Evolution of an isolated eddy near a coast and its relevance to the “Kyucho”

The evolution of an isolated meso-scale eddy near a coast is studied numerically. In particular, it is found that the translation speed of the adjusted eddy is estimated well by the mutual induction mechanism adapted to a rotating stratified fluid. The nonlinear Kelvin wave excited during the adjustment process is also discussed in connection with the Kyucho, the sudden warming of coastal waters associated with swift currents.     

A consideration on the mechanism of generation,stagnation and disappearance of the kuroshio Meander

A mechanism of the Kuroshio Meander is discussed by comparing some observed characteristics of the Kuroshio path with short- and long-term variations of the wind field over the North Pacific. It is suggested that the meander is caused by the blocking of the Kuroshio current by the Izu-Ogasawara Ridge. The blocking occurs when the depth of the main current increases or when the vertical shear becomes weak. These structural variations are closely related to the supposed baroclinic response of the North Pacific Subtropical Gyre to long-term variations of the wind field with a period of about 56 years. The Kuroshio Meander is initiated by a trigger meander at the offiing of Shikoku Island. The trigger meander is closely related to the supposed barotropic response of the gyre to short-term variations of the wind field with a period of about 34 months.The barotropic response of the North Pacific Subtropical Gyre to the short-term variation of the wind field yields the rapid change of the vertical structure of the Kuroshio current. This change generates the trigger meander in combination with the complicated pattern of the continental slope at the offing of Shikoku Island. The trigger meander is carried away toward the Izu-Ogasawara Ridge by the Kuroshio current. When the baroclinic response of the gyre is favourable for the blocking of the main current, the trigger meander and the cold eddy grow fed by the upwelling of the deep water of the Kuroshio which is blocked at the west of the ridge. The growing stops when the scale of the trigger meander reaches to the size of the steady Rossby wave which corresponds to the over-all mean velocity of the Kuroshio at that time, because the meander exceeding the size of the steady Rossby wave moves west-ward and separates from the ridge. Then the deep water of the Kuroshio at the west of the ridge which has been under the hard constraint of the cyclonic circulation in the form of the cold eddy becomes possible to flow arround the ridge. The upwelling stops and there remains only the general dissipation process of the available potential energy in the cold eddy. Then the meander gradually decreases its size and returns to the ridge when the meander becomes smaller than the steady Rossby wave at that time. It is blocked and begins to grow there again. In this way, the Kuroshio Meander behaves as a quasi-steady Rossby wave and stagnates at the west of the ridge until the baroclinic response of the gyre becomes unfavourable for the blocking of the Kuroshio current by the ridge.     

Rhines效应对高度计观测的海洋中尺度涡空间分布特征的影响

Rhines效应是指Rossby波和大湍流（中尺度涡）相互作用,将涡动能量以波的形式传播出去,从而使中尺度涡发生形变,最终消亡的一种动力学机制。本文通过比较海洋里涡特征速度和Rossby长波波速的方法,研究了一种广义的Rhines效应对高度计观测的海洋中尺度涡空间分布特征的影响。结果显示,广义Rhines效应比只考虑行星涡度梯度的传统形式对中尺度涡的分布具有更显著的影响。大部分中尺度涡分布在涡特征速度（U_e）大于由广义Beta值计算的Rossby长波波速（U_cg）的区域。这些涡可以由动能反向串级过程获取能量,成长为振幅和空间尺度较大的涡。热带海域以外的“涡旋沙漠”区域,中尺度涡的数量稀少,强度很弱,大都分布于U_ecg的海域。广义Rhines效应可能是这些海域中尺度涡难以成长的动力学机制。     

Rossby number dependence on meander dynamics of a potential vorticity front

Semi-geostrophic dynamics of jets are studied using a potential vorticity front in an equivalent barotropic model. Meandering processes of the front are examined in the thin-jet limit on a -plane by a curvilinear coordinate system. For calculated along-front velocity fields, asymmetrical profiles are caused by meandering. This asymmetry of the velocity profile is enhanced as the Rossby number becomes large. Using the along-front velocity fields, the normal velocity of front is expressed so that the Rossby number is explicitly included. This expression can be rewritten in the form of the mKdV equation.     

Calculation of Interannual Variations of Sea Level in the Subtropical North Pacific

The interannual variations of sea level at Chichi-jima and five other islands in the subtropical North Pacific are calculated for 1961–95 with a model of Rossby waves excited by wind. The Rossby-wave forcing is significant east of 140°E. Strong forcing of upwelling (downwelling) Rossby wave occurs during El Niño (La Niña) and warm (cold) water anomaly in the eastern equatorial Pacific. The first and second baroclinic modes of Rossby wave are more strongly generated than the barotropic mode in the study area. A higher vertical mode of Rossby wave propagates more slowly and is more decayed by eddy dissipation. The best coefficient of vertical eddy dissipation is determined by comparing the calculated sea level with observation. The variation in sea level at Chichi-jima is successfully calculated, in particular for the long-term change of the mean level between before and after 1986 with a rise in 1986 as well as the variations with periods of two to four years after 1980. It is concluded that variations of sea level at Chichi-jima are produced by wind-forced Rossby waves, the first baroclinic wave primarily and the barotropic wave secondly. The calculation for other islands is less successful. Degree of the success in calculation almost corresponds to a spatial difference in quantity of wind data, and seems to be determined by quality of wind data.     

An assessment of the fine-scale eddies in a high-resolution model of the shelf seas west of Great Britain

High-resolution (1.8 km) simulations of the shelf seas west of Great Britain with the Proudman Oceanographic Laboratory Coastal Ocean Modelling System (POLCOMS) demonstrate the formation of an intense field of baroclinic eddies in open stratified waters such as the Celtic Sea. These eddies are most likely to be the result of an inverse energy cascade resulting from tidal flow over rough topography, as demonstrated by a series of idealised model experiments. They are shown to possess many of the properties of eddies identified in idealised laboratory and numerical simulations. Namely, they are predominantly anticyclonic and they merge to increase their size up to a limit set by the internal Rossby radius. An investigation of satellite sea surface temperature observations provides indirect evidence that these model eddies are too energetic, long-lived and frequent. The inclusion of a horizontal diffusion term with a shear dependent diffusivity is shown to significantly reduce the eddy kinetic energy and improve the simulation, without significantly affecting the results in other regions. An optimal parameter value is suggested for this resolution, but the need to put the treatment of horizontal turbulence in such models on a sounder theoretical or empirical footing is identified.     

Study on the currents in Lake Biwa (II)

Some numerical experiments are made using a linear barotropic model of Lake Biwa to investigate the current induced by the spatially uniform wind stress. Concerning the phenomena whose time scale is longer than the inertial period, we integrate the non-divergent vorticity equation.It is found that the topographic curl of the wind stress which comes from the bottom topography and the wind stress induces circular currents and that the current, generated by the wind, attenuates gradually accompanying the topographic Rossby wave whose period is about 9 half-pendulum days in Lake Biwa. This mechanism of the barotropic response of the lake water to the wind will explain well the unsteady lake current in Lake Biwa in winter.     

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.     

Stability of a barotropic jet on a sloping bottom

Linear stability of a barotropic jet on a sloping bottom with and without a side boundary is examined. When a sloping bottom and a side boundary are absent, a symmetric jet generally has two unstable modes: a symmetric mode and an antisymmetric mode. In the presence of a sloping bottom or a side boundary, they are modified and lose their symmetry.The presence of a side boundary does not produce substantial change in the stability characteristics, except that it stabilizes the flow to some degree. In the presence of a sloping bottom, the following features are noted; 1) when the direction of the jet is opposite to the propagation direction of topographic Rossby waves, the change of a preferred mode occurs at a certain slope, 2) when the direction of the jet is opposite to 1), with a side boundary, the dispersion relations change from unstable mode type to shelf wave type at a certain slope, accompanied by kissing.     

A proof and applications of the expansion theorem for the Rossby normal modes in a closed rectangular basin

An expansion theorem is derived for Rossby normal modes in a closed rectangular basin and the set of Rossby normal modes is proved to be complete. This theorem provides a general linear solution to the initial value problem as well as to the response problem. In particular, the Green's function is obtained for the instantaneous localized torque anywhere in the basin. Weakly nonlinear versions are solved also by the combination of the general linear solution with the asymptotic expansion in terms of small amplitude. Further, an application is suggested to the spectral method of numerical simulation based on Rossby normal modes relevant to the more nonlinear evolution equation on a-plane, instead ofsin functions or Chebyshev polynomials, which have been employed conventionally for this purpose.     

On the instability of synoptic eddy movement in the ocean

The paper reports on the potential mechanism responsible for the instability of synoptic eddy movement which is coupled with eddy-generated Rossby waves. The variable part of the wave drag is calculated in a quasi-stationary approximation. It is shown that its action may be conductive to larger oscillating of the eddy.Translated by V. Puchkin     

Topographic effect of a marine ridge on the spin-down of a cyclonic eddy with mean flow

The topographic effect of a meridional marine ridge on the spin-down of a cyclonic eddy, which is embedded in a zonal mean flow, is examined by use of a two layer numerical model. It is shown that the cyclonic eddy initially given on the eastern flank of the marine ridge decays in a short time. This result is common to all cases with the different volume transports of the mean flow (3070 Sv) and of the cyclonic eddy (1535 Sv). During the decay process, the cyclonic eddy shifts mainly northward into the shallower region, which is different from the dominant westward shift of the isolated cyclonic eddy. If the mean flow across over the marine ridge at the more northern latitude, the cyclonic eddy spins down more rapidly. A mean flow shifts zonal or south-eastward over a western side of the ridge, while it deflects north-eastward over an eastern side. The deflection angle of mean flow over the ridge depends on the intensity of lower layer velocity and density stratification. It is suggested that the topographic effect of the meridional marine ridge on the cyclonic eddy with mean flow is influenced both by the global phenomena that controls the inclination of the mean flow from zonal direction and by the local phenomena that controls the intensity of the topographic effect of the marine ridge.     

Sequential updating assimilation of simulated Geosat altimeter data from mesoscale features into a two-layer quasi-geostrophic model

A sequential updating method for assimilating Geosat altimeter data into an eddyresolving, quasi-geostrophic model is examined using simulated data of mesoscale features taken from a control run solution. The upper-layer streamfunction in the model is updated by the altimeter data on satellite tracks (at 110 km intervals) at times of observations (with 17-day cycles). To evaluate data suitability, the correlation between the data and the assimilation solution just before update is compared with the correlation between the two data with a 1-cycle separation: i.e., predictability is compared with persistence. The assimilation method is tested on mesoscale features such as linear Rossby waves, unstable mesoscale meanders in a jet and dipole eddies over realistic deep ocean topography. The assimilation method is successful for reconstructing the mesoscale features that evolve gradually or extend over more than one track. Assimilation is degraded by quick evolution of smaller scale features; i.e the unstable meanders that have short wavelengths and are not well captured by the altimeter with the low cross-track resolution, and the mesoscale features, whose lower layer component receives effects of bottom topography in the data but is underestimated due to inefficient downward transfer of the surface data in the assimilation.     

How does the ocean response to the withdrawal of water from a watergate located at the eastern boundary on a beta-plane?

The formation of the spun up region by the withdrawal of water from a watergate located in the eastern boundary in a homogeneous ocean on a beta-plane at low Rossby number is presented. The spun up region penetrates only westward from the Watergate because of the special character of the generated Rossby waves. The growth rate and the final longitudinal length of the spun up region in the dissipative system is much affected by the watergate scale in the north-south direction.The relation with the experiment ofLong (1952) and the geophysical application are presented.     

Assimilation of simulated altimeter data in a two-layer linear Rossby wave model using the variational method

The variational assimilation method has been examined for ability of reconstructing mesoscale features in altimeter data using a simple dynamic model. A one-dimensional, two-layer Rossby wave model in a cross-track channel has been chosen. The simulated data are constructed from a theoretical solution, which is composed of any combination of two normal vertical (barotropic and baroclinic) modes. The data are collected along tracks and with repeat periods similar to those of the Geosat altimeter. The phase space of control variables is composed of initial and boundary conditions. A cost function is defined to measure differences between the simulated data and the model solution. Regularization (smoothing) terms are also included in the cost function in the form of secon-order spatial and time derivatives of the solution. In this paper, two potential problems existing in the altimeter data assimilation are addressed: one is low cross-track resolution, and the other is vertical projection of the data measured at the sea surface. A succesful metho is developed for reconstructing Rossby waves with wavelengths as short as twice the track intervals for any combination of two vertical modes. A key component to efficient assimilation is a preparation step prior to the actual variational assimilation: a uniform ratio of pressure amplitudes in the two layers is included as an optimization parameter. Starting with the first guess from the preparation step, the variational method is carried out based on adjoint equations without such constraint. Separation of the control variables into the two subsets of the initial and the boundary conditions is found useful. Characteristics of the Hessian matrix are related to the performance of this technique. The method developed for the linear system implies steps to be included in data assimilation for nonlinear meanders and eddies in a major current system as well.     

Geomorphology of a sand wave in lower Chesapeake Bay,Virginia, U.S.A.

Morphologic and sedimentologic studies of a single sand wave within a sand wave field in the lower Chesapeake Bay suggest that the bedform was originally formed by ebb currents, and is presently in static equilibrium with the circulation pattern. In this report, the concept of solitary sand wave is introduced to describe the state of a sand wave when further evolution of the sedimentary structure is mostly independent of adjacent bedforms. This concept can be applied to several bedforms in the area that are isolated from others by flats. A particular sand wave that is included in this category is discussed.Contribution number 79, Instituto Argentino de Oceanografia.     

Transmission and reflection of the Rossby waves in a stratified ocean with bottom topography

Transmission and reflection coefficients are calculated for Rossby waves incident on a bottom topography with constant slope in a continuously stratified ocean. The characteristics of the coefficients are interpreted in terms of the quasigeostrophic waves on the slope. In the parameter range where only the barotropic Rossby waves can propagate in the region outside the slope, the bottom trapped wave plays the same role as the topographic Rossby wave in a homogeneous ocean, and hence the transmission is weak unless phase matching takes place. When both of the barotropic and baroclinic Rossby waves can propagate outside the slope, the total transmission can be strong. The bottom trapped wave affects the transmission and reflection, and it leads to the possibility that the Rossby wave is transmitted as a mode different from the incident mode. When the number of the wavy modes on the slope is smaller than that of the Rossby wave modes outside the slope, strong reflection occurs.The results for an ocean with linear distribution of the squared Brunt-Väisälä frequency are compared to those in a uniformly stratified ocean. The weakening of the stratification near the bottom is almost equivalent to reducing the effect of the slope.     

On trajectories of Rossby wave-packets released in a lateral shear flow

The problem of reflexion and critical level absorption of barotropic non-divergent Rossby waves in a lateral shear flow is considered with a ray tracing method. The results are compared with those of a normal mode approach. Some oceanographical applications are suggested.     

Vertical structure variability in a seasonal simulation of a medium-resolution regional model of the Eastern South Pacific

A seasonal simulation from a medium-resolution ocean general circulation mode (OGCM) is used to investigate the vertical structure variability of the Southeast Pacific (SEP). The focus is on the extra-tropical Rossby wave (ETRW) variability and associated forcing mechanism. Some aspects of the model mean state are validated from available observations, which justifies a vertical mode decomposition of the model variability. The analysis of the baroclinic mode contributions to sea level indicates that the gravest mode is dominant over most of the domain at all frequencies. Annual variability is on average twice as large as the semi-annual variability which is confined near the coast for all the modes. The first baroclinic mode contribution to the annual cycle exhibits a clear westward propagation north of the critical latitude. The higher-order modes only contribute near the coast where they are associated with vertically propagating energy. The residual variability, which is the energy at all timescales other than annual and semi-annual periods peaks offshore between 20°S and 30°S for all baroclinic modes. The third baroclinic mode also exhibits a relative maximum variability off the coast of Peru south of the critical latitude of the annual cycle (13°S), where the Peru–Chile Undercurrent is the most intense. Sensitivity experiments to the atmospheric and boundary forcing suggest that the residual variability results from the non-linear interaction between annual Rossby waves and the mean flow, while the annual ETRWs in the model result from the summed-contribution from both the local wind stress and remote equatorial forcing. Overall the study extends the classical analysis of sea level variability in the SEP based on linear theory, and suggests that the peculiarities of the baroclinic modes need to be taken into account for interpreting the sea level variability and understanding its connection with the equatorial variability.     

Generation of a double Kelvin wave resulting from the reflection of the Rossby wave by the jump layer

This paper considers the evolution of a spatially-localized divergent Rossby wave field near the depth jump. If the jump magnitude is comparable to the depth, Rossby waves are fully reflected and a double Kelvin wave is then generated. The Rossby waves and the double Kelvin wave are described by the first- and zero-approximation fields of the asymptotic expansion, respectively. Over the characteristic Rossby wave period, the level elevation produced by the double Kelvin wave spreads over an extensive area, theraby making up for the change in the total fluid mass of the Rossby waves.Translated by Vladimir A. Puchkin.