Simulation of barotropic and baroclinic tides in the South China Sea

The four leading tidal constituents M2, S2, K1 and O1 in the South China Sea are simulated by using POM. The model is forced with tide-generating potential and four leading tidal constituents at the open boundary. In order to simulate more exactly, TOPEX/Poseidon altimeter data are assimilated into the model and the open boundary is optimized. The computed co-tidal charts for M2 and K1 constituents are generally consistent with previous results in this region. The numerical simulation shows that energetic internal tides are generated over the bottom topography such as the Dongsha Islands, the Xisha Islands, the Zhongsha Islands, the Nansha Islands and the Luzon Strait.     

A 3-dimensional baroclinic circulation model of the South China Sea

1 INTRODUCTIONThe SoUth China Sea (SCS) is the largest coastal sea of China. It is of great interestto researchers because of its abundant resources and geographical location. The SCS is inthe tropicaI and sub-tropical monsoon wind zone of the north-western Pacific and isSurrounded by China, Vietnam, Malaysia, Indonesia and the Philippines. lt has a complicatedRecclved 2 l March 200ltoPograPhy and is cormected with the Peeific through thc Bashi Channel which has a dePthof over 3…     

Seasonal variability of the barotropic and baroclinic motion in the Tsushima-Korea Strait

The aim of this study is to elucidate the seasonal variation in the volume transport through the Tsushima-Korea Strait using the sea level difference across the Strait. The sea level difference associated with the baroclinic motion is estimated from the geostrophic current profile, which is calculated as its vertical integrated transport is zero, using the CTD data from 1988 to 1990. The sea level difference associated with the barotropic motion is estimated by subtracting the sea level difference associated with the baroclinic motion from the observed one. The range (maximum-minimum) of the seasonal variation in the volume transport is evaluated about 0.7 Sv on the average, using the sea level difference associated with the barotropic motion. It is one third of the seasonal variation in the volume transport which is estimated from observed sea level difference on the assumption that no baroclinic component exists. Such analyses also indicate that the volume transport was at a maximum in early winter and at a minimum in early spring from 1988 to 1990. The negative correlation is also found between the volume transport through the eastern channel and that through the western channel. Moreover, it is noticed that the seasonal variation in the surface current velocity in the Strait largely contains baroclinic motions which are locally caused in the Tsushima-Korea Strait.     

The accuracy of surface elevations in forward global barotropic and baroclinic tide models

This paper examines the accuracy of surface elevations in a forward global numerical model of 10 tidal constituents. Both one-layer and two-layer simulations are performed. As far as the authors are aware, the two-layer simulations and the simulations in a companion paper (Deep-Sea Research II, 51 (2004) 3043) represent the first published global numerical solutions for baroclinic tides. Self-consistent forward solutions for the global tide are achieved with a convergent iteration procedure for the self-attraction and loading term. Energies are too large, and elevation accuracies are poor, unless substantial abyssal drag is present. Reasonably accurate tidal elevations can be obtained with a spatially uniform bulk drag c_d or horizontal viscosity K_H, but only if these are inordinately large. More plausible schemes concentrate drag over rough topography. The topographic drag scheme used here is based on an exact analytical solution for arbitrary small-amplitude terrain, and supplemented by dimensional analysis to account for drag due to flow-splitting and low-level turbulence as well as that due to breaking of radiating waves. The scheme is augmented by a multiplicative factor tuned to minimize elevation discrepancies with respect to the TOPEX/POSEIDON (T/P)-constrained GOT99.2 model. The multiplicative factor may account for undersampled small spatial scales in bathymetric datasets. An optimally tuned multi-constituent one-layer simulation has an RMS elevation discrepancy of 9.54 cm with respect to GOT99.2, in waters deeper than 1000 m and over latitudes covered by T/P (66N to 66S). The surface elevation discrepancy decreases to 8.90 cm (92 percent of the height variance captured) in the optimally tuned two-layer solution. The improvement in accuracy is not due to the direct surface elevation signature of internal tides, which is of small amplitude, but to a shift in the barotropic tide induced by baroclinicity. Elevations are also more accurate in the two-layer model when pelagic tide gauges are used as the benchmark, and when the T/P-constrained TPXO6.2 model is used as a benchmark in deep waters south of 66S. For Antarctic diurnal tides, the improvement in forward model elevation accuracy with baroclinicity is substantial. The optimal multiplicative factor in the two-layer case is nearly the same as in the one-layer case, against initial expectations that the explicit resolution of low-mode conversion would allow less parameterized drag. In the optimally tuned two-layer M₂ solution, local values of the ratio of temporally averaged squared upper layer speed to squared lower layer speed often exceed 10.     

Computations of the energy flux to mixing processes via baroclinic wave drag on barotropic tides

The geographical distribution of barotropic to baroclinic transfer of tidal energy by baroclinic wave drag in the abyssal ocean is estimated. Using tidal velocities from a state-of-the-art numerical tidal model, the total loss of barotropic tidal energy in the deep ocean (between 70°S and 70°N and at depths greater than 1000 m) is estimated to be about 0.7 TW (M₂) corresponding to a mean value of the energy flux (e) of 2.4×10⁻³ W/m². The distribution of e is however highly skewed with a median of about 10⁻⁶ W/m². Only 10% of the area is responsible for more than 97% of the total energy transfer.To assess the possible influence of the relatively coarse bathymetry representation upon the present estimate, complementary calculations using better resolved sea floor topography are carried out over a control area around the Hawaiian Ridge. There are no major differences between the results achieved using the two different bathymetry databases. Fluxes of about 16 GW or 6×10⁻³ W/m² are computed in both cases, and the main contributions to the total fluxes originate in the same range of e-values and cover equally large parts of the total area.It is not clear whether the present model is valid at flat or subcritical bottom slopes. However, for the Hawaiian region, only 2% of the total energy flux as calculated in the present study originates in areas of critical and subcritical slopes.     

A spectral barotropic model of the wind-driven world ocean

A global spectral barotropic ocean model is introduced to describe the depth-averaged flow. The equations are based on vorticity and divergence (instead of horizontal momentum); continents exert a nearly infinite drag on the fluid. The coding follows that of spectral atmospheric general circulation models using triangular truncation and implicit time integration to provide a first step for seamless coupling to spectral atmospheric global circulation models and an efficient method for filtering of ocean wave dynamics. Five experiments demonstrate the model performance: (i) Bounded by an idealized basin geometry and driven by a zonally uniform wind stress, the ocean circulation shows close similarity with Munk’s analytical solution. (ii) With a real land–sea mask the model is capable of reproducing the spin-up, location and magnitudes of depth-averaged barotropic ocean currents. (iii) The ocean wave-dynamics of equatorial waves, excited by a height perturbation at the equator, shows wave dispersion and reflection at eastern and western coastal boundaries. (iv) The model reproduces propagation times of observed surface gravity waves in the Pacific with real bathymetry. (v) Advection of tracers can be simulated reasonably by the spectral method or a semi-Langrangian transport scheme. This spectral barotropic model may serve as a first step towards an intermediate complexity spectral atmosphere–ocean model for studying atmosphere–ocean interactions in idealized setups and long term climate variability beyond millennia.     

A spectral barotropic model of the wind-driven world ocean

A global spectral barotropic ocean model is introduced to describe the depth-averaged flow. The equations are based on vorticity and divergence (instead of horizontal momentum); continents exert a nearly infinite drag on the fluid. The coding follows that of spectral atmospheric general circulation models using triangular truncation and implicit time integration to provide a first step for seamless coupling to spectral atmospheric global circulation models and an efficient method for filtering of ocean wave dynamics. Five experiments demonstrate the model performance: (i) Bounded by an idealized basin geometry and driven by a zonally uniform wind stress, the ocean circulation shows close similarity with Munk’s analytical solution. (ii) With a real land–sea mask the model is capable of reproducing the spin-up, location and magnitudes of depth-averaged barotropic ocean currents. (iii) The ocean wave-dynamics of equatorial waves, excited by a height perturbation at the equator, shows wave dispersion and reflection at eastern and western coastal boundaries. (iv) The model reproduces propagation times of observed surface gravity waves in the Pacific with real bathymetry. (v) Advection of tracers can be simulated reasonably by the spectral method or a semi-Langrangian transport scheme. This spectral barotropic model may serve as a first step towards an intermediate complexity spectral atmosphere–ocean model for studying atmosphere–ocean interactions in idealized setups and long term climate variability beyond millennia.     

Stability of a barotropic jet on a sloping bottom

Linear stability of a barotropic jet on a sloping bottom with and without a side boundary is examined. When a sloping bottom and a side boundary are absent, a symmetric jet generally has two unstable modes: a symmetric mode and an antisymmetric mode. In the presence of a sloping bottom or a side boundary, they are modified and lose their symmetry.The presence of a side boundary does not produce substantial change in the stability characteristics, except that it stabilizes the flow to some degree. In the presence of a sloping bottom, the following features are noted; 1) when the direction of the jet is opposite to the propagation direction of topographic Rossby waves, the change of a preferred mode occurs at a certain slope, 2) when the direction of the jet is opposite to 1), with a side boundary, the dispersion relations change from unstable mode type to shelf wave type at a certain slope, accompanied by kissing.     

Teleparallel equivalent theory of (1+1)-dimensional gravity

A theory of (1+1)-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity. The fundamental field variables are the tetrad fields e_i^μ and the gravity is attributed to the torsion. A dilatonic spherically symmetric exact solution of the gravitational field equations characterized by two parameters M and Q is derived. The energy associated with this solution is calculated using the two-dimensional gravitational energy--momentum formula.     

Consideration on the topographic control of a baroclinic ocean current

The stability of ocean currents is considered using a two-layer model including the vertical shear in the geostrophic balance and bottom topography. Applying the results, the Kuroshio current along the bottom contour seems to be more stable than any other combination of the current direction and the bottom contour.     

A barotropic model of the linear semidiurnal tide over a continental slope

Semidiurnal tides, and especially the lunar tide M₂, are dominant dynamics in the Bay of Biscay. Strong tidal currents are associated with the presence of a significant continental slope. By combining Newton's gravitation laws and Euler's equations, Laplace's equations contain the astronomical forcing responsible for the observed semidiurnal tides. In shallow waters, this direct forcing is often neglected. We study here its influence on the tidal dynamics over the continental slope through the development of a simple model describing the barotropic semidiurnal dynamics on a transect perpendicular to the slope. This new model results from the combination of two different models, i.e. the one developed by Rosenfeld and Beardsley (1987), which takes into account the tide-generating force, and that of Battisti and Clarke (1982), which neglects it. A first model is developed by neglecting the direct astronomical forcing in equations: it consists in solving a second-order homogeneous propagation equation for the barotropic semidiurnal tide and needs only coastal conditions as well as the knowledge of the along-slope wave number of the solution. For a mean slope typical of the South Brittany area, this non-forced model provides results in accordance with those of Battisti and Clarke and Le Cann (1990): in particular, in the upper part of the slope, it shows a polarization inversion of tidal ellipses characteristic of the tidal dynamics observed in this area. Then, the direct astronomical forcing is kept in equations. The simple model developed without this forcing is fitted in order to solve the resulting forced propagation equation for the barotropic tide. The solution of this second model is the sum of a forced wave responding to the direct astronomical forcing and of a free wave generated at the coastal boundary. Under the same boundary conditions, the results obtained with the influence of the tide-generating force are then compared with those obtained without it. This comparison allows one to apprehend the importance of the direct astronomical forcing on tidal dynamics across the slope: in particular, the main difference appears in deep waters where this forcing induces a phase-lag between the plain and the shelf for the sea-surface slope.     

A note on significant wave height

In this note conservative bounds for significant crest height and amplitude obtained from the crossing intensity of a sea are presented. For Gaussian models of a sea level, the Rayleigh approximation for the distributions of amplitude and crest height is proved to provide conservative values for the expected significant wave characteristics. The results are illustrated by examples in which both Gaussian and non-Gaussian models for a sea are considered.     

A note on surface wind-driven flow

A simple operationally oriented model of surface wind-driven currents is presented in which Lagrangian surface drift is assumed to be composed of a linear combination of a wave-induced Stokes drift plus a wind-driven Ekman drift. Using this approach, Stokes drift accounts for as much as half the total surface current magnitude. The Lagrangian current is predicted to be about 3.5% of the 10 m wind magnitude directed in the sense of an Ekman spiral about a 20° deviation angle. For comparison to this model, a second model is proposed that accounts for the interaction of Stokes current and Coriolis force. An inference drawn from this model is that there is only weak coupling between Coriolis force and Stokes drift. Such a conclusion, if correct, leads one to focus attention on the Lagrangian model for operationally oriented current estimates. Results of the Lagrangian model agree with observations of investigators for currents at the air-sea interface and may have application in the movement f oil slicks or surface drifters at sea under fetch or duration limited sea states.     

Effect of the baroclinic tide on impurity diffusion in the ocean

The paper studies the effect of the baroclinic tidal wave on the diffusion of a patch of impurities in a continuously stratified fluid. The turbulent diffusion equation is solved numerically, with wave currents being considered. The diffusion characteristics depend upon the parameters of a baroclinic wave and upon the location of the patch. Translated by Vladimir A. Puchkin.     

两层简单斜压海洋模式及冬、夏季平均海流模拟

设计了一个两层简单斜压海洋模式(H₁=501,H₁+H₂=250m),利用1月和7月多年平均的海平面气温场、海平面气压场和由该气压场诊断出的海面风场,对此模式的性能进行了检验.结果表明,模拟得出的冬、夏季海洋表层及次表层流与实况较为一致.     

Notes on linear and nonlinear barotropic flows in a polar circular basin

Barotropic flows in a circular ocean are studied. Flows are driven by an inflow and an outflow through openings at the circumference. A linear, steady state solution is interpreted in terms of dissipating planetary waves. A weakly nonlinear, steady state solution is obtained numerically. It differs remarkably from the linear solution; an intense anticyclonic polar gyre extending over the whole basin is formed. The nonlinear term is essential to the gyre and can not be neglected, although the Rossby number is small.