Two-layer quasi-geostrophic model of contour dynamics for a round basin

A quasi-geostrophic contour dynamics model permitting one to study flows induced by a system of vortex patches in a two-layer ocean with round shore boundaries in the presence of specified background flows caused by the bottom relief, the β effect, and sources and sinks at the boundaries is proposed. The principal relations of the model are presented and the algorithm of its numerical realization is described. Some experimental results of the study of the evolution of unstable two-layer vortices are demonstrated.     

The study of tidal currents in the seamount area in a continuously stratified ocean

In the framework of the linear theory and without using the hydrostatics approximation, we study the wave motions produced by a barotropic tide impinging upon a bottom topography feature in a continuously stratified ocean. Numerical techniques are used to estimate the effects of the stratification and the Coriolis parameter on the tidal flows in the seamount area. Translated by V. Puchkin.     

Vertical transport in a stratified oceanic medium

On the basis of the analysis of the data of hydrological observations, we construct an empirical dependence of the vertical heat fluxQ on the temperature gradientT _z . The integral advective-diffusive transfer is taken into account by the method of Kolesnikov. We obtain a generalized dependence of the coefficient of vertical thermal diffusivityK _z onT _z and note that the well-known Rossby-Montgomery relation and Kolesnikov formula are its special cases. We analyze the possibility of application of this dependence to linear and nonlinear problems of thermal conductivity and diffusion in the ocean. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

The mixing efficiency and the processes of restratification in a stably stratified medium

The mechanism of the effect of a collapsing turbulent eddy on diapycnal transport in a stably stratified fluid is considered. It is shown that at small Richardson turbulent numbersRi ₀ the mixing efficiency increases asRi ₀, and at large numbers it decreases in proportion toRi ₀ ^–1/2 .Translated by Mikhail M. Trufanov. UDK 551.465.15.     

Long nonlinear topographic planetary waves in a rotating stratified ocean

Long nonlinear topographic waves in a continuously stratified ocean with a linear bottom slope are investigated. It is shown that odd cross-channel modes are governed by the Korteweg-de Vries (K-dV) equation. The solitary waves are those of a low pressure type. The long waves are shown to be modulationally stable because of the nonlinear effect due to irrotational motion. All these results are missed if the conventional quasi-geostrophic approximation is adopted.     

Evolution and breaking of a propagating internal wave in stratified ocean

The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is testified clearly. It dominates gradually in nonlinear resonant interactions. As a consequence, the energy cascades to a second plant wave packet which has lower frequencies and higher wavenumbers than that of the primary wave. With the growth of this wave packet, wave breaking occurs and causes strongly nonlinear regime, i.e. stratified turbulence. The strong mixing and intermittent of the turbulence can be learned from the evolution of the total energy and kurtosis of vorticity vs. time. Some statistic properties of the stratified turbulence are also analyzed, including the spectra of KE （kinetic energy） and PE （potential energy）. The results show that the PE spectra display a wavenumber range scaling as 0. 2 N^4ky^-3 （N is the Brunt - Vaisala frequency, k, is the vertical wavenumber）, which is called buoyancy sub-range. However, the KE spectra cannot satisfy the negative cubic law of vertical wavenumber, which have a much larger downtrend than that of the PE spectra, for the potential energy is transferred more efficiently toward small scales than the kinetic energy. The Cox number of diapycnal diffusivity is also calculated, and it shows a good consistency with the observations and deductions in the ocean interior, during the stage of the stratified turbulence maintaining a fairly active level.     

Transmission and reflection of the Rossby waves in a stratified ocean with bottom topography

Transmission and reflection coefficients are calculated for Rossby waves incident on a bottom topography with constant slope in a continuously stratified ocean. The characteristics of the coefficients are interpreted in terms of the quasigeostrophic waves on the slope. In the parameter range where only the barotropic Rossby waves can propagate in the region outside the slope, the bottom trapped wave plays the same role as the topographic Rossby wave in a homogeneous ocean, and hence the transmission is weak unless phase matching takes place. When both of the barotropic and baroclinic Rossby waves can propagate outside the slope, the total transmission can be strong. The bottom trapped wave affects the transmission and reflection, and it leads to the possibility that the Rossby wave is transmitted as a mode different from the incident mode. When the number of the wavy modes on the slope is smaller than that of the Rossby wave modes outside the slope, strong reflection occurs.The results for an ocean with linear distribution of the squared Brunt-Väisälä frequency are compared to those in a uniformly stratified ocean. The weakening of the stratification near the bottom is almost equivalent to reducing the effect of the slope.     

On the application of a turbulence closure modified model to the description of the density jump evolution in a stably stratified medium

The self-similar turbulent density jump evolution has been studied in the scope of a turbulence closure modernized theory which takes into account the anisotropy and mutual transformation of the turbulent fluctuation kinetic and potential energy for a stably stratified fluid. The numerical calculation, performed using the equations for the average density and kinetic and potential energies of turbulent fluctuations, indicates that the vertical profiles of the buoyancy frequency, turbulence scale, and kinetic and potential energies drastically change when the turbulence anisotropy is strong. The vertical profiles of the corresponding energy and spatial discontinuity parameters, calculated at a weaker anisotropy, indicate that similar drastic changes are absent and a qualitative agreement exists with the known analytical solution, which describes the density jump evolution in a freshwater basin and was obtained previously [5, 8] in the scope of a turbulence local-similarity hypothesis applied in combination with the budget equation for the turbulent fluctuation kinetic energy.     

Influence of asymmetric wind stress curl on the general ocean circulation using an eddy-resolving quasi-geostrophic model

On the general ocean circulation forced by the asymmetric wind stress curl, the role of the eddies which are detached from the western boundary current is studied using an eddy-resolving two-layered quasi-geostrophic numerical model with free-slip boundary condition. An ideal sinusoidal function is used as the wind stress curl, and amplitude is assumed to be larger over the southern basin than over the northern one. In contrast with the antisymmetric wind forcing, in the asymmetric wind stress case, the subtropical western boundary current overshoots to the north from the zero wind stress curl line. As the asymmetricity of the wind forcing becomes larger, the separation point of the time mean field is located further north. The eddies generated in the region of the subtropical recirculation are advected northward by the western boundary current and they are detached from subtropical gyre. The release of these eddies to the north basin leads to weaken the subtropical recirculation system. From the analysis of the potential vorticity budgets, in the asymmetric case, it is shown that detached eddies play an important role in transporting the negative vorticity which is excessively inputted into the southern basin, to the northern basin, in addition to the terms which transport vorticity in the antisymmetric case, i.e., the vorticity transport by the meander of the jet. Under the free-slip boundary, more than a quarter of that excess vorticity is transported by those detached eddies in some cases.     

分层流体中细长体波浪力的数值计算

利用边界元法计算了层化流体中细长体受到的一阶垂荡波浪力和一阶纵摇波浪力矩，计算了近水面细长体的波浪力及力矩，与水池实验结果相吻合。     

Generation of internal waves by moving non-stationary disturbances in a real stratified ocean

The plane problem on the generation of linear internal waves by a moving area of time-harmonic surface pressures in a continuously-stratified ocean of constant depth is considered. An analytical relation has been derived for forced internal waves off the site of their generation in the form of an internal wave field superposition corresponding to individual vertical modes. The possible wave regimes are determined. For the Brunt-Väisälä frequency distribution in the North Atlantic, the generation conditions and amplitudes of diverse radiated waves are numerically determined.Translated by Vladimir A. Puchkin.     

The role of nonhydrostatic dynamics in controlling development of a surface ocean front

Numerical studies of surface ocean fronts forced by inhomogeneous buoyancy loss show nonhydrostatic convective plumes coexisting with baroclinic eddies. The character of the vertical overturning depends sensitively on the treatment of the vertical momentum equation in the model. It is less well known how the frontal evolution over scales of O(10 km) is affected by these dynamics. Here, we compare highly resolved numerical experiments using nonhydrostatic and hydrostatic models and the convective-adjustment parametrization. The impact of nonhydrostatic processes on average cross-frontal transfer is weak compared to the effect of the O(1 km) scale baroclinic motions. For water-mass distribution and formation rate nonhydrostatic dynamics have similar influence to the baroclinic eddies although adequate resolution of the gradients in forcing fluxes is more important. The overall implication is that including nonhydrostatic surface frontal dynamics in ocean general circulation models will have only a minor effect on scales of O(1 km) and greater.     

The study of ocean circulation dynamics with numerical models

Summarized is the author's study of the ocean circulation dynamics with numerical models, for which he was honored by the Okada Prize (1979). Cited topics are formation of the western boundary current and its variation associated with imposed wind stress, some effects of a marine ridge on the boundary current, coastal upwelling circulation and coastal thermohaline front formation. Recent modelling efforts in Japan, specifically on numerical study of ocean circulation dynamics are also reviewed.     

On nonlinear planetary waves: A class of solutions missed by the traditional quasi-geostrophic approximation

Weakly nonlinear quasi-geostrophic planetary waves on a beta-plane and topographic waves over a linearly inclined bottom are examined by use of shallow water equations for a small beta parameter. Long solitary wave solutions missed by the use of the traditional quasi-geostrophic approximation are found in a channel ocean with neither a sheared current nor a curved (non-linearly inclined) bottom topography. The solutions are missed in the traditional approach because the irrotational motion associated with the geostrophic divergence is neglected by the quasi-geostrophic approximation. Another example which calls attention to the limitation of the traditional quasi-geostrophic approximation is the nonlinear evolution of divergent planetary eddies whose scale is much larger than the Rossby's radius of deformation. Some aspects of a new evolution equation are briefly discussed.     

层化海洋中的二阶波散射作用问题

引入Stokes有限振幅水波的多色波作用机制 ,采用二层层化海洋模型 ,分析了层化海洋中非线性波对结构的散射作用问题。提出了二层海洋中二阶水波散射条件的数学表达式 ,进而推导了二层海洋中二阶波对一般型圆柱散射作用的格林积分解式 ,并给出了对解式中自由面及分层界面无限积分的递推算式。     

On the stability of vortex streets in a stratified fluid

On the basis of the perturbation theory developed previously by the authors for localized hydrodynamic vortices, the influence of a specified jet flow and of the structure of individual vortices on the stability of the Karman street is investigated. It is shown that, for a street of vortices with a power law of decrease in the azimuthal velocity, the jet flow suppresses instability only with respect to perturbations with wavelengths from a certain range determined by the parameters of the flow. At the same time, for streets formed from vortices with a Gaussian profile of the azimuthal velocity, even in the absence of a specified flow, there is a certain region of the street’s parameters in which the street is stable against perturbations of all scales. Thus, for the purposes of modeling quasi-two-dimensional flows in a stratified fluid by a sequence of localized vortices, which is discussed in this study, vortices with a Gaussian profile of the azimuthal velocity turn out to be preferable. The results of this study are consistent with numerous experiments on the structure of a quasi-two-dimensional wake behind a body in a stratified fluid at large Reynolds and Froude numbers.     

Nonlinear dynamics of a coupled surge-heave small-body ocean mooring system

An investigation of coupled surge-heave motion of a symmetric small-body ocean mooring system is carried out in this paper. The dynamical system, formulated using a Lagrangian approach in the vertical plane of motion, is characterized by a strong geometric mooring nonlinearity and includes a quadratic relative motion Morison form for the hydrodynamic damping. Numerical simulations reveal complex periodic and aperiodic solutions which include torus multiplying and chaotic motion. The onset of instabilities is discussed and a comparison with a limiting decoupled surge model is performed.