Long-period topographic trapped waves in a two-layer ocean with basic flow

The characteristics of free topographic trapped waves are investigated numerically for a two-layer model with basic flow, which is uniform, geostrophically balanced motion flowing parallel to the coast. Six modes are identified for this model with depth variations. They are external and internal Kelvin modes, a topographic Rossby mode, and additional three modes. The two of the additional modes are interesting. The first one is a quasi-geostrophic surface-trapped mode, while the second one is a quasi-geostrophic bottom-trapped mode. It is suggested that baroclinic instability takes place when these two modes take a resonance coupling each other.     

Dynamics of long spatial nonlinear waves in an ocean with a density jump and a gently sloping bottom

This paper deals with the modeling of the propagation of three-dimensional gravitational perturbations of small but finite amplitudes in shallow two-layered water in basins with a gently sloping bottom. A single integral-differential evolution equation is derived that takes into account the long-wave contributions of the inertia of liquid layers and surface tension and the weak nonlinearity of the disturbances, as well as the nonstationary water shear srtess at the bottom. A numerical implementation of the model equation that allows us to adequately describe the processes considered is suggested. The transformations of spatial solitary perturbations in the pycnocline of basins with different bottom topographies are presented.     

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.     

Wave propagation in a transversely isotropic porous ocean bottom

Abstract

The equations of wave motion are considered in this article for three-layered medium which consists of liquid and porous layers with finite depth and solid half-space such as ocean bed. By virtue of scalar potential functions for each layer, complicated differential equations of layers are reduced to ordinary differential equations. An analytical method is applied to determine the Green’s functions of media based on an arbitrary shaped time-harmonic excitation at the interface of liquid and porous layers. A Mathcad code is provided to compute the complex integrals. Displacement and stress fields of three layers are discussed. Comparing with special cases, existing answers represent the validity of the proposed method. Numerical results are carried out for circular patch, ring and point loads, and the effects of various parameters on the behavior of the system are plotted. Finally, the achieved results were under discussion.     

Intrusion layering and vertical diffusion in the ocean owing to tidal mixing at a sloping bottom

The empirical and analytical relationships between the vertical scale of intrusions, which are formed owing to the layering of the mixed boundary layer at a sloping bottom, and the determining parameters are obtained on the basis of field measurements in the coastal zone and energy considerations. An estimate of the vertical diffusion coefficient is given which allows us to determine the role of tidal mixing at the rigid boundaries as a mixing factor for the entire world's oceans.Translated by Mikhail M. Trufanov.     

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.     

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.     

The effect of large-scale bottom irregularities on the dynamics of Rossby waves in the ocean

This paper discusses, in terms of the geometrical optics approximation, how large-scale bottom irregularities influence the propagation of Rossby waves in the ocean. To describe the major peculiarities of the phenomenon, a two-layer model is applied, with the depth of the upper layer being considerably smaller than that of the lower layer. However, even with the bottom topography being allowed for, the wave motion is described by two Rossby wave modes, namely, a barotropic mode and a baroclinic mode. It is demonstrated that barotropic mode transformation caused by large irregularities of the sea-floor may lead to wave interaction, resulting in their anomalous distribution. Translated by Vladimir A. Puchkin.     

An inverse method for reconstructing the density and sound speed profiles of a layered ocean bottom

A standard inverse problem in underwater acoustics is the reconstruction of the ocean subbottom structure (e.g., the density and sound speed profiles) from an aperture- and bandlimited knowledge of the reflection coefficient. In this paper we describe an inverse solution method due to Candel et al. [12] which is based on the scattering of acoustic plane waves by a one-dimensional inhomogeneous medium. As a consequence of applying the forward scattering approximation to a local wave representation of the acoustic field, they obtain an expression for the reflection coefficient in the form of a nonlinear Fourier transform of the logarithmic derivative of the local admittance. Inversion of this integral transform enables the recovery of the admittance profile via the numerical integration of two first-order differential equations which require as reflection data a single impulse response of the medium. Separate recovery of both the density and sound speed profiles requires two impulse responses for two different grazing angles. In this case, four differential equations need to be integrated instead of two. To illustrate the capability of the method, we present numerical reconstructions which are based on synthetic reflection data for a geoacoustic model that represents the acoustic properties of the surficial sediments for a site in the Hatteras Abyssal Plain.     

Sinking of less dense water in the bottom Ekman layer formed by a coastal downwelling current over a sloping bottom

Laboratory experiments on the dynamics of a downwelling coastal current over a sloping bottom were conducted in a tank on a rotating platform. The current was generated by a source of stable water flow of the same density (barotropic case) or of lesser density (baroclinic case) compared with the surrounding water in the tank. It was found that even in the case of the baroclinic current, a less dense water downflow in the bottom Ekman layer was formed under certain conditions. At some moment, this downflow undergoes convective instability. Taking into account the results of the experiment, the parameters of the bottom Ekman layer on the continental shelf/slope of the Black Sea were preliminarily estimated and the possible sinking depth of less dense water was calculated.     

Reflection profiling in the deep ocean using a near bottom hydrophone

A 20 km long high resolution seismic reflection profile was carried out approximately 300 km southwest of Bermuda. The data were collected using a small airgun sound source and a single hydrophone receiver towed 100 m above the seafloor at a depth of 5400 m. Comparisons with nearby conventional seismic reflection profiles show the considerable improvement of resolving power provided by this method, particularly of the basement morphology beneath the 700 m thick sediment column. The data were recorded digitally and selected data examples show the enhancement provided by filtering, stacking, source deconvolution and corrections for hydrophone motion. The precise picture of basement topography that results from this data is compared with deep tow bathymetry profiles of the present day mid-Atlantic Ridge flanks, and is seen to be remarkably similar.     

Response of a two-layer ocean to typhoon passage in the western boundary region

Effect of the typhoon passage on the western boundary region of a two-layer ocean with bottom topography is studied. The ocean is initially at rest and is set in motion by a typhoon passing parallel to the west coast. Equations that represent barotropic and baroclinic modes of motions are solved numerically by means of the method of finite differences. Motions of the barotropic mode are assumed to be horizontally non-divergent. In this mode, an elongated vortex is produced by the typhoon and propagates toward the south after passage of the typhoon. Behavior of the vortex may be interpreted as continental shelf waves. It is found that the formation and propagation of continental shelf waves are hardly affected by the density stratification. As for the baroclinic response, the typhoon causes considerable interface displacements along its track. The interface displacements are associated with geostrophic motions and remain for long time, though they are formed on the continental slope. Besides the large scale baroclinic response, internal Kelvin waves are induced along the artificial east wall.     

On some peculiarities of the dispersion properties of internal waves in the ocean

The effect of mean flows on the dependence of the internal waves' group velocity on the wavenumber is considered. Experimental data on the behaviour of internal wave packets propagating in the ocean at an extreme group velocity are reported.Translated by Vladimir A. Puchkin.     

Horizontal circulations caused by the bottom oscillatory boundary layer in a bay with a sloping bed

The horizontal circulations caused by the combined effect of the bottom oscillatory boundary layer (Stokes layer) and a sloping bed have been investigated both theoretically and experimentally. The generating mechanism is analogous to that for horizontal circulation induced by wind or by density variation. This horizontal circulation can account for a part of the tidal residual current observed in a tidal hydraulic model.     

Generation of internal waves resulting from the interaction of a barotropic tide with a horizontallyinhomogeneous density field and bottom topography

This paper addresses the problem of the generation of internal waves by a barotropic tide propagating in a uniformly stratified sea across the frontal zone overlying a submerged ridge or a continental slope. Using Riemann's technique, we have performed computations and analysed the wave fields' spatial characteristics and have defined the dependences of the generated wave amplitudes, bottom topography parameters, and density field. It is shown that the presence of a horizontally-inhomogeneous density region over a subwater feature may lead to substantial alteration of the maximum amplitudinal values of internal waves, both inside and around the frontal zone.Translated by Vladimir A. Puchkin.     

Laboratory modeling of the structure of a thermal bar and related circulation in a basin with a sloping bottom

Development of a thermal bar in a laboratory flume with an inclined bottom (3.7°–12°) under the conditions of cooling/heating of the water with a temperature close to that of the maximal density is studied. The structure of the temperature field and currents during different stages of the circulation is examined: (i) formation of an along-slope gravity current, (ii) generation of a subsurface jet, and (iii) transformation of one type of the circulation into another at passing the temperature of the maximum density. The “fall” and “spring” types of the thermal bar are shown to be dynamically equivalent: the transport of the near-shore waters to the deepwater part, which is driven by the buoyancy flux rather than by the heat flux across the surface, transforms stage (i) into stage (ii), while the opposite (on-shore) flow is generated in the intermediate layers. A comparison of the results with the field and laboratory data published allows us to suggest that the propagation of the thermal bar front in the “fast” stage can be considered as the development of a convective jet with its velocity U ～ h ^3/4, which is proportional to the growing thickness of the upper layer h affected by the heating/cooling processes     

Wave boundary layers near the surface and bottom in a stratified fluid

The paper examines so-called wave boundary layers arising in a bounded stratified fluid for large times. Each the layer is a narrow domain in the vicinity of the fluid surface and/or bottom characterized by sharp, growing with increasing time, vertical gradients of the buoyancy and horizontal velocity. The layers arise as a result of free linear wave evolution of the initial fields if the initial buoyancy at the boundaries depends on the horizontal coordinates. An asymptotic solution for the boundary layer for large times is presented, and it is shown that this solution describes exact fields fairly well even for moderate times.     

两层流体中内波作用下Spar平台运动响应

研究两层流体中Spar平台在内波作用下的运动响应问题。在线性势流理论框架,提出在内波作用下Spar平台运动响应及分段式悬链线系泊张力特性的计算方法。数值分析两层流体内界面位置、入射内波的波长以及系泊索初始预张力对Spar平台运动响应及其系泊索张力特性的影响规律,结果表明内波对Spar平台纵摇运动响应的影响是小的,但对Spar平台纵荡与垂荡运动响应及其系泊索张力的影响是不可忽视的。因此,在Spar平台的设计中,考虑内波的影响是重要的。     

Generation of long internal waves in the ocean by a moving pressure zone

The generation of plane internal waves in a continuously stratified ocean by a steadily moving anomaly of the atmospheric pressure is studied in a linear statement using a quasi-static approximation. Quantitative estimates for the parameters of internal waves in the wake are obtained for the average distribution of the Väisälä-Brunt frequency in the Caribbean Sea.Translated by Mikhail M. Trufanov.     

An investigation on internal solitary waves in a two-layer fluid: Propagation and reflection from steep slopes

Experimental investigations on internal solitary wave (ISW) propagation and their reflection from a smooth uniform slope were conducted in a two-layered fluid system with a free surface. A 12-meter-long wave flume was in use which incorporated with: (1) a movable vertical gate for generating ISW; (2) six ultrasonic probes for measuring the fluctuation of an ISW; and (3) a steep uniform slope (from one of θ=30°, 50°, 60°, 90°, 120° and 130°) much greater than those ever published in the literature. This paper presents the wave profile properties of the ISW recorded in the flume and their nonlinear features in comparison with the existing Korteweg de Vries (KdV) and modified Korteweg-de Vries (MKdV) theories. Experimental results show that the KdV theory is suitable for most small-amplituded ISWs and MKdV theory is appropriate for the reflected ISWs from various uniform slopes. In addition, both the amplitude-based reflection coefficient and reflected energy approach a constant value asymptotically when plotted against the slope and the characteristic length ratio, respectively. The reflected wave amplitudes calculated from experimental data agree well with those reported elsewhere. The optimum reflection coefficient is found within the limit of 0.85 for wave amplitude, among the test runs from steep normal slope of 30° to inverse angle of 130°, and around 0.75 for the reflected wave energy, produced by an ISW on a vertical wall.