Wave/wave interaction producing horizontal mean flows in stably stratified fluids

We show that internal wave/wave interactions in stratified fluids are able to produce strong horizontal mean currents. A simple analytical model allows us to estimate the amplitude of the time-periodic horizontal mean flow induced by the interaction of two monochromatic waves. This model shows that in some cases, the mean flow velocity can overgo a threshold beyond which critical layers and intense energy transfers from the waves to the mean flow are expected. This prediction is confirmed by direct pseudo-spectral simulations of the Navier–Stokes equations under the Boussinesq approximation. Such interactions may help to further understand the presence of strong vertical shear observed in the final stage of stratified flows in oceans and atmospheres.     

Non-modal baroclinic instability

A class of non-linear instabilities of a vertically sheared zonal flow is discussed. This is a type of baroclinic instability that lies outside the purview of a linear eigenmode analysis of baroclinic instability problems. The form taken by the instability is that of an ensemble of three neutral Rossby waves whose amplitudes are slowly modified by their mutual non-linear interactions. For a triad of small amplitude, these interactions introduce a weak, vertical variation of phase to the structure of the individual waves. This allows the generation of rectified heat fluxes and an exchange of energy with the mean flow.This instability exhibits explosive growth and spans a range of horizontal wavenumbers that exceeds the range that is unstable in the corresponding linear model. It is shown that the type of instability discussed can only occur when the model used admits unstable eigenmodes as well as neutral Rossby waves.The mechanism for the non-linear instability discussed here is believed to be fairly general and should exist also in the context of a horizontally sheared flow where it would take the form of a barotropic instability.     

Numerical experiments on internal gravity waves in an accelerating shear flow

The influence of an accelerating shear flow on the propagation of an internal gravity wave in a continuously stratified fluid is studied by means of two-dimensional numerical simulations. These are motivated by earlier laboratory experiments [Thorpe, S.A. 1978b. On internal gravity waves in an accelerating shear flow, Vol. 88. J. Fluid Mech. pp. 623–639]. In these experiments the mean flow is an accelerated Couette flow and the mean density profile is linear. The laboratory experiments revealed the striking effect of the unsteady shear flow in the evolution of an internal gravity wave leading to the wave focusing in a region where the flow is extremum. This phenomenon is associated with the growth of small scale density fluctuations. As a result density overturns are sometimes observed. This behaviour is well reproduced by the numerical simulations. We provide insights on the flow dynamics in particular on the possible occurrence of wavebreaking. We show that the dynamics is characterized by two competitive mechanisms that is a damping of the wave and a local enhancement of its steepness leading sometimes to density overturns. The budget for the energy of the wave reveals that the initial damping of the wave results from wave-mean flow interactions. These interactions lead to the development of a fine scale vertical density structure which is associated with high vertical shear. We find that in some cases wavebreaking occurs as a result of shear instability. The value of the acceleration of the mean flow is very likely to influence the onset of the instability. The scaling laws of the wave evolution, in particular the rate of decrease of its energy, are determined. From these laws the lifetime of the wave is found as a function of the acceleration of the shear. It may be expected that, in the ocean, this development will result in the largest fluctuations derived from wave-flow interactions occurring where the mean flow in the wave direction is greatest. Waves travelling normal to a two-dimensional shear flow will be unchanged. Waves travelling parallel will be damped. This may have particular application at the continental shelf where flow, mainly parallel to the isobaths, will damp waves travelling along-slope, but allows waves travelling normal to the isobaths (e.g., directly across the shelf-break) to be transmitted without attenuation. Similar effects are expected for the evolution of a high frequency wave interacting with a lower frequency (e.g., near inertial) motion.     

Kinetic energy exchanges between the time scales of ENSO and the Pacific decadal oscillation

This paper examines the non-linear kinetic energy interactions of the atmospheric ENSO and decadal oscillations over the Pacific. The calculations are based on a 54-year dataset of tropospheric winds from NCEP reanalysis. We verify that the decadal oscillations have two dominant modes, corresponding well to the pentadecadal and bidecadal modes reported in the literature. Energy interactions involving the range of decadal oscillations and the range of ENSO oscillations are considered in the context of kinetic energy exchanges in the frequency domain. We quantify the relative amplitudes and spatial structures of the quadratic and triplet terms of the kinetic energy exchanges over the Pacific and conclude that quadratic interactions with the mean flow are the dominant term in the kinetic-to-kinetic energy exchanges. Additionally, we show that triplet interactions provide a non-trivial contribution to the total. The interactions between the range of decadal oscillations and the range of ENSO oscillations are found to be the strongest near the regions of maximum oscillation amplitude and of the maximum oscillation amplitude gradient. Due to their similar spatial structures, the two dominant ENSO modes and the bidecadal mode are found to interact in a resonant way. The interactions among the range of ENSO modes and the range of decadal modes are found to strengthen the ENSO modes in the equatorial, subtropical and midlatitude belts, and to weaken the decadal modes in all but the equatorial belt.     

环境流场对双涡相互作用的影响

本文在文献[1]的基础上,进一步应用正压无辐散模式就环境流场对双涡相互作用的影响进行了数值模拟研究。试验结果表明,环境流场对双涡的相互作用确有重要影响,它可以加剧双涡的气旋性互旋和促使其相互趋近.也可以抵销双涡间的互旋作用,并且还可使相距较近的两个涡旋重新分开。上述各种情况取决于双涡的相对位置及其与环境流场的不同配置。      

Tide,Wind, and River Forcing of the Surface Currents in the Fraser River Plume

A long-term record of surface currents from a high-frequency radar system, along with near-surface hydrographic transects, moored current meter records, and satellite imagery, are analyzed to determine the relative importance of river discharge, wind, and tides in driving the surface flow in the Fraser River plume. The observations show a great deal of oceanographic and instrumental variability. However, averaged quantities yielded robust results. The effect of river flow, which determines buoyancy and inertia near the river mouth, was found by taking a long-term average. The resulting flow field was dominated by a jet with two asymmetric gyres; the anticyclonic gyre to the north had flow speeds consistent with geostrophy. The mean flow speed near the river mouth was 14.3?cm?s^–1, while the flow further afield was 5?cm?s^–1 or less. Wind stress and surface currents were highly coherent in the subtidal frequency band. Northwesterly winds drive a surface flow to the southeast at speeds of nearly 30?cm?s^–1. Southeasterly winds drive a surface flow to the northwest at speeds reaching 20?cm?s^–1; however, there is more spatial variability in speed and direction relative to the northwesterly wind case. A harmonic analysis was used to extract the tidally driven flows. Ellipse parameters for the major tidal constituents varied considerably in both alignment and aspect ratio over the radar domain, in direct contrast to a barotropic model which predicted rectilinear flow along the Strait of Georgia. This is a result of water filling and draining the shallow mud flats north of the Fraser's main channel. The M₂ velocities at the surface were also weaker than their barotropic counterparts. However, the shallow water constituent MK₃ was enhanced at the surface and nearly as strong as the mean flow, implying that non-linear interactions are important to surface dynamics.     

平均流变化对波反馈的A-B混合方程理论及应用

从两层模式的基本方程出发,推导了描述平均流对波振幅反馈的A-B混合方程,并通过适当变换把混合方程转化为洛仑兹系统,用于研究平均流对边缘波扰动振幅增长的反馈机制,以及在中性廓线附近边缘波的稳定性问题。这是对研究波流相互作用的E-P通量理论的一个重要扩充。同时,作者还指出了A-B混合方程理论在研究大气中的波流相互作用及对流方面有相当应用前景。     

平均流变化对波反馈的A-B混合方程理论

从两层模式的基本方程出发，推导了描述平均流对波振幅反馈的A－B混合方程，并通过适当变换把混合方程转化为洛仑兹系统，用于研究平均流对边缘波扰动振幅增长的反馈机制，以及在中性廓线附近边缘波的稳定性问题。这是对研究波流相互作用的E-P通量理论的一个重要扩充。同时，作者还指出了A－B混合方程理论在研究大气中的波流相互作用及对流方面有相当应用前景。     

Boundary-layer flow and turbulence near porous obstacles

We derive a set of governing equations for flow through porous obstacles by employing a two-step averaging processes. The Navier-Stokes equations under the Boussinesq approximation that describe the air space of the porous obstacle are subjected to high-wavenumber a veraging, which leads to a set of high-frequency (wake) turbulence equations. We then use conventional Reynolds-averaging methods to obtain statistically steady mean and turbulence equations that include interactions between wake and shear turbulence. Our method provides a theoretical basis for the cascade of turbulent kinetic energy. We use this approach to analyze the constants and parameters of simpleK-theory and higher-order closure models. We also discuss qualitatively the theory of the turbulence energy generation process and the significance of interactions between different turbulent mechanisms.     

An analysis of the topographical effect on turbulence and diffusion in the atmosphere's boundary layer

An analysis of the wind data recorded at the fifteen stations in the Salt Lake Valley indicates that the distributions of the kinetic energy of the mean and turbulent motions in the valley are generally inhomogeneous and nonstationary. The mean motion in the valley, which is strongly affected by the mountain-valley winds, shows a southeasterly flow in the evening and early morning, a northwesterly flow in the afternoon, and a transitional flow in the late morning and after sunset. The mountain winds generally associate with a horizontally convergent flow, whereas the valley winds associate with a horizontally divergent flow. The distributions of the kinetic energy of the mean and turbulent motions show a maximum occurring in the central part of the valley and two minimums, one in the northern and one in the southern part of the valley. In the afternoon, both the mean and turbulent motions increase their intensities, particularly in the western part of the valley. An analysis of the dispersion characteristics indicates that the rate of diffusion in the valley changes with time and space, with a maximum occurring in the early afternoon and minimum in the early morning.     

Spectral features of the energy transfer between internal waves and a larger-scale shear flow

Internal waves propagating in a larger-scale shear flow slowly change their amplitudes and wavenumbers. For moderate shear flows the secular effect of these changes reduces to a diffusion of wave action in wavenumber space. The diffusion coefficients are derived under the assumption that relaxation processes exist within the internal wave field. Associated with the diffusion of wave action is an energy transfer between the mean flow and the wave field. The wavenumber—frequency dependence of this energy transfer is evaluated for the Garrett and Munk (1975) spectral model. For this spectrum the transfer shows a characteristic +—+ signature with a weak source of internal wave energy at near-inertial frequencies, a weak sink at medium frequencies, and a strong source at high frequencies. The integrated energy transfer is from the mean flow to the internal wave field.     

Influence of bottom topography roughness on the jet and inertial recirculation of a mid-latitude gyre

Several numerical experiments are conducted to examine the influence of mesoscale, bottom topography roughness on the inertial circulation of a wind-driven, mid-latitude ocean gyre. The ocean model is based on the quasi-geostrophic formulation, and is eddy-resolving as it features high vertical and horizontal resolutions (six layers and a 10 km grid). An antisymmetrical double-gyre wind stress curl forces the baroclinic modes and generates a strong surface jet. In the case of a flat bottom, inertia and inverse energy cascade force the barotropic mode, and the resulting circulation features strong, barotropic, inertial gyres. The sea-floor roughness inhibits the inertial circulation in the deep layers; the barotropic component of the flow is then forced by eddy-topography interactions, and its energy concentrates at the scales of the topography. As a result, the baroclinicity of the flow is intesified: the barotropic mode is reduced with regard to the baroclinic modes, and the bottom flow (constrained by the mesoscale sea-floor roughness) is decoupled from the surface flow (forced by the gyre-scale wind). Rectified, mesoscale bottom circulation induces an interfacial form stress at the thermocline, which enhances horizontal shear instability and opposes the eastward penetration of the jet. The mean jet is consequently shortened, but the instantaneous jet remains very turbulent, with meanders of large meridional extent. The sea-floor roughness modifies the energy pathways, and the eddies have an even more important role in the establishment of the mean circulation: below the thermocline, rectification processes are dominant, and eddies transfer energy toward permanent mesoscale circulations strongly correlated with topography, whereas above the thermocline mean flow and eddy generation are influenced by the mean bottom circulation through interfacial stress. The topography modifies the vorticity of the barotropic and highest baroclinic modes. Vorticity accumulates at the small topographic scales, and the vorticity content of the highest modes, which is very weak in the flat-bottom case, increases significantly. Few changes occur in surface-intensified modes. In the deep layers of the model, the inverse correlation between relative vorticity and topography at small scales ensures the homogenization of the potential vorticity, which mainly retains the largest scales of the bottom flow and the scale of β.     

AGEOSTROPHIC THEORY OF ZONAL FLOW ACCELERATION AND WAVE-ACTIVITY CONSERVATION LAW

Motivated by ageostrophic interactions of wave and basic flow,the generalized relationships between 3-dimensional Eliassen-Palm flux and basic flows,which are suitable for small-amplitude and finite-amplitude disturbances,are derived.The local area-averaged and density-weighted mean flows are chosen as the basic flows.Under the assumption that the steady basic flows vary slowly in time and space,a quasi-conservative law of small amplitude wave activity is derived from Ertel's potential vorticity equation in isentropic coordinates. The expressions of the new 3-D Eliassen-Palm flux and wave activity are presented in terms of Eulerian quantities so that they can be readily calculated by using observation data or model output data.     

Low-Order Point Vortex Models of Atmospheric Blocking

Summary Conceptual models of blocking structures are constructed by reducing the two-dimensional atmospheric vorticity field to a few point vortices. The flow is assumed to be barotropic and divergence-free, and a blocking event is represented by a point vortex dipole. The focus is here on the motion of the blocking dipole under the influence of the zonal mean flow. This is modelled in three different ways: A dipole embedded in a latitude-dependent zonal mean flow exhibits neutrally stable oscillations; their period is estimated analytically. A cyclonic point vortex approaching from upstream can either pass the dipole or break it up, so that an Ω-shaped pattern of three vortices emerges. The stationarity of a blocking between two troughs is modelled by four point vortices. These low-order point vortex models are compared with the dynamics of real blockings in case studies. Despite their high degree of simplification, those models reproduce the kinematics of blocking events properly. This results from the discretization of the flow to its actual physical states, the vortices, in contrast to the common, purely mathematical discretization to grid points. Thus, point vortex dynamics are proposed to be a powerful completion of continuous fluid dynamics in explaining blocking events. Received August 30, 1999 Revised December 22, 1999     

Effects of Turbulence and Flow Inclination on the Performance of Cup Anemometers in the Field

Four commercial and one research cup anemometers were comparatively tested in a complex terrain site to quantify the effects of turbulence and flow inclination on the wind speed measurements. The difference of the mean windspeed reading between the anemometers was as much as 2% for wind directions where the mean flow was horizontal. This difference was large enough to be attributed to the well-known overspeeding effect related to the differing distance constant (ranging from 1.7 to 5 m) of the cup anemometers. The application of a theoretical model of the cup-anemometer behaviour in athree-dimensional turbulent wind field proved successful in explaining theobserved differences.Additional measurements were taken with the anemometers tilted at known angles into and out of the incident wind flow. Thus, a field-derived angular response curve is constructed for each anemometer and the deviations from publishedwind-tunnel results are discussed.The uncertainties of, or false assumptions about, the angular response characteristics of the anemometers contribute the largest amount inthe observed errors of mean wind speed even for a horizontal mean flow. The angular response curves are finally used to correct the 10-min mean windspeed. The necessary information for the correction is the turbulent intensity (preferably in the vertical direction) and the mean flow inclination.For demanding applications, the angular response parameters of cup anemometers should be taken into account. The incorporation of the angular response parameters in a correction scheme would be most robustly applied if their variation with inclination and wind speed was smooth.     

东亚夏季两类阻塞高压维持的诊断分析

文章对两类东亚阻塞高压维持进行了诊断分析,结果表明:两类阻高的准地转位涡的平均流输送和瞬变扰动气流输送的分布是不同的,阻高维持机制也可能不同;两类阻高的瞬变扰动在分流区呈现南北向拉长,产生形变,对阻高维持有一致的作用;天气尺度扰动在东移过程中尺度缩小,当能量转化服从双向转化原则时,有大量扰动动能向平均场转化,使阻高维持。     

Model Study on the Interannual Variability of Asian Winter Monsoon and Its Influence

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INTERACTION OF TOPOGRAPHY WITH SOLITARY ROSSBY WAVES IN A NEAR-RESONANT FLOW

An inhomogeneous KdV equation including topographic forcing is derived by usingperturbation expansions and stretching transforms of time and space.The generation of forcedsolitary Rossby waves by topography in a near-resonant flow and their interactions with freesolitary waves are discussed,and some interesting results are obtained.The numerical resultsshow that the topography has obvious effect on enhancing the amplitude of disturbances,and itmay explain to some degree the formation of blocking by localized topography.     

Response of the Kuroshio Current to Eddies in the Luzon Strait

The impact of eddies on the Kuroshio Current in the Luzon Strait (LS) area is investigated by using the sea surface height anomaly (SSHA) satellite observation data and the sea surface height (SSH) assimilation data. The influence of the eddies on the mean current depends upon the type of eddies and their relative position. The mean current is enhanced (weakened) as the cyclonic (anticyclonic) eddy becomes slightly far from it, whereas it is weakened (enhanced) as the cyclonic (anticyclonic) eddy moves near or within the position of the mean current; this is explained as the eddy-induced meridional velocity and geostrophic flow relationship. The anticyclonic (cyclonic) eddy can increase (decrease) the mean meridional flow due to superimposition of the eddy-induced meridional flow when the eddy is within the region of the mean current. However, when the eddy is slightly far from the mean current region, the anticyclonic (cyclonic) eddy tends to decrease (increase) the zonal gradient of the SSH, which thus results in weakening (strengthening) of the mean current in the LS region.     

轴对称加热条件下圆盘实验中波的转变过程的初步分析

对于一控制在中心降冷、边缘加热的旋转圆盘内的流体,增加或减少其温差,可引起流体中波数的转变。本文对四波向三波及三波向四波的转变过程作了较详细的分析,发现在四波向三波转变时,平均经圈环流和西风强度均发生迅速的变化。维持四波时,平均经圈环流为靠近热源处下沉和靠近冷源处上升的反环流。当转变过程发生时,经圈环流转变成正环流,转换完成后则恢复成反环流。在经圈环流变化的同时,西风强度也发生由弱变强而后再由强变弱的转变。三波向四波转变时,经圈环流及西风强度没有上述变化,只有强度的不同。 根据热量输送的计算结果,波数不同,它所产生的热量的涡动输送也不一样,三波时热量的涡动输送较强,四波时热量的涡动输送较弱。最后,我们联系热量输送的特点对上述结果进行了初步的讨论。