FES95.2, the results of FES95.2 were needed to interpolate to the boundary of our model by means of linear interpolation, afterwards the interpolated results were processed by smooth technology. The bering sea has its unique topographic character (Fig.1). The modeling region covers from 162ºE to 157ºW，and 51ºN to 66.5ºN. The spatial resolution is 10´ in latitude, and 20´ in longitude (Fig.2). There are 12 grids in the vertical direction. The topography comes from a data set provided by the Institute of Oceanography, Chinese Academy of Sciences. The open boundary is placed at 162ºE, 51ºN and 157ºW. We close the Bering Strait because there is a small contribution from the Arctic Ocean through the Bering Strait (Pearson et al., 1981; Mofjeld, 1984).

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The phase-lag is unstable when the amplitude is small, and the variance of phase-lag affects little when the amplitude is small. So it is not very reasonable to compare the computed amplitude and phase-lag with observations by the root mean square error respectively. A relative distance H S (Davies et al., 1997) was used besides the root mean square error in this paper. Fig.1 Map of the Bering Sea and stations for observation (the bottom depth is given in meters)

HS =

1 N

n

∑

( HCi )2 + ( HSi )2

(7)

i =1

where N is the number of observation stations. HCi = Aoi cos g oi − Aci cos g ci

(8)

HSi = Aoi sin g oi − Aci sin gci where

Aoi and

g oi

(9) are the observed amplitude and

phase-lag at the ith station respectively. Aci and g ci are those of simulating results. Fig.2 Computational grid and sections for calculating energy fluxes

The simulation begins from a state of rest

(u = v = ξ = 0)

using external model time step ∇t E =30 s and internal model time step ∇t I =600 s. The simulation is carried out for 45 d, and the initial part of the computed time series of 15d is discarded. The computed month-long time series of ξ , u and v are analyzed by a conventional tidal harmonic analysis program to yield harmonic constants.

3 Result of simulation and discussion 3.1 Comparison of the computed results with observations There are only seven stations’ data we can get from Mofjeld (1986). Table 1 shows the comparison of tidal harmonic constants observed on the Northeastern Bering Sea Shelf with our numerical results.

Based on the data of the seven stations, a comparison of the maximum semidiurnal constituents M2 and N2 suggests that those results agree well with observation. The root mean square errors of the amplitude are 2.6 cm and 1.2 cm, for M2 and N2, respectively, and those of phase-lag are 21.8° and 15.8° respectively. The relative distances H S are 6.2 cm and 1.9 cm, respectively. The biggest difference of M2 amplitude is −4.2 cm at station NC19C which is in the middle of Anadyr Strait. There are bigger difference of M2 phase-lag at LD15A (30°), NC17C(−25°) and LD10A (−40°). LD15A (30°) and LD10A (−40°) are near the amphidromic points (Fig.3(d)). The bigger difference of NC17C and NC19C may be caused by the inaccurate topography we used. Our results of M2 constituent are better than those of Sunderman (1977), whose RMS (root mean square) errors are 6.3cm for amplitude, 32.1° for phase-lag and 10.5 cm for relative distance H S .

Table 1 Comparison of tidal harmonic constants observed on the northeastern Bering Sea shelf with our numerical results Stations LDI3A LDI4A LDI5A LDI6A RMS NCI7C NCI9C LDI10A HS /cm HO/cm 22.6 21.9 21.4 16.8 25.5 23.5 7.6 6.2 ΔH/cm −2 −0.4 −2.8 −2.4 2.3 −4.2 2.7 2.6 GO/(°) 106 180 87 145 336 172 202 M2 ΔG/(°) 9 −8 30 2 −25 7 −40 21.8 H1/cm 0.4 3.1 −0.4 3.2 −15.5 −3.5 −1.6 6.3 10.5 9 −30 28 −5 −6 68 28 32.1 ΔG1/(°) HO/cm 6.3 6.6 5.4 4.5 7.3 5.9 2.3 1.9 ΔH/cm 1.6 1.4 1.3 0.9 1.4 0.5 0.5 1.2 N2 62 134 44 101 283 120 130 GO/(°) ΔG/(°) 13 −8 31 5 −13 17 −8 15.8 Note: RMS means root mean square error. The superscript “1” means the results of Sunderman (1977).

3.2 Spatial variation of the tides In order to understand differences in the spatial distributions of various tidal constituents in the shallow sea, it is instructive to consider the energy flux of each constituent and the spatial

distribution of its BBL dissipation. Energy flux vectors at each grid point over a period T (taken as a tidal period) (Greenberg, 1979) can be readily computed from the energy

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flux components E fx , E fy defined by Eq.(10), and be plotted as a vector. ( E fx , E fy ) =

ρ

T

1

0

0

(u , v) h[ gζ + T∫ ∫

u 2 + v2 ]dσ dt 2

The larger tidal current amplitude region for M2 is at the eastern part of the Bering Sea and the largest velocity appears around the Nunivak Island (up to 50 cm/s).

(10)

In Eq.(10), ρ denotes density, and g is acceleration due to gravity. The second term in Eq.(10) is the advective kinetic energy flux which in deep water is significantly smaller than the first term, although it needs to be included in shallow water (Greenberg, 1979). The BBL dissipation per unit area d over a period T is given by C ρ T 2 2 3/ 2 d= Z (ub + vb ) dt (W/m2) (11) T 0 where CZ is the drag coefficient in the ocean bottom

∫

boundary layer, ρ denotes density, ub and vb are the bottom currents. 3.2.1 Spatial variation of M2 The M2 tidal energy flux vectors (Fig.3(a)) show a significant energy flux in the deep basin of the Bering Sea. Although distribution of tidal current ellipse (Fig.3(c)) indicates small tidal currents (Fig.3(b)) in this region, the energy flux is large in the deep basin because of the significantly greater water depths in this area (Fig.2). It is evident from Fig.3(a) that the majority of the tidal energy flux off the deep basin is along the shelf edge, although some of this flux crosses the shelf edge, especially in the southeast of the shelf break. It is also evident that the maximum tidal energy flux is in the Amukta Pass. Tidal energy of the M2 constituent from the Pacific ocean can enter the Bering Sea through several passages, such as Amukta Pass, Unimak Pass, Akutan Pass, Samalga Pass and Seguam Pass. Most of the tidal energy through Unimak Pass and Akutan Pass turns to right and enters Bristol Bay along the Alaska Peninsula in the Bering Sea. And the energy comes through Amukta Pass is separated into two branches. One of them reaches Bristol Bay across the continent slope. And most of the other propagates towards northwest along the isobaths, however, a little portion of it can enter Gulf of Anadyr and Norton Sound across the continent slope. Although the tidal current here is very strong (Fig.3(c)), the tidal energy flux over the continent shelf in the north is not so big as the depth of the area which is usually less than 100 meters. After dissipation in the propagation, tidal energy of the basin comes into the Pacific Ocean through Near Strait and Kamchatka Strait. The maximum BBL dissipation (because of the large range of tidal dissipation values, contours of log10 of dissipation are given in Fig.3(b) occurs in the shallow coastal regions where the tidal current is very strong, and the case is very obvious in the Bristol Bay. BBL dissipation in the basin is just 1/10 000 of that over the continent shelf.

The modeled distribution of amplitudes and phases in this paper (Fig.3(d)) is similar to the distribution derived through numerical models by Liu and Leenderste (1982), and Kowalik (1999). Propagation of the M2 constituent follows bathymetric division of the Bering Sea into the deep basin, where a small change in amplitude (about 20 cm) and phase occurs, and in the shelf basin there are many amphidromic points which due to partial reflection of the tide wave in the semi-enclosed water bodies. The amplitudes increase in the narrow and shallow bays, to 35 cm in the Norton Sound, and to 60 cm in the gulf of Anadyr. The most conspicuous amplitude enhancement occurs in triangular-shaped Bristol Bay (more than 180 cm). There are five tidal systems, the amphidromic points for M2 are as follows: one is in Norton Sound, one is at south of Bering Strait, one is off Cape Navarin in Gulf of Anadyr, one is near the southern coast of St. Lawrence Island, and the other is at the entrance of the Bristol Bay. Sunderman (1977) gains a minimum in the M2 amplitude to the southeast of the St. Lawrence Island. Although a preliminary analysis of 1984-1985 bottom pressure observations from the vicinity of the island tends to favor the Sunderman’s result (Mofjeld, 1986), the five amphidromic points of Liu and Leenderste (1982), and Kowalik (1999) are very similar to ours.

(a) M2 tidal energy flux vectors at every two grid points

(b) Contours of log10 of the BBL dissipation (W/m2)

(c) Spatial distribution at very two grid point of the major and minor axis of the current ellipse

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Pei-liang Li, et al. Tidal Energy Fluxes and Bottom Boundary Layer Energy Dissipation in the Bering Sea

Section C and D have energy fluxes 9.1 GW and 1.4 GW in our results respectively, but zero and 15.8 GW in their results respectively.

(d) Cotidal chart with co-amplitude lines (cm, dashed) and co-phase lines (degrees, solid)

Fig.3 Property distribution of M2 constituent

3.2.2 Spatial variation of N2 and S2 The tidal system pattern of N2 and S2 is similar to M2. There are five amphidromic points in the Bering Sea. Magnitude of N2 is larger than that of S2 because of the high latitude. In deep basin, the amplitude is less than 10 cm. In the Bristol Bay, the amplitude is about 70 cm. Because of the topography, the Bristol Bay is a strong tidal region, where the total tide range is up to 7 m. The spatial distribution pattern of the N2 and S2 is similar to M2. Although their spatial distribution pattern of energy flux is similar to M2 too, the magnitude is only about 10% of M2. Section B is the main entrance for the three semidiurnal energy fluxes (Table 2). At section A and C entrance, M2 and N2 have similar magnitude of energy flux. But the energy flux passing section C is about 1/3 of that passing section A for S2. There are homogeneous conditions at exits. At sections E and F, M2 and N2 have similar magnitude of energy flux, but the energy flux passing section F is about half of that passing section E for S2. BBL dissipation of the constituents S2 and N2 can be smaller than M2 by 2 magnitudes in the basin and 1 magnitude in the shallower area. Tidal energy dissipation of the constituent S2 is larger than N2 in the deep basin, while the BBL dissipation of S2 is smaller than N2 by 1 magnitude in the coastal area (Fig.4(b) and Fig.5(b)). 3.3 Energy fluxes through the passes and traits Six sections are selected to calculate the energy flux entering the Bering Sea from the Pacific Ocean for a better understanding of the tidal energy dissipation in this region and the magnitude of the flux. Position of the six sections and the corresponding passages to them can be found in Fig.2 and Table 2. The total energy dissipation (A+B+C+D+E+F) in the Bering Sea is 30.43 GW. It is very close to Egbert and Ray (2000) dissipation estimate of 30GW, less than total energy dissipation estimate of 34.4GW by Foreman et al. The tidal energy enters the Bering Sea from the eastern part of the Aleutian Islands and exits from the western part of the Aleutian Islands. The strongest energy fluxes (29.8 GW) appear in the section B (Samalga Pass, Amukta Pass and Seguam Pass). Those are similar to the result of Foreman et al., which are 30.5 GW at section B, 8.4 GW at section E and 9.0 GW at section F. There are differences between our results and results of Foreman et al. in the middle of Aleutian Islands.

For the M2 constituent, the tidal energy enters the Bering Sea across the main passage Section B, accounting 63% of the total across Section A, B, C and D. And the tidal energy across other Sections A, C, and D account 15%, 19% and 3% of the total respectively. Sections E and F are two main exits, with energy flux of 8.0 GW and 9.0 GW respectively. It suggests that 64% of the tidal energy of M2 into the Bering Sea is dissipated here.

(a) N2 tidal energy flux vectors at every two grid points

(b) Contours of log10 of the BBL dissipation (W/m2)

(c) Spatial distribution at very two grid point of the major and minor axis of the current ellipse

(d) Cotidal chart with co-amplitude lines (cm, dashed) and co-phase lines (degrees, solid)

Fig.4 Property distribution of N2 constituent

(a) S2 tidal energy flux vectors at every two grid points

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4 Summary and conclusion In earlier papers, the emphasis was on the spatial distribution of cotidal charts, tidal current ellipses, and comparison between computed and observed tides. In this paper we have also examined tidal energy flux and BBL dissipation in detail. There are five tidal systems in the Bering Sea, the amphidromic points for the three major semidiurnal constituents are as follows: one in Norton Sound, one at south of Bering Strait, one off Cape Navarin in Gulf of Anadyr, one near the southern coast of St. Lawrence Island, and the other at the entrance of the Bristol Bay.

(b) Contours of log10 of the BBL dissipation (W/m2)

(c) Spatial distribution at very two grid point of the major and minor axis of the current ellipse

(d) Cotidal chart with co-amplitude lines (cm, dashed) and co-phase lines (degrees, solid)

Fig.5 Property distribution of S2 constituent

The tidal energy dissipation of N2 and S2 in the Bering Sea are 3.43 GW and 1.88 GW, accounting 11% and 6% of that of M2. Section B is also the main passage for them to enter the Bering Sea, with a tidal energy flux of 3.09 GW for N2 and 2.57 GW for S2. The tidal energy of S2 across Section D propagates outward with a flux of 0.04 GW, different from N2 and M2 which propagates inward. Sections E and F are still the most important exits of N2 and S2.

Section A

Table2 Energy fluxes through the sections Passes or traits M2/GW N2/GW S2/GW Unimak Pass and 7.12 0.73 0.81 Akutan Pass

B

Samalga Pass, Amukta Pass and Seguam Pass

29.81

3.09

2.57

C

Atka Pass and Adak Strait

9.07

0.97

0.30

D

Tanaga pass, Amchitka Pass and Buldir Pass

1.40

0.13

−0.04

E

Near Strait

−7.99

−0.79

−0.66

F Total

Kamchatka Strait A+B+C+D+E+F

−8.89 30.34

−0.70 3.43

−1.10 1.88

Note: The energy flux entering the Bering Sea is positive.

Although spatial distribution pattern of energy flux of N2 and S2 is similar to that of M2, the magnitude is only about 10% of M2. Six sections are selected to calculate the energy flux entering the Bering Sea from the Pacific Ocean for a better understanding of the tidal energy dissipation in this region and the magnitude of the flux. The total energy dissipation for the M2, N2 and S2 in the Bering Sea is 30.43, 3.43 and 1.88 GW respectively. The tidal energy enters the Bering Sea across the main passage Section B, accounting more than 60% of the total energy entering the Bering Sea from the Pacific Ocean. Although the improvement of the present results is obvious, greater efforts are still needed to accurately depict the spatial distribution of tides in the Bering Sea. First of all, the coastal and offshore measurements are the preliminary task because the observed data is very useful in verifying the model results and enhancing accuracy of the model. Second, higher resolution model is needed to simulate the spatial distribution of tidal current or the detailed energy fluxes between islands. Third, accurate harmonic constants in the north of Pacific Ocean are also very important in providing the proper open boundary conditions. The numerical models can also be further improved by assimilating the altimetry data.

References Egbert GD, Ray RD (2000). Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature, 405, 775-778. Davies AM, Kwong SCM, Flather RA (1997). Formulation of a variable-funcyion three-dimensional model, with applications to the M2 and M4 tide on the North-west European. Continental Shelf Research, 17, 165-204. Greenberg DA (1979). A numerical model investigation of tidal phenomena in the Bay of Fundy and Gulf of Maine. Marine Geodesy, 2, 161-187. Huang Ruixin (1998). On the balance of energy in the oceanic general circulation. Journal of Scientia Atmospherica Sinica, 22(4), 562-574. Kowalik Z (1999). Bering Sea tides. Loughlin T and Ohtani K. The Bering Sea: physical, chemical and biological dynamics. Alaska Sea Grant Press, Fairbanks, 93-127. Li Peiliang, Zuo Juncheng, Wu Dexing, Li Lei, Zhao Wei (2005a). Numerical simulation of semidiurnal constituents in the Bohai Sea, the Yellow Sea and the East China Sea with assimilating

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Pei-liang Li, et al. Tidal Energy Fluxes and Bottom Boundary Layer Energy Dissipation in the Bering Sea

Topex/Poseidondata. Jourmal of Oceanologia et Limnologia Sinica, 36(1), 30-36. (in Chinese) Li Peiliang, Li Lei, Zuo Juncheng, Chen Meixiang, Zhao Wei (2005b). Tidal energy fluxes and dissipation in the Bohai Sea, the Yellow Sea and the East China Sea. Journal of Ocean University of China, 35(5), 713-718. (in Chinese) Liu SK, Leenderste JJ (1979). Three-dimensional model for estuaries and coastal seas: Bristol Bay simulations. The Rand Corp, R-2405-NOVA. Liu SK, Leenderste JJ (1981). A three-dimensional model of Norton Sound under ice cover. Proceedings of the Sixth International Conference on Port and Ocean Engineering under Arctic Conditions, Quebec, Canada, 433-443. Liu SK, Leenderste JJ (1982). Three-dimensional model of Bering and Chukchi Sea. Journal of Coastal Engineering, 18, 598-616. Liu SK, Leenderste JJ (1990). Modeling of the Alaskan continental shelf waters. OCSEAP Final Reports, 123-275. Mellor J (1998). Users guide for a three dimensional, primitive equation numerical ocean mode. Princeton University Press, Princeton. Mofjeld HO (1984). Recent observations of tides and tidal currents from the northeastern Bering Sea shelf. NOAA Technical Memo ERL PME-57, 36. Mofjeld HO (1986). Observed tides on the northeastern Bering Sea shelf. Journal Geophysical Research, 91, 2593-2606. Mofjeld HO, Schumacher JD, Pashinski DJ (1984). Theoretical and observed profiles of tidal currents at two sites of the southeastern Bering Sea shelf. NOAA Technical Memo ERL

PMEL-62, 60 Munk W, Wunsch C (1998). Abyssal recipes II: Energetics of tidal and wind mixing. Jourmal of Deep-Sea Research I , 45(12), 1977-2010. Pearson CA, Mofjeld HO, Tripp RB (1981). Tides of the eastern Bering Sea shelf. Proceedings of Oceanography and Resources. University of Washington Press, Seattle, 111-130. Sunderman J (1977). The semidiurnal principal lunar tide M2 in the Bering Sea. Journal of Deutsche Hydrographie Zeitschrift, 30, 91-101. Wan Zhenwen, Qiao Fangli, Yuan Yeli (1998). Three-dimensional numerical modeling of tidal waves in the Bohai, Yellow and East China Seas. Chinese Journal of Oceanology and Limnology, 18, 611-616. (in Chinese ). Foreman M, Cherniawsky J, Cummins P. A high resolution assimilating tidal model for the Bering Sea. http://www.pices. int/publications/presentations/PICES_13/PICES_13_S7/Forem an_S7.pdf Pei-liang Li received a bachelor's degree in Oceanography from Ocean University of China (OUC) in 1998 and got a master's degree and doctor’s degree in Physical Oceanography from the same university in 2000 and 2003, respectively. Recently, he is an Associate Professor and studies on tides and sea level variations, wind-wave-current interactions.