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.     

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.     

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.     

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.     

Monitoring of the large-scale dynamics of the ocean based on the assimilation of satellite data

An examle of satellite monitoring of the large-scale dynamics of the eastern sector of the tropical Atlantic Ocean in April 1990 is considered. As the satellite-derived data, a series of averaged 5-day maps of the remote data on the upper ocean temperature field obtained from satellites of the NOAA series was used. The profundity of the effect of the satellite data is estimated. Recommendations are provided. for selecting the regions most appropriate for rapid analysis of the circulation using satellite data.Translated by Mikhail M. Trufanov.     

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.     

Coupling of ocean bottom seismometers to soft bottom

Unlike response of seismometers resting on hard rock where the seismometer case moves with the rock to high frequencies, the response of ocean bottom seismometers (OBS) can be strongly affected by the low mechanical strength of ocean sediments. The motion as measured by the seismometer will not follow the expected relationships between pressure and particle motion for different wave types. Cross coupling between horizontal and vertical motions can occur, especially when there is differential motion between water and sediment. Resonant amplification and attenuation of higher frequencies also occur. Secondary seismic arrivals are especially subject to distortion. Overall response is strongly dependent upon the mass and configuration of the OBS and the rigidity and density of the bottom material. Tests at Lopez Island, Puget Sound using both directly applied mechanical transients and seismic signals with various instrument configurations demonstrate the above effects and provide some guidance for improved designs.Hawaii Institute of Geophysics Contribution No. 1172.     

Trapped bottom topographic waves over the inclined bottom

In the Boussinesq approximation, we study baroclinic topographic waves trapped by the flat meridional slope. The existence of these waves is explained by stratification, inclined bottom, and Earth's rotation. We deduce the evolutionary equation for the square of the envelope of a narrow-band wave packet of trapped waves. In the second order of smallness relative to the wave amplitude, we find the mean fields of velocity and density induced by the packet. It is shown that, in the limiting case of weakly nonlinear plane waves, the induced current is zonal. In the Northern hemisphere, depending on the slope of the bottom γ₁, the sign of the phase velocity σ/k (k is the zonal wave number) is either always positive (for γ₁>γ_1cr) or always negative (for γ₁<γ_1cr). If we neglect the vertical component of the Coriolis acceleration, then γ_1cr=0. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Instrumental waveform distortion on ocean bottom seismometers

Data from the 1978 Lopez Island OBS Intercomparison Experiment and deep sea data from University of Washington OBSs show that there is a considerable amount of waveform distortion resulting from the conversion of horizontal motion into vertical motion, here called cross-coupling distortion. This distortion, which substancially reduces the significance of waveform matching with synthetic seismograms, appears to result from rotation imparted to the OBS package by near-vertically traveling shear energy. The degree of this rotation seems to depend on the instrument surface area above the seafloor and the geometry and surface area of the feet connecting the package to the seafloor. The sensitivity and response of the seismometers within the package to this rotation depends on the precise location of the seismometers with respect to the axis of rotation. The results suggest how to modify OBS designs to minimize these effects.University of Washington Contribution No. 1225.     

Non-hydrostatic Kelvin waves in the ocean

A theory of the coastal Kelvin wave is presented in which the pressure is assumed not to be hydrostatic. The results show that the non-hydrostatic Kelvin wave is dispersive and that the e^–1 decay distance of the wave amplitude from the coast decreases as the wave length becomes shorter. Similar conclusions can be drawn on the equatorial Kelvin wave.     

Current-generated noise recorded on ocean bottom seismometers

High-amplitude, anrrow band noise that correlates with periods of high ocean bottom currents and the tidal cycle is occasionally observed on ocean bottom seismometers (OBS). The geophones on OBSs of different configurations are not equally sensitive to this noise and hydrophones are almost unaffected. With a suitable design, it should be possible to eliminate this noise problem.Hawaii Institute of Geophysics Contribution No. 1173     

The mixing mechanism in the formation of ocean shear waves

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OBS海洋环境信号分析与应用

为研究海洋环境信号在OBS(Ocean Bottom Seismograph)原始数据中的规律及应用,根据OBS原始数据的波形及频谱特征,将研究区划分为5个时间段,依次为旧涌浪阶段、风浪渐强阶段、风浪全盛阶段、风浪消退阶段和新涌浪阶段。结合海洋天气预报,认为上述现象是由偏南风风浪对海流的影响造成的。参考野外地震数据采集记录班报,得到各阶段的时长和距离,计算风浪渐强、全盛和消退阶段OBS附近海流的平均速度。结果表明:OBS原始资料中浅海海洋环境噪音增强的主要因素是风浪,且风浪引起的噪音信号的波形变化特征是渐进式的;OBS可用于接收某种特殊阶段(如台风、海啸等)的噪音信号,并根据噪音信号的波形特征、频谱变化规律和持续时间估算该阶段的海流速度变化。     

The role of surface waves in the ocean mixed layer

Previously, most ocean circulation models have overlooked the role of the surface waves. As a result, these models have produced insufficient vertical mixing, with an under - prediction of the ,nixing layer （ML） depth and an over - prediction of the sea surface temperature （SST）, particularly during the summer season. As the ocean surface layer determines the lower boundary conditions of the atmosphere, this deficiency has severely limited the performance of the coupled ocean - atmospheric models and hence the climate studies. To overcome this shortcoming, a new parameterization for the wave effects in the ML model that will correct this systematic error of insufficient mixing. The new scheme has enabled the mixing layer to deepen, the surface excessive heating to be corrected, and an excellent agreement with observed global climatologic data. The study indicates that the surface waves are essential for ML formation, and that they are the primer drivers of the upper ocean dynamics; therefore, they are critical for climate studies.     

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.     

Coastal trapped waves in a two-layer ocean: Wave properties when the density interface intersects a sloping bottom

Properties of coastal trapped waves when the pycnocline intersects a sloping bottom are studied using a two-layer model which has slopes in both layers. In this system there is an infinite discrete sequence of modes, and four different sorts of waves exist: the barotropic Kelvin wave, the upper shelf wave, the lower shelf wave and the internal Kelvin-type wave. They all propagate with the coast to their right in the Northern Hemisphere. The upper and lower shelf waves are due to the topographic-effect on the upper-layer and lower-layer slopes, respectively. Their motions are dominant in the respective layers being accompanied by significant interface elevations. The properties of the upper (lower) shelf wave are almost unaffected by the existence of a lower-layer (upper-layer) slope. The motion of the internal Kelvin-type wave is confined to the region around the line where the density interface intersects the bottom slope.The modes, except that with the fastest phase speed (the barotropic Kelvin wave), are assigned mode numbers in order of descending frequency. Characteristics of Mode 1 change with wavenumber; the upper shelf wave for small wavenumbers and the internal Kelvin-type wave for large wavenumbers (high frequencies). The higher modes of Mode 2 and above can be classified into the upper and lower shelf waves.