Topographically forced three-wave quasi-esonant and non-resonant interactions among barotropic rossby waves on an infinnite beta-plane

In this paper, we first apply the assumption h = εh′ of topographic variation (h is the nondimensional topographic height and is a small parameter) to obtain nonlinear equations describing three-wave quasi-resonant and non-resonant interactions among Rossby waves for zonal wavenumbers 1—3 over a wavenumber-two bottom topography (WTBT). Some numerical calculations are made with the fourt-order Rung-Kutta Scheme. It is found that for the case without topographic forcing, the period of three-wave quasi-resonance (TWQR) is found to be independent of the zonal basic westerly wind, but dependent on the meridional wavenumber and the initial amplitudes. For the fixed initial data, when the frequency mismatch is smaller and the meridional wavelength is moderate, its period will belong to the 30–60-day period band. However, when the wavenumber-two topography is included, the periods of the forced quasi-resonant Rossby waves are also found to be strongly dependent on the setting of the zonal basic westerly wind. Under the same conditions, only when the zonal basic westerly wind reaches a moderate extent, intraseasonal oscillations in the 30–60-day period band can be found for zonal wavenumbers 1–3. On the other hand, if three Rossby waves considered have the same meridional wavenumber, three-wave non-resonant interaction over a WTBT can occur in this case. When the WTBT vanishes, the amplitudes of these Rossby waves are conserved. But in the presence of a WTBT, the three Rossby waves oscillate with the identical period. The period, over a moderate range of the zonal basic westerly wind, is in the intraseasonal, 30–60-Day range.     

正压准地转模式中大地形作用下的低频波

利用包含大地形和常速纬向基本气流的正压准地转位涡度方程,研究了大地形对低频波激发的作用,结果表明,起作用的地形因子主要是地形的最大高度和地形坡度。地形最大高度的作用主要是使Rossby波趋向低频,而地形坡度的作用主要是对Rossby波的稳定性起决定作用,同时适当的地形坡度也可导致低频波的形成。而常速纬向基流在总体上的作用是使波动变得趋向低频,且西风基流更有利于低频（30～60天）波的形成。从纬向波数上看,纬向3波以上的波动更容易出现低频（30～60天）。     

Dynamics of the Leeuwin Current: Part 2. Impacts of mixing,friction, and advection on a buoyancy-driven eastern boundary current over a shelf

The boundary currents over the Western Australian continental shelf and slope consist of the poleward flowing Leeuwin Current (LC) and the equatorward flowing Leeuwin Undercurrent (LUC). Key properties of the LC are its poleward strengthening, deepening to the south, and shelfbreak intensification. The alongshore flow reverses direction below about 300 m, forming the LUC at greater depths. To investigate the processes that cause these features, we obtain solutions to an idealized, regional ocean model of the South Indian Ocean. Solutions are forced by relaxing surface density to a prescribed, meridionally varying density profile ρ^*(y) with a timescale of δt. In addition, vertical diffusion is intensified near the ocean surface. This diffusion establishes the minimum thickness over which density is well-mixed. We define this thickness as the “upper layer”. Solutions are obtained with and without a continental shelf and slope off Western Australia and for a range of values of δt and mixing parameters. Within this upper layer, there is a meridional density gradient that balances a near-surface, eastward geostrophic flow. The eastward current downwells near the eastern boundary, leading to westward flow at depth. The upper layer's meridional structure and zonal currents crucially depend on coastal processes, including the presence of topography near the eastern boundary. Kelvin waves inhibit the upper layer from deepening at the coast. Rossby waves propagate the coastal density structure offshore, hence modifying the interior currents. A comparison of the solutions with or without a continental shelf and slope demonstrate that topographic trapping of Rossby waves is a necessary process for maintaining realistic eastern boundary current speeds. Significant poleward speeds occur only onshore of where the upper layer intersects the slope, that is, at a grounding line. Its poleward transport increases when surface-enhanced vertical mixing is applied over a greater depth. When the timescale δt is sufficiently short, the poleward current is nearly barotropic. The current's spatial structure over the shelf is controlled by horizontal mixing, having the structure of a Munk layer. Increasing vertical diffusion deepens the upper layer thickness and strengthens the alongshore current speed. Bottom drag leads to an offshore flow along the bottom, reducing the net onshore transport and weakening the current's poleward acceleration. When δt is long, poleward advection of buoyancy forms a density front near the shelf break, intensifying poleward speeds near the surface. With bottom drag, a bottom Ekman flow advects density offshore, shifting the jet core offshore of the shelf break. The resulting cross-shelf density gradient reverses the meridional current's direction at depth, leading to an equatorward undercurrent.     

Low—frequency waves forced by large—scale topography in the barotropic model

A barotropic model containing large-scale topography and zonal mean flow is established to discuss the effects of large-scale topography on the low-frequency waves. The results show that what affects low-frequency waves mostly is maximal height of topography and topographic slope. The former makes frequency of topographic Rossby waves decrease, the latter makes Rossby waves instable. Moreover, when topographic slope is appropriate, it can also make Rossby waves turn into low-frequency waves.     

正压模式中大地形作用下的低频波

利用包含大地形和常数纬向基本气流的正压模式方程组,研究了大地形对低频波激发的作用,结果表明：起作用的地形因子主要是地形的最大高度和地形坡度,地形最大高度的作用主要是使Ｒｏｓｓｂｙ波趋向低频,而地形坡度的作用主要是对Ｒｏｓｓｂｙ波的稳定性决定作用。同时,适当地形坡度也可导致低频波的形成。     

Some effects of truncation on topographic instability

Abstract

The topographic stability of forced planetary waves in α β‐channel is investigated using a barotropic model. The equilibrium forced waves are the result of the interaction of a constant mean zonal wind over finite‐amplitude surface orography. Small‐amplitude perturbations of the equilibrium flows are considered that have a wavy part with the same zonal wavenumber as the forcing but an arbitrary meridional structure. The mean zonal part of the perturbations is also taken to be arbitrary. This configuration allows us to (1) isolate those instabilities that depend crucially on topography through form drag and (2) investigate non‐topographic effects on topographic instability that arise from the convergence of Reynolds stresses. A numerical stability analysis is then performed wherein the effects of truncation are emphasized.

This numerical approach casts doubts about the results obtained from some earlier studies involving various ad hoc assumptions. We find, in particular, that unstable long waves (i.e. waves with the zonal wavelength greater than the meridional wavelength) exist under superresonant conditions. This contradicts some previous results that suggest long waves are unstable only when the flow is subresonant. Further, our model reveals the existence of some interesting travelling instabilities. The latter are shown to depend on both form drag and Reynolds stresses in that these two mechanisms alternate in time in supplying the perturbation with the required energy to maintain the exponential growth.     

瞬时经圈环流与西风带环流变化的关系

用一九七六年冬半年八个个例,对纬圈平均非热成风,瞬时经圈环流和西风带环流变化的关系进行了个例分析和统计分析。指出。当纬圈平均非热成风产生率为较大的负值时,出现逆瞬时经圈环流,并有利于长波的阻尼和纬向环流的维持或加强;反之,当为正值时,出现正瞬时经圈环流,并有利于长波的发展和纬向环流的减弱或崩溃。对于上述关系,本文还从物理上进行了初步的讨论。     

Meridional component of oceanic Rossby wave propagation

A three-dimensional spectral analysis of Topex altimeter data reveals a large meridional component k_y of the wavevector k for baroclinic Rossby waves of all timescales. Its existence necessitates some refinements in our estimates of certain basic properties of the Rossby wave field. In particular, by taking into account an actual off-zonal direction of k (often exceeding 70°), one finds that the wavelength, phase speed, and group velocity of mid-latitude Rossby waves (with periods less than 2 years) are much smaller than they appear to be on the assumption of a purely zonal wavenumber vector. Because of a shorter wavelength (yielding kL as high as 0.6, where L is the Rossby radius of deformation), these waves are essentially dispersive. Their group velocity vector may depart from zonal by more than 30°. An important intrinsic feature of the wave spectrum confirmed by our analysis is a broad-band distribution with respect to k_y. Some of the dynamical implications of the large k_y/k_x ratio are discussed.     

切变基本纬向流中赤道Rossby包络孤立波

利用多重尺度摄动法，从描写赤道Rossby波的正压大气位涡度方程中推导出在切变基本纬向流中非线性赤道Rossby波包演变所满足的非线性Schrodinger方程，并得到其单个包络孤立子波解，分析基本流切变对非线性赤道Rossby波动的影响。     

A fluid experiment of large-scale topography effect on baroclinic wave flows

The effects of topography on baroclinic wave flows are studied experimentally in a thermally driven rotating annulus of fluid.Fourier analysis and complex principal component (CPC) analysis of the experimental data show that, due to topographic forcing, the flow is bimodal rather than a single mode. Under suitable imposed experimental parameters, near thermal Rossby number ROT = 0.1 and Taylor number Ta = 2.2 × 107, the large-scale topography produces low-frequency oscillation in the flow and rather long-lived flow pattern resembling blocking in the atmospheric cir-culation. The ‘blocking’ phenomenon is caused by the resonance of travelling waves and the quasi-stationary waves forced by topography.The large-scale topography transforms wavenumber-homogeneous flows into wavenumber-dispersed flows, and the dispersed flows possess lower wavenumbers.     

The domain of validity of the KdV-type solitary rossby waves in the shallow water β-plane model

The Domain, where the necessary and sufficient conditions for the existence of the KdV-type solitary Rossby waves are satisfied is defined in the shallow water β-plane model. The KdV-type solitary Rossby waves are the Rossby waves whose time-longitude dependence is determined by the KdV equation. As far as an appropriate amplitude and an appropriate ratio of the scales of the east-west and north-south directions are given, the KdV-type solitary Rossby waves can exist for every basic zonal flow. This result suggests the large validity of the soliton model in geophysical fluid dynamics. The KdV-type solitary Rossby waves are classified into four categories: (1) shear solitons studied by Long, Larsen, Benny, Redekop, and Hukuda, (2) β-divergent solitons studied by Clarke, Yamagata, and Nogami, (3) β-solitons found in the case of the strong stratification, and (4) divergent solitons which exist in the planetary-geostrophic-scale zonal flow. A remarkable result is that, in addition to the conventional east-west elongated solitons, the north-south elongated solitons can also exist for the case of the divergent solitons.     

青藏高原热力作用下的非绝热Rossby波

从含非绝热项的准地转运动方程组出发，分析了青藏高原大尺度热力作用下非绝热Rossby波的一些性质，从理论上证明当背景西风气流为正压时，冬季高原冷却作用有利于Rossby波的经向传播，夏季高原大尺度热力作用不利于波动的经向传播。非绝热Rossby波的频率方程说明冬季高原的热力作用是中纬季节内振荡的重要激发机制。同时，在背景西风气流为纯斜压条件下，求解了高原热力作用下非绝热Rossby波的频率，并由频率方程说明冬季高原热力作用有利于波动向不稳定方向发展，而夏季高原的大尺度热力作用对波动稳定性的影响存在临界值。     

初始扰动垂直结构对热带斜压大气半地转适应过程的影响

文中利用一个半位势涡度时间不变式对热带斜压大气地转适应过程中的尺度准则进行了研究。结果表明 :对深厚系统而言 ,只要初始扰动的纬圈特征尺度足够大 ,则不论其初始扰动的经圈特征尺度多大 ,适应后的压力场的变化都很大 ,而纬圈流几乎维持不变 ,压力场向纬圈流适应 ;至于浅薄系统 ,对纬圈和经圈特征尺度都很大的初始扰动而言 ,适应后的压力场易于维持 ,主要是纬圈流向压力场适应 ;但当初始扰动呈现出纬圈型扰动特征时 ,适应后的压力场变化也很大 ,压力场向纬圈流适应     

On the low-frequency,planetary-scale motion in the tropical atmosphere and oceans

Scale analyses for long wave, zonal ultralong wave (with zonal scale of disturbance L1~104 km and meridional scale L2~103 km) and meridional ultralong wave (L1~103 km, L2~104 km) are carried out and a set of approximate equations suitable for the study of these waves in a dry tropical atmosphere is obtained. Under the condition of sheared basic current, frequency analyses for the equations are carried out. It is found that Rossby waves and gravity waves may be separated for n ≥ l where n is the meridional wave number, whereas for n = 0 and L1~1000 km, the mixed Rossby-gravity wave will appear. Hence it is confirmed that the above results of scale analyses are correct. The consistency be-tween frequency analysis and scale analysis is established.The effect of shear of basic current on the equatorial waves is to change their frequencies and phase velocities and hence their group velocities. It increases the velocity of westward travelling Rossby waves and inertia-gravity and mixed waves, but decelerates the eastward inertia-gravity waves and the Kelvin wave. The recently observed low-frequency equatorial ocean wave may be interpreted as an eastward Kelvin wave in a basic current with shear.     

THE EFFECTS OF THE PLATEAU'S TOPOGRAPHIC GRADIENT ON ROSSBY WAVES AND ITS NUMERICAL SIMULATION

By using barotropic model equations, this article analyzed the characteristics of Rossby waves, the propagation features of wave energy and the influence of dynamic and thermal effects of the Tibetan Plateau on Rossby waves, and the focus is on discussing the plateau's topographic gradient effects on atmospheric Rossby waves. Then based on the WRF3.2 and the NCEP/NCAR FNL reanalysis data, we devised comparative tests of changing the plateau's topographic gradient and simulated a process of persistent heavy rain that happened in May 2010 in South China. The results are shown as follows. The Tibetan Plateau’s topography is conducive to the formation of atmospheric Rossby waves. while the plateau's terrain, its friction and heating effects can all make the atmospheric Rossby waves develop into the planetary waves; The effects of plateau's north and south slopes on the Rossby wave’ phase velocity is opposite, and when the slope reached a certain value can the quasi-steady normal fluctuations be generated; Simultaneously, due to the plateau's topographic gradient, descending motion appears at the west side of the plateau while ascending motion appears at the east side, and the vertical movement increased with the amplification of topographic gradients. The plateau's topographic gradient also obviously amplified the precipitation in South China, and the rainfall area increased with the amplification of topographic gradients and gradually moved from south to north and from west to east, which is conducive to the occurrence and development of convective activities in the downstream areas of the Tibetan Plateau; Moreover, for the plateau’s dynamic and thermal effects, the Rossby wave’ propagation shows upstream effects of energy dispersion, so the plateau can then affect the weather in downstream areas. Moreover, the wave group velocity increased with the degree of topographic slope.     

The global energy cycle of stationary and transient atmospheric waves: Results from ECMWF analyses

Summary The role of stationary (monthly mean) and transient (departure from monthly mean) waves within the atmospheric energy cycle is examined using global analyses from the European Centre for Medium Range Weather Forecasts (ECMWF) for the period 1980–1987. Only January and July averages are considered.It is confirmed that planetary stationary waves are basically baroclinic. Their contribution to the globally averaged energy cycle of the atmosphere is comparable to that of the transient waves. In January they contribute about 40% to the baroclinic conversion (CA) from zonal mean to eddy available potential energy. Local values for the northern hemisphere even show a predominant role of the stationary wave conversions over those originating from transient waves. Part of the available potential energy of stationary waves (A _SE) is converted to kinetic energy by warm air rising and cold air sinking. Nonlinear energy conversion, which can be interpreted as destruction of stationary temperature waves by transients, is the second sink forA _SE. The order of magnitude of these two processes is similar.Barotropic nonlinear conversions, though negligible in the global average, reveal large conversion rates between the mean positions of the polar and the subtropical jets. Their orientation is suggestive of a tendency to increase stationary wave kinetic energyK _SE at its local minimum between the jets at the expense of the synoptic scale transients.While all terms of the energy cycle related to stationary waves reveal a predominance of the planetary scale (zonal wave numbers 1–3) transient waves are governed by synoptic scale waves (zonal wave numbers 4–9) only with respect to the baroclinic and barotropic conversions: a significant amount of transient wave energy (50% for the global average ofA _TE) is due to planetary scale waves.With 15 Figures     

Planetary geostrophic equations for the atmosphere with evolution of the barotropic flow

Atmospheric phenomena such as the quasi-stationary Rossby waves, teleconnection patterns, ultralong persistent blockings and the polar/subtropical jet are characterized by planetary spatial scales, i.e. scales of the order of the earth’s radius. This motivates our interest in the relevant physical processes acting on the planetary scales. Using an asymptotic approach, we systematically derive reduced model equations valid for atmospheric motions with planetary spatial scales and a temporal scale of the order of about 1 week. We assume variations of the background potential temperature comparable in magnitude with those adopted in the classical quasi-geostrophic theory. At leading order, the resulting equations include the planetary geostrophic balance. In order to apply these equations to the atmosphere, one has to prescribe a closure for the vertically averaged pressure. We present an evolution equation for this component of the pressure which was derived in a systematic way from the asymptotic analysis. Relative to the prognostic closures adopted in existing reduced-complexity planetary models, this new dynamical closure may provide for more realistic increased large-scale, long-time variability in future implementations.     

地形强迫对大气长波调整的可能影响

地形作为大气的外部强迫,其动力和热力作用对波动结构演变及极端天气出现都有不能忽视的作用。本文通过数值求解考虑地形强迫的β平面正压准地转位势涡度方程,探讨了地形强迫作用对大气长波调整的可能影响,结果表明:同非线性作用和纬向非均匀基流作用一样,无基流情形下具有纬向差异的地形分布影响了大气长波结构的演变,也能强迫出大气长波调整现象。大气长波调整依赖于地形的高度和地形分布,地形越高,长波越容易出现波数的调整;地形波数越大,即地形结构复杂,越不易出现波数变化。大气长波调整还与纬度有关,纬度越高,β越小,地形强迫作用越突出,长波调整容易出现;反之,低纬度以β效应为主的线性波动不易出现波数调整。大气长波调整对波动初始波动的振幅不敏感,但依赖于波动的初始结构。此外,有基流作用时,地形强迫还是诱发定常波的重要因素,且定常波流场结构依赖于地形高度分布,与波动初始结构无关。     

The exchange of fluid mass between quasi-geostrophic and ageostrophic motions during the reflection of Rossby waves from a coast. I. The case of an infinite rectilinear coast

When the problem of the reflection of spatially localized Rossby waves from a coast is treated using the quasigeostrophic (QG) approximation, the total fluid mass and the along-shore circulation calculated from the geostrophic height field are not conserved. To understand the correct mass balance and the degree to which the QG equations and boundary conditions may be in error, we analyze an initial-value problem for the Laplace tidal equations on a β-plane in the asymptotic limit 1, where is the ratio of the spatial scale of the motion to the Earth's radius.It is shown that there is a coupling between QG and O() fields. Physically, the coupling occurs by a peculiar adjustment process in the O() approximation in which fast gravity waves are permanently generated to build up a quasi-stationary edge Kelvin wave. Different temporal scales (large for O(1) Rossby waves and small for the O() gravity waves make comparable the contributions of the waves to the mass and circulation balance equations. However, QG analysis itself describes the reflection of Rossby waves correctly, but is incomplete, and for satisfactory balances one has to take into account the fields of both orders of the approximation.Applications of the results to closed basins, baroclinicity, and variable bottom topography are discussed. It is conjectured that an interaction of strong oceanic eddies with a coast (continental slope) may give rise to noticeable along-shore jet currents.     

四川地形扰动对降水分布影响

引入一维加权平均的谱分析方法定量研究四川地形强迫对该区域降水分布的影响。结果表明:纬向地形和冬季降水谱峰锁相于同一波长（475.8 km）,呈共振关系,地形与其他季节降水呈漂移关系,这与经向和纬向上环流变动有关,即冬季纬向环流占主导,纬向地形触发的大气波动对冬季降水策动作用大;夏季降水是各种不同尺度系统相互作用的结果,地形是重要因素之一。经向和纬向地形特征尺度分别为296.8 km和475.8 km,反映了地形强迫的中尺度特征,且纬向地形谱峰比经向大1个数量级,纬向强迫更明显。夏季降水谱峰比冬季大2个数量级,降水系统纬向特征尺度比冬季小约150 km,说明夏季在纬向地形强迫下,降水系统尺度减小的同时其强度大大增加,这在一定程度上可以解释中尺度对流性降水在夏季偏多。四川夏季最大降水位于雅安地区,其地形扰动比四川整体扰动更明显,故产生的降水也更大。夏季降水和经向地形锁相于同一波长（37.1 km）,经向地形对雅安夏季强降水起关键作用。