A New Class of Edge Baroclinic Waves and the Mechanism of Their Generation

Edge baroclinic waves are generated in a geostrophic flow with a vertical shear near a solid surface. The study investigates a new class of baroclinic waves in flows with horizontal and vertical shears and a linear distribution of potential vorticity. It is shown that taking account of the horizontal shear leads to the appearance of new features of wave dynamics. These include the nonmodal growth of energy in the initial stage of development, the time dependence of the vertical wave scale, and the possibility of generation of stationary or blocked waves. The horizontal shear makes the mechanism of generation of baroclinic waves by initial vortex perturbations more efficient. One important feature is associated with vortex paths, which are formed by the superposition of a baroclinic wave on the flow with horizontal shear.     

Resonant Excitation of Baroclinic Waves in the Presence of Ekman Friction

The quasi-geostrophic dynamics of disturbances of a flow with a vertical shear is described by a transfer equation for potential vorticity. Wave solutions of this equation are represented by edge baroclinic waves (modes in a discrete spectrum) and singular modes in a continuous spectrum. When frequencies of these modes coincide, the effect of resonant excitation occurs in which the amplitude of baroclinic waves increases linearly. This paper studies this effect in the presence of Ekman bottom friction. It is shown that friction suppresses linear wave growth and gives rise to baroclinic waves of finite amplitude.     

Diagnosing cyclogenesis by partitioning energy and potential enstrophy in a linear quasi‐geostrophic model

Baroclinic development is studied with 2 linear, quasi‐geostrophic models. One model is the Eady model, the other uses more realistic wind, density, Coriolis, and static stability. Initial‐value solutions are diagnosed using time series of potential enstrophy ( H ), total energy ( E ), the components of H and E , and the amplitude norm. Two vertical structures for the initial condition are used for both models. One initial condition is representative of a class of initial conditions studied previously having enhanced nonmodal growth (NG). The other initial condition approximates observed conditions prior to cyclogenesis. Results are shown for the most unstable normal mode wavelength of each model. The growth rates of the components of H and E evolve quite differently for different initial states and models tested. NG in H is shown to be sensitive to the contribution of the boundary potential vorticity (BPV) of the initial state; small adjustments in eddy structure at the boundary significantly alter BPV and H growth rates. The amount of NG is related to how far BPV present initially differs from the asymptotic normal mode. The effect upon NG of each approximation present in the Eady model (but not in the other model) are considered. Using realistic mean flow shear, static stability, or compressibility can significantly reduce NG but including linearly varying Coriolis parameter did not. Two conceptual models of NG are considered. Growth by increasingly favorable superposition remains relevant. Growth by "tilting into the vertical" is shown to be incorrect.     

On the vertical distribution of

The aim of this paper is to present an analytical expression for the vertical distribution of the correlation between the horizontal ( ) and vertical ( ) wave velocity components. This quantity, , which appears explicitly in the time-averaged momentum balance equations, has been shown to play an important role in the vertical distribution of wave-induced currents.The proposed formulation for is based on an identity that relates the effective (wave) shear stress to the effective (wave) normal stresses ( ² and ²) and to the vorticity of the oscillatory flow gw. This general expression has been applied to simplified situations and has been shown to degenerate into other existing formulations with comparable simplifying assumptions, viz. irrotational waves in shallow water over an arbitrary bottom topography and breaking waves over a horizontal bottom.The model has also been applied to the case of waves interacting with a depth-varying current over a horizontal bottom, in which preliminary results have been obtained for a simplified situation invoking linear (small-amplitude) wave theory.     

On the onset of the instability of a three-dimensional jet in a stratified fluid

The onset of a three-dimensional jet flow in a stratified fluid is studied with the aid of a direct numerical simulation. An initially cylindrical jet with a Gaussian velocity profile is considered in a fluid with stable linear density stratification. The results indicate that, if an initial small perturbation of the velocity field has a wide spectrum, an exponential growth of the isolated quasi-two-dimensional mode occurs and its spectral maximum is shifted toward smaller wave numbers in comparison with the maximum of the helical mode of the instability of a nonstratified jet. The growth rate is proportional to Ri^0.5, where Ri is the global Richardson number. The onset of the instability leads to the formation of the flow’s vortex structure, which consists of a collection of different-polarity quasi-two-dimensional vortices located in a horizontal plane near the longitudinal axis of the jet. At sufficiently long times (Nt > 100, where N is the buoyancy frequency and t is time), the growth of instability reaches the saturation stage and further fluctuations in velocity and density decay under the effect of viscous diffusion. At this stage, the flow becomes self-similar and the time dependences of the transverse and vertical widths of the jet are consistent with the asymptotic behaviors of integral parameters of the flow that are observed experimentally in the far stratified wake. The results suggest that the onset of the instability of a quasitwo-dimensional mode can play the determining role in the dynamics of flow in the far stratified wake.     

A proposed adiabatic formulation of 3‐dimensional global atmospheric models based on potential vorticity

A 2‐time‐level finite difference atmospheric general circulation model based on the semi‐Lagrangian advection of pseudo potential vorticity (which becomes potential vorticity in that part of the domain where the hybrid vertical coordinate becomes isentropic) has been formulated. At low levels, the hybrid vertical coordinate is terrain following. The problem of isentropic potential vorticity possibly becoming ill‐defined in the regions of planetary boundary layer is thus circumvented. The divergence equation is a companion to the (pseudo) potential vorticity equation and the model is thus called a PV‐D model. Many features of a previously developed shallow water PV‐D model are carried over: a modification of the PV equation needed to give computational stability of long Rossby waves; a semi‐Lagrangian semi‐implicit treatment of both the linear and the nonlinear terms; the use of an unstaggered grid in the horizontal; the use of a nonlinear multigrid technique to solve the nonlinear implicit equations. A linear numerical stability analysis of the model's gravity–inertia waves indicates that the potential temperature needs to be separated into horizontal mean and perturbation parts. This allows an implicit treatment of the vertical advection associated with the mean in the thermodynamic equation. Numerical experiments with developing baroclinic waves have been carried out and give realistic results.     

Hamiltonian description of shear and gravity shear waves in an ideal incompressible fluid

Methods of studying the dynamics of wave disturbances in st;ratified shear flows of an ideal incompressible fluid are considered. The equations governing the motions of interest represent Hamilton equations and are derived by writing the velocity field in terms of Clebsch potentials. Equations written in terms of semi-Lagrangian variables are integrodifferential equations, which make it possible to consider both continuous and discontinuous solutions, as well as the cases where the parameters of the undisturbed medium are step functions. Two dynamic systems are presented. The first, canonical system of equations is most suitable for describing gravity waves in a shear flow in the case where the undisturbed medium is characterized by sharp gradients of density and flow velocity. The simplest model in which disturbances obey this system of equations is the well-known Kelvin-Helmholtz model. The second dynamic system describes, in particular, gravity-shear waves and, in the case of a homogeneous medium, shear waves in a two-dimensional flow. This system is most suitable for studying the dynamics of disturbances in models with sharp gradients of vorticity. On the basis of the approach developed in this study, the problem of the dynamics of disturbances in a flow with a continuous distribution of vorticity in a finite-thickness layer is solved. If the thickness of this layer is small compared to the characteristic wavelength and the gradient of the undisturbed vorticity in this layer is large, the solution has the form of a mode whose frequency is close to the frequency of the shear wave on a vorticity jump that would be obtained by letting the layer’s thickness approach zero. The results obtained allow, in particular, the estimation of the range of validity of finite-layer approximations for models with smooth profiles of flow and density. In addition, these results can be interpreted as the basis for the development of nonlinear aspects of the theory of hydrodynamic stability.     

Formula for a baroclinic adjustment theory of climate

Recently, a theory relating baroclinic neutrality and midlatitudes tropopause height has been proposed. However, GCM results have shown that the dependence of the theory on external parameters is not consistent with that displayed by these numerical experiments. In the present paper we suggest an analytic formula for baroclinic adjustment to the neutrality of Eady waves through tropopause modification. This formula extends considerably the abovementioned theory by taking into account both a simple representation of the stratosphere and the topography. These modifications alter the tropopause condition for a baroclinically neutral state and its sensitivity to the external parameters. In particular, the topography introduces a dependence on the tropospheric vertical wind shear of the neutrality condition. This feature is not present in other models that assume a background state with a zero potential vorticity gradient in the troposphere. We show, furthermore, that the modified neutrality condition has sensitivities that may resemble those displayed by GCM simulations, with respect to the parameters defining the background flow.     

Rotational instability of a horizontal shear flow in a stratified rotating fluid

The rotational instability of a thermally stratified, viscous, conducting, rotating fluid is investigated by means of linearized perturbation equations. It is assumed that the basic horizontal flow is vertically uniform and that the horizontal shear is confined in a thin layer. By solving a simplified boundary value problem as a model of rotational instability in the sea, we have shown that the vertical wave length of the neutral disturbance is of order 10 times as large as the laminar Ekman layer thickness, and that this scale is proportional to (L/N)^1/3, whereL is the width of the shear layer andN is the Brunt-Vaisala frequency.     

Resonant interaction of waves of continuous and discrete spectra in the simplest model of a stratified shear flow

The equations of dynamics of eddy—wave disturbances of two-dimensional stratified flows in an ideal incompressible fluid that are written in a Hamiltonian form are used to study the resonant interaction of waves of discrete and continuous spectra. A gravity—shear wave generated at a jump of the density and vorticity of the undisturbed flow and a wave generated at a weak vorticity jump, which is similar to a wave of a continuous spectrum, participate in the interaction. The equations are written in terms of normal variables to obtain the system of evolution equations for the amplitudes of the interacting waves. The stability condition for eddy—wave disturbances is derived within the framework of the linear theory. It is shown that a cubic nonlinearity may lead to the stabilization of unstable disturbances if the coefficient of the nonlinear term is positive.     

Dynamics of a Wave Packet on the Surface of an Inhomogeneously Vortical Fluid (Lagrangian Description)

A nonlinear Schrödinger equation (NSE) describing packets of weakly nonlinear waves in an inhomogeneously vortical infinitely deep fluid has been derived. The vorticity is assumed to be an arbitrary function of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. It is shown that the modulational instability criteria for the weakly vortical waves and potential Stokes waves on deep water coincide. The effect of vorticity manifests itself in a shift of the wavenumber of high-frequency filling. A special case of Gerstner waves with a zero coefficient at the nonlinear term in the NSE is noted.     

SPH方法的孤立波与部分淹没结构物相互作用数值计算研究

为研究孤立波作用下结构物周围流场特征,基于无网格SPH方法,建立孤立波与海洋结构物相互作用模型,对不同波幅孤立波作用下部分淹没矩形结构物周围波面、流速、涡量及结构受力特征进行计算分析,探索了相对波高对非淹没结构物周围流场的影响规律。结果表明:流场特征与相对波高密切相关,相对波高较小时,波面、流速、涡量及结构荷载均较为光滑,相对波高在0.2以上时,波峰爬升至结构物顶部并在越过结构物后与水槽内水体碰撞造成流场波动,波面、流速、涡量及结构荷载的波动幅度随着相对波高增大而增大,流场更加复杂,结构物水平和垂向负压也越大,且结构物周围涡分布逐渐向深度方向和下游方向发展。     

Experimental Study on Ocean Internal Wave Force on Vertical Cylinders in Different Depths

A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary waves are produced by means of gravitational collapse at the layer thickness ratio of 0.2, and the internal periodic waves are produced with rocker-flap wave maker at the layer thickness ratio of 0.93. The wave parameters are obtained through dyeing photography. The vertical cylinders of the same size are arranged in different depths. The horizontal force on each cylinder is measured and the vertical distribution rules are researched. The internal wave heights are changed to study the impact of wave heights on the force. The results show that the horizontal force of concave type internal solitary wave on vertical cylinder in the upper-layer fluid has the same direction as the wave propagating, while it has an opposite direction in the lower-layer. The horizontal force is not evenly distributed in the lower fluid. And the force at different depths increases along with wave height. Internal solitary wave can produce an impact load on the entire pile. The horizontal force of internal periodic waves on the vertical cylinders is periodically changed at the frequency of waves. The direction of the force is opposite in the upper and lower layers, and the value is close. In the upper layer except the depth close to the interface, the force is evenly distributed; but it tends to decrease with the deeper depth in the lower layer. A periodic shear load can be produced on the entire pile by internal periodic waves, and it may cause fatigue damage to structures.     

规则波作用下台阶地形上墩柱绕流三维数值研究

利用Flow-3D建立三维数值波浪水槽,模拟波浪在不对称台阶地形上的传播。系统研究规则波作用下墩柱周围水流的流动特性,分析墩柱周围的瞬时速度场、涡量场以及KC值变化,不同相位时墩柱前、后水平流速分布情况。结果表明:波浪在台阶地形传播的过程中,墩柱迎水面的涡动结构不够明显;高涡量呈对称状聚集在墩柱的背水面,并形成一对旋转方向相反的涡结构;周期对KC值的影响比波高的影响要明显;墩柱迎水面水平方向流速变化较大,侧面水平流速变化最为剧烈,背面由于受到墩柱的掩护作用水平方向流速变化不大,在墩柱的正面和侧面竖向环流明显。     

Numerical Simulation of Spatial Lag Between Wave Breaking Point and Location of Maximum Wave-Induced Current

A quasi three-dimensional numerical model of wave-driven coastal currents with the effects of surface rollers is developed for the study of the spatial lag between the location of the maximum wave-induced current and the wave breaking point.The governing equations are derived from Navier-Stokes equations and solved by the hybrid method combining the fractional step finite different method in the horizontal plane with a Galerkin finite element method in the vertical direction.The surface rollers effects are considered through incorporating the creation and evolution of the roller area into the free surface shear stress.An energy equation facilitates the computation process which transfers the wave breaking energy dissipation to the surface roller energy.The wave driver model is a phase-averaged wave model based on the wave action balance equation.Two sets of laboratory experiments producing breaking waves that generated longshore currents on a planar beach are used to evaluate the model's performance.The present wave-driven coastal current model with the roller effect in the surface shear stress term can produce satisfactory results by increasing the wave-induced nearshore current velocity inside the surf zone and shifting the location of the maximum longshore current velocity landward.     

Application of a Boussinesq model for the computation of breaking waves: Part 2: Wave-induced setdown and setup on a submerged coral reef

Based on a set of Boussinesq-type equations with improved linear frequency dispersion characteristics in deeper water, the present paper incorporates the simplified effect of spilling wave breaking into the equations. The analysis is restricted to a single horizontal dimension but the method can be extended to include the second horizontal dimension. Inside the surf zone the vertical variation of the horizontal velocity profile is assumed to be composed of an (initially unknown) organised velocity component below the roller and a surface roller travelling with the wave celerity. This leads to a new set of equations which is capable of simulating the transformation of waves before, during and after wave breaking. The model is calibrated and verified by comparison with several wave flume measurements. The results show that the model produces sound physical results.     

Measurements of higher harmonic wave forces on a vertical truncated circular cylinder

Wave forces on a vertical truncated circular cylinder in Stokes waves with the wave slopes ranging from 0.06 to 0.24, are measured in a wave tank. The higher harmonic wave forces are compared with the available values from theories of the FNV (Faltisen–Newman–Vinje) model and Varyani solution. The first harmonic horizontal forces measured are much larger than the theoretical values from the FNV model, while the first harmonic vertical forces are well predicted by the Varyani theory. It was also found that the FNV model significantly overpredicts the second harmonic horizontal forces in high frequency waves, but under predicts the third harmonic forces. The differences between the actual measurement and the theory, in the second and third harmonic horizontal forces, become smaller at low wave frequencies as the wave slope increases. In addition, the transverse instabilities in the incoming waves with high wave slope were observed, which is due to the nonlinear modulation. Measurements were, thus, carried out before the instability occurred.     

On the spatial instability of internal waves in continuously stratified flows

A stationary parallel current in a continuously stratified incompressible fluid of finite depth is considered. The instability of internal waves is studied with the assumption that the current has only a vertical velocity shear.Translated by Vladimir A. Puchkin.     

Infragravity waves with internal wave characteristics in the south of the Bohai Sea of China

The measurements by using ADCP (500 KH) and CTD were made during August 2000 in the south (37°55''N, 120°25''E) of the Bohai Sea, where the water depth was about 16.5m. The data of horizontal velocity with sampling interval of 2 min in 7 layers were obtained. The power spec-trum analysis of these data indicates that there are very energetic infragrvity waves with a period of about 6 min. The coherence spetrum analysis and the analysis of temporal variation of shear show that these infragravity waves are mainly the free wave model (properties of edge waves), in the meantimethey possess some characteristics of internal waves, which are likely due to the distinctive marine environment in this area. It is speculated on that the instability processes (chiefly shear instability) of sheared stratified tidal flow owing to the effect of sea-floor slope in the coastal area might be the main mechanism generating these infragravity waves.     

Numerical study on vertical structures of undertow inside and outside the surf zone

Nearshore shoaling and breaking waves can drive a complex circulation system of wave-induced currents. In the cross-shore direction, the local vertical imbalance between the gradient of radiation stress and that of pressure due to the setup drives an offshore flow near the bottom, called ‘undertow’, which plays a significant role in the beach profile evolution and the structure stability in coastal regions. A 1DV undertow model was developed based on the relationship between the turbulent shear stress and t...