Group velocity and energy transport by Rossby waves

A variational method gives a proof that, for normal modes of Rossby waves in the ocean on a-plane with depth variable in the meridional direction, the time average of the energy flux defined as the product of the pressure and the fluid-particle velocity agrees with the time average of the energy density multiplied by the group velocity. This conclusion holds in considerably general situations and sheds light on the controversial problem of the energy transport by Rossby waves. Moreover, the variational method gives a remarkable relation between the group velocity and the phase velocity. In particular this relation shows that the absolute value of the group velocity never exceeds that of the phase velocity.     

Oceanic Rossby waves induced by the meridional shift of the ITCZ in association with ENSO events

This study investigated the eastern Pacific Intertropical Convergence Zone (ITCZ) as an atmospheric forcing to the ocean by using various observed and reanalysis data sets over 29 years. Climatologically, a zonal band of positive wind stress curl (WSC) with a 10° meridional width was exhibited along the ITCZ. A southward shift of the positive WSC band during the El Niño phase induced a negative (positive) WSC anomaly along the northern (southern) portion of the ITCZ, and vice versa during the La Niña phase. This meridional dipole accounted for more than 25 % of interannual variances of the WSC anomalies (WSCAs), based on analysis of the period 1993–2008. The negative (positive) WSCA in the northern portion of the ITCZ during the El Niño (La Niña) phase was collocated with a positive (negative) sea surface height anomaly (SSHA) that propagated westward as a Rossby wave all the way to the western North Pacific. This finding indicates that this off-equatorial Rossby wave is induced by the WSCA around the ITCZ. Our analysis of a 1.5-layer reduced gravity model revealed that the Rossby waves are mostly explained by wind stress forcing, rather than by reflection of an equatorial Kelvin wave on the eastern coastal boundary. The off-equatorial Rossby wave had the same SSHA polarity as the equatorial Kelvin wave, and generation of a phase-preserving Rossby wave without the Kelvin wave reflection was explained by meridional movement of the ITCZ. Thus, the ITCZ acts as an atmospheric bridge that connects the equatorial and off-equatorial oceanic waves.     

Observations of Rossby waves near site D1

A theory of Rossby waves makes a number of predictions about motions below the thermocline at Site D (39°10'N, 70°W). An experiment was made to test these predictions. Kinetic energy spectra show most of the energy is associated with periods of a week to a few months. The Reynolds' stress is negative for these periods. There is high coherence and on phase shift between 1000 m and 2000 m depths. Most of the wave-number estimates point to the south-west quadrant, consistent with westward propagation and with momentum flux into the Gulf Stream and energy flux out of it. There is enough consistency between statistics based on successive 8-month records to conclude that statistics based on a single 8-month record near Site D are meaningful. In an 8-month array of twenty-six current meters, for periods of a week to a month, the divergence is small compared to the vorticity, and the motion is transverse. The energy increases toward the bottom. The observed wave-numbers and frequencies fit the theoretical dispersion relationship satisfactorily. The kinetic energy of the fluctuations is much larger near the Gulf Stream than farther upslope. The vorticity is in quadrature with the upslope velocity. I conclude there is strong evidence that topographic Rossby wave mechanics are dominant below the thermocline on the continental rise north of the Gulf Stream.     

Topographic Rossby waves in the Gulf of Mexico

Observations of topographic Rossby waves (TRW), using moored current meters, bottom pressure gauges, and Lagrangian RAFOS floats, are investigated for the deep basin of the Gulf of Mexico. Recent extensive measurement programs in many parts of the deep gulf, which were inspired by oil and gas industry explorations into ever deeper water, allow more comprehensive analyses of the propagation and dissipation of these deep planetary waves. The Gulf of Mexico circulation can be divided into two layers with the ∼800-1200 m upper layer being dominated by the Loop Current (LC) pulsations and shedding of large (diameters ∼300-400 km) anticyclonic eddies in the east, and the translation of these LC eddies across the basin to the west. These processes spawn smaller eddies of both signs through instabilities, and interactions with topography and other eddies to produce energetic surface layer flows that have a rich spectrum of orbit periods and diameters. In contrast, current variability below 1000 m often has the characteristics of TRWs, with periods ranging from ∼10-100 days and wavelengths of ∼50-200 km, showing almost depth-independent or slightly bottom intensified currents through the weakly stratified lower water column. These fluctuations are largely uncorrelated with simultaneous upper-layer eddy flows. TRWs must be generated through energy transfer from the upper-layer eddies to the lower layer by potential vorticity adjustments to changing depths of the bottom and the interface between the layers. Therefore, the LC and LC eddies are prime candidates as has been suggested by some model studies. Model simulations have also indicated that deep lower-layer eddies may be generated by the LC and LC eddy shedding processes.In the eastern gulf, the highest observed lower-layer kinetic energy was north of the Campeche Bank under the LC in a region that models have identified as having strong baroclinic instabilities. Part of the 60-day TRW signal propagates towards the Sigsbee Escarpment (a steep slope at the base of the northern continental slope), and the rest into the southern part of the eastern basin. Higher energy is observed along the escarpment between 89°W and 92°W than either under the northern part of the LC or further south in the deep basin, because of radiating TRWs from the western side of the LC. In the northern part of the LC, evidence was found in the observations that 20-30-day TRWs were connected with the upper layer through coherent signals of relative vorticity. The ∼90° phase lead of the lower over the upper-layer relative vorticity was consistent with baroclinic instability. Along the Sigsbee Escarpment, the TRWs are refracted and reflected so that little energy reaches the lower continental slope and a substantial mean flow is generated above the steepest part of the escarpment. RAFOS float tracks show that this mean flow continues along the escarpment to the west and into Mexican waters. This seems to be a principal pathway for deepwater parcels to be transported westward. Away from the slope RAFOS floats tend to oscillate in the same general area as if primarily responding to the deep wave field. Little evidence of westward translating lower-layer eddies was found in both the float tracks and the moored currents. In the western gulf, the highest deep energy levels are much less than in the central gulf, and are found seaward of the base of the slope. Otherwise, the situation is similar with TRWs propagating towards the slope, probably generated by the local upper-layer complex eddy field, being reflected and forcing a southward mean flow along the base of the Mexican slope. Amplitudes of the lower-layer fluctuations decay from the northwest corner towards the south.     

Stationary Rossby waves and shocks on the Sverdrup coordinate

Gyre-scale frontal structures, e.g., the Subtropical Front, have been well documented in the oceans. Although the generation mechanism of such a front remains unclear, it may be ascribed to the steepening of nonlinear planetary waves as discussed by Dewar (1992). To discuss the stationary wave characteristics and their shock formation in a two-layer wind-driven gyre, the present paper introduces a new coordinate, referred to as theSverdrup coordinate here, in which the Sverdrup function is used instead of the longitudinal coordinate, and especially, investigates the possibility of the frontgenesis caused by the Rossby waves emanating from the western boundary region. On theSverdrup coordinate, since the advection by the Sverdrup flow is in the direction normal to that of the Rossby wave propagation, the system becomes much simpler than that on the (x,y)-coordinate, and the solution to this coordinate does not explicitly depend on the distribution of the Ekman pumping, i.e., we can treat cases, in which the Ekman pumping is a function of bothx andy, in a similar way to the case with zonally uniform Ekman pumping.     

A conservative leapfrog time stepping method

This paper addresses the issue of the non conservation of tracer that occurs when a leapfrog time stepping scheme is used in association with a Robert-Asselin time filter within the framework of a time varying vertical coordinate system. A re-formulation of both the forcing and filtering terms that provides a globally conservative scheme is presented. Local conservation is then achieved when the model levels and subsequently the sea surface height satisfy a local compatibility condition. The properties of the resulting scheme are illustrated by a global coupled ocean–sea ice model based on the Nucleus for European Modelling of the Ocean (NEMO).     

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.     

On diapycnal mixing induced by internal tidal waves in the Arctic Ocean

In order to reproduce the diapycnal mixing induced by internal tidal waves (ITWs) in the Arctic Ocean, we use a modified version of the three-dimensional finite-element hydrothermodynamic model QUODDY-4. We found that the average (over the tidal cycle) and integral (by depth) baroclinic tidal energy dissipation rate in individual areas of the Siberian continental shelf and in the straits between the Canadian Arctic archipelago are much higher than in the open ocean and its values on ridges and troughs are qualitatively similar to one another. Moreover, in the area of open-ocean ridges, the baroclinic tidal energy dissipation rate increases as it approaches the bottom, but only in the bottom boundary layer; on the Mid-Atlantic and Hawaii ridges, such an increase is observed within a few hundreds of meters away from the bottom. The average (in area and depth of the open ocean) coefficient of diapycnal mixing defined by the baroclinic tidal energy dissipation rate is higher than the coefficient of molecular kinematic viscosity and only a few times lower than the canonical value of the coefficient of vertical turbulent viscosity, which is used in models of global oceanic circulation. Coupled with the reasoning on the localization of baroclinic tidal energy dissipation, this fact leads to the conclusion that disregarding the contribution that ITW-induced diapycnal mixing makes to the ocean-climate formation is hardly justified.     

On nonlinear sea waves and the induced mean flow

The nonlinear modulation of water wave groups is investigated and the interaction equations with induced flows are obtained. The analysis is performed up to the third order of the wave steepness a by treating it as a small parameter in the singular perturbation technique by means of the Krylov-Bogoliubov-Mitropolski method. The equation which governs the development of the wave envelope is found by a modification of the ordinary nonlinear Schroedinger equation for the case of uniform depth. The equations governing the behavior of the induced mean flow are examined by deriving the second order flow when the form of the modulated wave train is prescribed. The present theory can describe the mean flow caused by the radiation stress. Some applications containing the monochromatic wave instability are given to confirm the theoretical results.An outline of this paper was presented at The Ocean Surface Symposium (Sendai, 1984).     

Transmission and reflection of planetary and topographic Rossby waves in a two-layer ocean

Transmission and reflection problems when kissing≓ occurs among planetary and topographic Rossby waves in a two-layer ocean are studied. The slope parameterS(=dh ₂/dx, whereh ₂is the thickness of the lower layer) is assumed to have constant values in the regionsx 0 andxL and to vary linearly with the increase ofx in the region0xL (refer to Fig. 2 in the text). Furthermore, a wave is entered fromx=– and kissing is assumed to occur in the region (0<)x _axx_b(<L).It is found that a wave of the same type as the incident wave is mainly transmitted when the width of the region in which kissing occurs,L _kiss(=tx _b–x_a), is smaller than _kiss=2/(¦K¦+ _y/2), whereK is a representative wavenumber in the regionx _ab, _y is they-component of , and is the frequency. WhenL _kiss is larger than _kiss, on the other hand, the main wave transmitted is of a different type to the incident wave. As an application, transmission and reflection problems of planetary Rossby waves are considered, and it is shown that when an external (internal) planetary Rossby wave is entered, an internal (external) one can be transmitted due to the effect of kissing.     

Spectral characteristics of Rossby waves in the Northwestern Pacific based on satellite altimetry

Using satellite altimetry measurement data for 1993–2013, we study the spectral characteristics of Rossby waves in the Northwestern Pacific (25°–50° N, 140°–180° E). For each latitude degree, we draw integral plots of spectral power density calculated with a two-dimensional Fourier transform (2D-FFT). We compare the dispersion equations of Rossby waves calculated from the WKB-approximation and an approximation of a two-layer ocean model with the empirical velocities determined by the slope of isopleths by the Radon method; also, we compare the dispersion equations with the spectral distributions of level variations. It is shown that the main energy of Rossby waves in the Northwestern Pacific corresponds to the first baroclinic mode. At almost all latitudes, there is good agreement between the empirical phase velocities calculated by isopleths by the Radon method and the theoretical values; also, the spectral peaks correspond to graphs of the dispersion equations for the first baroclinic mode Rossby waves, except for the Kuroshio region, where some peaks correspond to the second mode.     

Water waves induced by a fluctuating tangential stress

In the framework of linear wave theory both the effects of tangential and normal stresses on the water waves are discussed without the assumption of irrotational water motion. A formal solution initially at rest with level surface and developed under the actions of the surface stresses depending arbitrarily on time and sinusoidally on space is obtained.A progressive wave type tangential stress whose wave number and frequency are satisfying the dispersion relation of the water waves is shown to be equivalent to the normal stress of the same type on the growth of the waves except the phase relations between the stresses and the water motion. The growth rate of the waves induced by the tangential stress is also shown to be quite insensitive to the actual value of the viscosity.The rotational part of the water motion can dominate only in the early stage of wave generation and becomes negligible with the growth of the waves relative to the irrotational part of the motion even in the case where the motion is induced by the tangential stress alone. Therefore it is not reasonable to neglect effect of the tangential stress on wind waves even if the developed wind waves seem to be irrotational.     

Harbor resonance induced by subaerial landslide-generated impact waves

Past studies of harbor resonance have mainly been restricted to the quasi-steady oscillations induced by steady wave conditions. This paper investigates the response of a rectangular harbor to subaerial landslide-generated impact waves based on physical models, in order to compare the oscillations induced by steady and transient waves. In response to steady incident waves, oscillations within the harbor need to experience a long process to obtain their maximum value before the input energy and the losses are balanced. Landslide-generated impact waves usually include components with solitary wave characteristics and also components with dispersive wave characteristics. Each component travels with a different celerity. Usually, solitary wave components propagate faster, and arrive in the harbor first. Oscillations attain their maximum status as soon as these components arrive. The subsequently arriving components with dispersive characteristics do not enhance the resonance oscillations. So the waves with solitary characteristics are considered to play an important role in harbor resonance. Numerical experiments, using the FUNWAVE model, were conducted in order to further verify these conclusions.     

ENSO to multi-decadal time scale changes in East Australian Current transports and Fort Denison sea level: Oceanic Rossby waves as the connecting mechanism

The connection between East Australian Current (EAC) transport variability and Australia’s east coast sea level has received little treatment in the literature. This is due in part to the complex interacting physical processes operating in the coastal zone combined with the sparsity of observations available to improve our understanding of these possible connections. This study demonstrates a statistically significant (at the >90% level) relationship between interannual to decadal time scale variations in observed estimates of the EAC transport changes and east coast sea level measured at the high-quality, long record Fort Denison tide-gauge in Sydney Harbour, Australia (33°51′18″S, 151°13′32″E). We further demonstrate, using a linear reduced-gravity ocean model, that ENSO to decadal time-scale variations and the ocean-adjusted multi-decadal trend (approx. 1 cm/decade) in observed sea level at Fort Denison are strongly connected to modulations of EAC transports by incoming westward propagating oceanic Rossby waves. We show that EAC transport and Fort Denison sea level vary in a manner expected from both Tasman Sea generated Rossby waves, which account for the interannual and multi-annual variability, and remotely forced (from east of New Zealand) Rossby wave connections through the mid-latitudes, accounting for the ocean-adjusted multi-decadal trend observed at the New South Wales coast - with the regional-Tasman Sea forcing explaining the greatest overall proportion of EAC transport and sea-level variances.     

Elementary properties of internal Rossby waves in a two-layer ocean with a uniform current

The elementary properties of internal Rossby waves in a horizontally infinite two-layer ocean with a uniform east-west current, apparently not previously reported in the literature, are documented.     

随机波浪下泰勒离散系数的时域解

利用Wolk提出的粒子追踪方程,通过等分频率法划分不规则波谱,利用MATLAB做粒子运动模拟计算,得到无因次化泰勒离散系数K/D随时间t变化的曲线;通过与Huang等得到的P-M谱的泰勒离散系数K/D计算结果比较证明了本计算方法的可靠性。采用该方法研究了不规则波条件下,波序列(同一谱型不同波面序列)和谱型(谱峰周期、有效波高、谱峰升高因子)对波浪离散系数的影响;计算结果表明:同一谱型不同波序列对泰勒纵向离散系数稳定值和稳定时间无影响;不规则波谱峰周期越大,纵向离散系数K/D越小,稳定时间越短;有效波高越大,纵向离散系数K/D越大,稳定时间越长;谱峰升高因子越大,泰勒离散系数K/D越大,稳定时间越长;与规则波相比,不规则波的泰勒离散系数K/D的值略小10%~30%。