Note on the viscous smoothing of the discontinuities in an inviscid model of abyssal circulation

Calculations for the thermohaline circulation for an inviscid model over the slope regions of a homogeneous and of a two-layer system with sloping western and northern boundaries and driven by uniform upwelling through the thermocline were carried out by Andersson and Veronis [2004. Thermohaline circulation in a two-layer model with sloping boundaries and mid-ocean ridge. Deep-Sea Research Part I 51, 93–106]. The results showed discontinuities in certain regions of the flow over the western and northern slopes where inviscid flows from different regions merged. A speculation that those discontinuities would be smoothed over when friction is added to the model is verified here in a numerical calculation for the homogeneous model in which the value of friction ranges over three orders of magnitude. The inviscid solution is approached as friction is reduced. The conclusion is that obtaining a solution using an inviscid model over the slope regions is a valid first step in solving a problem of this type.     

Alternating zonal flows in a two-layer wind-driven ocean

Alternating zonal flows in an idealized wind-driven double-gyre ocean circulation have been investigated using a two-layer shallow-water eddy-permitting numerical model. While the alternating zonal flows are found almost everywhere in the time-mean zonal velocity field, their meridional scales differ from region to region. In the subpolar western boundary region, where the energetic eddy activity induces quasi two-dimensional turbulence, the alternating zonal flows are generated by the inverse energy cascade and its arrest by Rossby waves, and the meridional scale of the flows corresponds well to the Rhines scale. In the eastern part of the basin, where barotropic basin modes are dominant, the zonal structure is formed through the nonlinear effect of the basin modes and is wider than the Rhines scale. Both effects are likely to form zonal structure between the two regions. These results show that Rossby basin modes become an important factor in the formation of alternating zonal flows in a closed basin in addition to the arrest of the inverse energy cascade by Rossby waves. The wind-driven general circulation associated with eddy activities plays an essential role in determining which mechanism of the alternating zonal flows is possible in each region.     

Numerical Model of Internal Solitary Wave Evolution on Impermeable Variable Seabed in A Stratified Two-Layer Fluid System

1.IntroductionIn mathematics and physics,a soliton is a self-reinforcing solitary wave caused by nonlinear ef-fectsinthe medium.Solitons are found in many physical phenomena(Chou and Shih,1996;Chouand Quyang,1999;Chouet al.,2003;Chenet al.,2004;Wang,2004;…     

Stabilization of a linearly unstable wave participating in a three-wave resonant interaction

An analytical study of the influence of three-wave resonant interactions on the evolution of unstable wave disturbances is presented in the Kelvin-Helmholtz model. These results may be of interest in analyzing the dynamics of disturbances at the ocean-atmosphere interface and in two-layer flows which arise in the ocean and are characterized by large gradients of flow velocity at the boundary of layers. In the case under consideration, the instability arises when eigenfrequencies coincide in the framework of a single mode and the instability is algebraic. The amplitudes of the two other interacting stable waves are assumed to be small compared to the amplitude of the third, unstable, mode. The system of amplitude equations for this case is investigated using the WKB method. As a result, we obtain the formulas coupling the solutions for the time before and after a transition through a singular point, where the amplitude of the linearly unstable wave has a local minimum. These formulas give the rule of transformation of the parameter that characterizes a phase shift between fast and slow modes and determines the behavior of the system. It is shown that, in a transition through a singular point, this parameter changes randomly. As long as the parameter is positive, the amplitude of the linearly unstable wave remains limited and oscillates stochastically. In a transition of the parameter through zero, we exit the stabilization region and have an infinite growth of amplitude. The transition into the instability region is random. However, if the time interval where the amplitude remains limited is large enough, the scenario of the behavior of the system we have obtained can be treated as the partial stabilization of instability. The results make it possible for us to investigate the stochasticity caused by the nonlinear interaction of gravity-capillary waves in a two-layer model of a shear flow. These results are also of interest in analyzing secondary flows in laboratory facilities modeling the ocean and atmospheric processes.     

The instability of viscous two-layer oscillatory flows

The instability of oscillatory flows in a two-layer fluid where the two layers differ in density and viscosity has been analysed using a perturbation method for long waves with special interest on effects of viscosity, time scale, density and depth of the fluid. The flow of a fluid with homogeneous density can be unstable, when the kinematic viscosity of the upper fluid layer is different from that of the lower one. Viscosity stratification results in unstable oscillatory flows. Two limiting cases of single-layer flow are also considered.     

Measurement and evaluation of the hydrodynamics and secondary currents in and near a strait connecting large water bodies—A field study

The straits connect two large water bodies show highly strong and stratified currents related to meteorological, morphological and hydrodynamic conditions. In some cases, spatial and temporal changes of the stratified currents and their thickness, direction and magnitude are so complex. This complexity directly affects the circulation pattern in the region, water exchange between both ends of the straits and migration of fish species. In order to understand general characteristics of this kind of straits and identifying the complexity of the hydrodynamics of the region and evaluate the secondary currents and recirculation need long term, intensive, field work and measurement studies. As an example of this kind of hydrodynamically complex straits, Bosphorus strait is selected for a field study. The Bosphorus strait has a strongly stratified two-layer system and a unique case of the maximal exchange regime typical of strait flows, which is largely determined by conditions at the Black Sea. Although the Bosphorus strait has distinct two-layer stratification with an associated two-layer system exchange, no continuous current measurements have been made so far, previous measurements all having been random sampling.In this paper, a detailed measurement program has been applied to Bosphorus strait. In the measurement program, a short-term current profile measurement at selected locations at southern part of the strait has been conveyed. Additionally a long-term measurement of current profile has been performed at a selected critical location (in front of the Dolmabahçe Palace) where a recirculation flow exists in the strait. The scope of this paper is to present the techniques and the results of analysis of measurement data. In the measurements the current profile (magnitude and direction) has been determined at every 1 m depth intervals from the surface to the sea bottom at 3 min duration at every hour. Measurements provide that lower-layer flows in northward direction from the Sea of Marmara towards the Black Sea, whereas the upper-layer flow comes from the Black Sea and flows towards the Sea of Marmara in the opposite direction of lower layer. The Bosphorus strait exhibits distinctive features associated with variations in its width and depth. The meandering features of Bosphorus also cause recirculation flows. These results of measurements are presented, discussed and compared with previous studies.     

Internal bores in two-layer exchange flows over sills

Internal bores are a common feature of tidally modulated two-layer exchange flows through straits and over sills. Even where the forcing changes smoothly, the flow may adjust with sudden jumps in the position of the interface between the two layers. The resulting flow configuration, with a hydraulically controlled exchange flow (at the sill) coupled with a propagating internal hydraulic jump (known as a bore), is investigated with mathematical models and laboratory experiments. The study concentrates on two-dimensional flow in a rectangular channel with a sill. The parameters considered are the depth of the channel compared to the depth over the sill, the depth of the interface before the passage of the bore and the strength of the net flux through the channel.The theory is based on shallow water equations and hydraulic control theory and includes the effects of a steady net flow through the channel (driven, for example, by the tide). Once the depth of the channel is twice the depth over the sill, further changes in geometry have relatively little effect on the flow. The bore velocity and fluxes are strongly affected by the strength of any net flow. The laboratory experiments model pure exchange flows (with no net flow) and give detailed information about the bores themselves. In many cases an undular bore is produced, with a well-defined wave train on the interface behind the front of the bore. The wavelengths and amplitudes of these internal waves are quantified and a brief comparison with similar internal waves observed in the Strait of Gibraltar is presented.     

南海北部内孤立波数学模型

在二层内潮数学模型的基础上,考虑非静力平衡扰动压力的影响,导出潮频内孤立波产生、传播的数学模型。该模型不受小地形假设的限制,并适用于南海。应用该模型能解释说明产生以下现象的物理机制：潮流流过巴坦-萨布坦海脊时,在一定海洋环境条件下,通过潮流与起伏的底地形相互作用可激发产生潮频内孤立波,并西传至东沙群岛附近的海域。     

PSME model of parametric excitation of two-layer liquid in a tank

Internal waves driven by external excitation constitute important phenomena that are often encountered in environmental fluid mechanics. In this study, a pseudospectral σ-transformation model is used to simulate parametric excitation of stratified liquid in a two-layer rectangular tank. The σ-transformation maps the physical domain including the liquid free surface, the interface between the liquid layers, and the bed, onto a pair of fixed rectangular computational domains corresponding to the two layers. The governing equation and boundary conditions are discretised using Chebyshev collocation formulae. The numerical model is verified for two analytical sloshing problems: horizontal excitation of constant density liquid in a rectangular tank, and vertical excitation of stratified liquid in a rectangular tank. A detailed analysis is provided of liquid motions in a shallow water tank due to excitations in the horizontal and the vertical directions. Also, the effect of pycnocline on the wave motions and patterns is studied. It is found that wave regimes and patterns are considerably influenced by the pycnocline, especially when the excitation frequency is large. The present study demonstrates that a pseudospectral σ-transformation is capable to model non-linear sloshing waves in a two-layer rectangular tank.     

Nonlinear dynamics of phase transitions during seawater freezing with false bottom formation

This paper concerns mathematical modeling of the processes of false bottom evolution taking into account water freezing in the opposite direction from the cooled boundary with the atmosphere. The model of the crystallization process is based on the two-phase zone theory complicated by the moving boundaries of phase transitions and turbulent flows of fluid in the ocean near the false bottom boundary. Analytical solutions of the nonlinear problem are found (the distributions of the temperature and the salinity, the proportion of the solid fraction, the laws of the motion of the boundaries between the phase transitions, and the heat fluxes) and a comparative analysis of the results with the field data observations is performed. It is shown that the heat flux caused by the growing false bottom makes a significant contribution to the heat exchange processes between the ocean and the atmosphere.     

On the use of a two-layer fluid stratification model in studies of topographically-generated baroclinic tides

Internal waves generated by a baroclinic internal wave impinging on an oceanic ridge are studied. Two stratification models are considered: a two-layer ocean model (with a density jump) and a continuously stratified ocean model (model pycnocline). The results yielded by different stratification models are compared analytically. The analysis makes possible the application of a piecewise-constant approximation of the fluid stratification to study topographically-generated baroclinic tides. Translated by V. Puchkin.     

Open boundary conditions for nonlinear channel flow

Open boundary conditions are derived for the one-dimensional nonrotating two-layer shallow-water equations. The conditions are based on characteristics of the external and internal modes. It is possible to find exact nonlinear characteristic conditions for the external mode, as well as approximate nonlinear conditions for the internal mode. These conditions can also be linearised by Taylor expansion; the approximate linear conditions are similar to those used in several previous studies. Both of the nonlinear and linearised conditions perform well, indicating that either the nonlinear or linearised conditions may potentially be extended to the more general case of multi-layer flows.     

Dynamics of Rossby waves in an ocean with inhomogeneous currents

A model for a two-layer ocean is applied to consider, in terms of the geometrical optics approximation, the effect of mean flows propagating within the upper layer upon the dynamics of Rossby waves. The case is theoretically analysed, with the depth of the ocean's upper layer much smaller than that of the underlying layer. In this case, the flow's impact upon the baroclinic mode of Rossby waves is ubiquitous, with the exception of synchronicity. Depending on the parameters, four types of wave packets' behaviour in the vicinity of synchronicity points are singled out, namely, the elimination of the peculiarity, shadowing, and convective/absolute instability. For the mean flow profile simulating cyclonic and anticyclonic gyres, we have obtained wave packet trajectories and have studied the wave packet's interaction with the current. Specifically, it has been demonstrated that, given some modulus of the wave packet, vigorous energy exchange between the wave vector and the flow takes place. Translated by Vladimir A. Puchkin.     

A model of submarine channel-levee evolution based on channel trajectories: Implications for stratigraphic architecture

Channel-levee systems are frequently interpreted as having a long history of cut-and-fill by channel-shaped features of different scales. Results from a simple geometric model based on a centerline migration algorithm combined with a vertical channel trajectory show that an incising-to-aggrading trajectory of a single channel can produce realistic morphologies similar to systems observed on the seafloor and subsurface, including features such as a basal erosional surface, coeval inner and outer levees, internal erosional boundaries, and terraces draped by inner levee deposits. Channel migration results in composite erosional surfaces that are distinct from topographic surfaces, and their formation does not require larger than usual erosional flows. Many submarine channels interpreted as underfit were probably carved by flows similar to the ones that eroded and deposited the entire channel system. We suggest that the features of most submarine channel-levee systems do not require large temporal variations in flow magnitude but can be explained by a simpler model whereby incision, migration and aggradation of a single channel form over time results in an apparently complex system.     

Influence of delta growth on paleo‐tidal flow: Fraser River delta,British Columbia—Part 2: Tidal model

Abstract

The paleo‐tidal flows in the waters in the vicinity of Point Roberts and the Fraser River delta were numerically simulated through the development of a coarse grid model (2 km mesh size) and a fine grid model (2/3 km mesh size). The basic hydrodynamic equations, the numerical grid layout, and the finite‐difference forms are given. Special attention was given to transferring the boundary grid data generated from coarse grid model to the boundaries of the fine grid model. Diagrams are presented to show that the fine grid model yields much superior results in the sense of providing a greater amount of detail, in the current patterns and the eddy structure, than is provided by the coarse grid model, in the application to estimating sedimentary patterns.     

Effects of bottom topography and density stratification on variations of western boundary currents caused by periodic change in wind stress

Variations of the western boundary currents induced by a periodic change in wind stress are studied in a two-layer model with a continental slope along the western boundary. The variation of the total transport of the western boundary current over the continental slope shows a considerable phase lag with the wind stress and a decrease in amplitude compared with for the flat bottom ocean, though the interior barotropic response is to adjust almost instantaneously to the wind stress. The total transport variation of the western boundary current is well approximated by the upper layer transport variation. That is, almost complete separation of the upper- and lower-layer flows takes place over the slope, and only the upper layer flow contributes to the change in total transport of the western boundary current. Contributions of the interior barotropic and baroclinic responses to the upper layer transport variation depend on the forcing period. With decrease in the forcing period, the barotropic response becomes relatively important for determining the upper layer transport variation although the amplitude of the variation is smaller.     

区域性海洋环流数值模式研究及对南海环流与海峡流量的模拟

基于MOM模式的物理框架,妥善考虑了开边界的物理过程,改造和发展了一个区域海洋数值模式。本模式不仅可以方便地调整开边界条件,使之满足边界的特定物理条件,而且可以方便地做针对性修改,使模式更加可靠。改进后的模式具有MOM模式物理概念明确、公式便于理解、结果便于表达的全部特点,同时克服了MOM模式边界条件不完整、程序不易调整、参数难以改变的缺点。区域性模式比全球模式的计算速度快很多倍,可以成为区域性研究的有效工具。将此模式应用于南海,利用Hellerman＆Rosenstein气候态风应力驱动模式10a,得到与全球模式效果相当的结果。模式模拟结果展现了南海流场的季节特征,在模式分辨率下表现出了多涡结构。根据模拟的流场计算了南海与其它海域的水交换通量。在年平均意义下,外海水通过吕宋海峡进入南海,南海水通过台湾海峡、民都洛海峡和卡里马塔海峡流出南海。各海峡水通量具有明显的季节变化。     

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.     

Modeling residual circulation and stratification in Oujiang River estuary

A 3D,time-dependent,baroclinic,hydrodynamic and salinity model was implemented and applied to the Oujiang River estuarine system in the East China Sea.The model was driven by the forcing of tidal elevations along the open boundaries and freshwater inflows from the Oujiang River.The bottom friction coefficient and vertical eddy viscosity were adjusted to complete model calibration and verification in simulations.It is demonstrated that the model is capable of reproducing observed temporal variability in the water surface elevation and longitudinal velocity,presenting skill coefficient higher than 0.82.This model was then used to investigate the influence of freshwater discharge on residual current and salinity intrusion under different freshwater inflow conditions in the Oujiang River estuary.The model results reveal that the river channel presents a two-layer structure with flood currents near the bottom and ebb currents at the top layer in the region of seawater influenced on north shore under high river flow condition.The river discharge is a major factor affecting the salinity stratification in the estuarine system.The water exchange is mainly driven by the tidal forcing at the estuary mouth,except under high river flow conditions when the freshwater extends its influence from the river’s head to its mouth.     

Three-dimensional instability of shear flows with inflection-free velocity profiles in stratified media with a high Prandtl number

In stably stratified media with a Prandtl number Pr ≫ 1, vertical scales of the density (ℓ) and horizontal velocity variation (L) are quite different, ℓ/L = O(Pr^−1/2) ≪ 1, and this influences the flow stability. In particular, shear flows without inflection points on the velocity profile are unstable even in an ideal incompressible fluid. The maximum instability growth rate for sufficiently small ℓ/L is of the same order as in homogeneous mixing layers, with mainly three-dimensional rather than two-dimensional oscillations increasing in a wide range of parameters. This paper focuses on the three-dimensional instability of such flows. It is shown that the spectrum of unstable oscillations is essentially anisotropic in the case of a relatively weak stratification when the bulk Richardson number J ≤ O[(ℓ/L)^3/2]. The results of the asymptotic analysis are illustrated by calculations for a model flow in a two-layer medium (ℓ = 0) as well as for flows with values of ℓ/L corresponding to a temperature or salinity stratification of the water.