The instability of viscous two-layer oscillatory flows

The instability of oscillatory flows in a two-layer fluid where the two layers differ in density and viscosity has been analysed using a perturbation method for long waves with special interest on effects of viscosity, time scale, density and depth of the fluid. The flow of a fluid with homogeneous density can be unstable, when the kinematic viscosity of the upper fluid layer is different from that of the lower one. Viscosity stratification results in unstable oscillatory flows. Two limiting cases of single-layer flow are also considered.     

On the onset of the instability of a three-dimensional jet in a stratified fluid

The onset of a three-dimensional jet flow in a stratified fluid is studied with the aid of a direct numerical simulation. An initially cylindrical jet with a Gaussian velocity profile is considered in a fluid with stable linear density stratification. The results indicate that, if an initial small perturbation of the velocity field has a wide spectrum, an exponential growth of the isolated quasi-two-dimensional mode occurs and its spectral maximum is shifted toward smaller wave numbers in comparison with the maximum of the helical mode of the instability of a nonstratified jet. The growth rate is proportional to Ri^0.5, where Ri is the global Richardson number. The onset of the instability leads to the formation of the flow’s vortex structure, which consists of a collection of different-polarity quasi-two-dimensional vortices located in a horizontal plane near the longitudinal axis of the jet. At sufficiently long times (Nt > 100, where N is the buoyancy frequency and t is time), the growth of instability reaches the saturation stage and further fluctuations in velocity and density decay under the effect of viscous diffusion. At this stage, the flow becomes self-similar and the time dependences of the transverse and vertical widths of the jet are consistent with the asymptotic behaviors of integral parameters of the flow that are observed experimentally in the far stratified wake. The results suggest that the onset of the instability of a quasitwo-dimensional mode can play the determining role in the dynamics of flow in the far stratified wake.     

Chaotic Advection of a Passive Admixture in a Circular Barotropic Jet Flow

Izvestiya, Atmospheric and Oceanic Physics - The chaotic advection of a passive admixture during the excitation of chains of vortex structures in circular barotropic flows with a complex two-jet...     

Radiative Instability of a Barotropic Jet Flow in a Rotating Stratified Atmosphere

Izvestiya, Atmospheric and Oceanic Physics - This paper investigates the stability of a jet flow with a piecewise linear velocity profile in a rotating stratified atmosphere. The linearized set of...     

Barotropic disturbances caused by a point storm in aβ-plane ocean

Barotropic equation for vorticity balance in the-plane is solved for a volume transport stream function with a northward moving wind stress torque concentrated at a point (tweak). Asymptotic techniques are applied to the solution expressed by Fourier type integrals. In the front zone (northern half from the tweak) the stream function behaves asO(¦X¦^–5) whereX is a scaled eastward coordinate. In the wake, the stream function behaves asO(¦X¦^–1/2) within a wedge bounded by the westward axis and a line directed SSE approximately, but behaves asO(¦X¦^–5) in the rest of the half plane. On these boundaries it behaves asO(¦X¦^–5/2) andO(¦X¦^–1/3), respectively. East-west asymmetry is a result of asymmetry in zonal propagation of the planetary waves, which also cause the wavy pattern of the streamline in the western half of the wake. Friction is most effective in decreasing the stream function in the south to SSW sector and least effective to the west. Effect of divergence changes the wave pattern in the western half of the wake but does not change magnitude of the stream function. It is speculated that abnormal changes in daily mean sea levels observed in 1965 to 1971 along the south coast of Japan may be caused by the wake effect of moving typhoons east off Japan.     

Study on instability and nonlinear evolution of density fronts and coastal boundary currents

This article reviews the author's study on the instability and nonlinear evolution of density fronts and boundary currents, for which the Okada Prize was awarded in 1990. Cited topics are (i) theory for nonlinear longwaves on a coastal density current and the propagation of a density front along a coast, (ii) instabilities contained in one-layer frontal models, and (iii) nonlinear stability theory of two-layer boundary currents. Although much of these works were carried out by using frontal models, results obtained under the quasi-geostrophic approximation are also reviewed.     

On the importance of boundary layer calculations instead of viscous correction in heavily loaded marine propellers while using a surface panel method

A surface panel method is employed for the thin boundary layer calculation of heavily loaded marine propellers in steady state conditions. Employing the surface panel method, known as the “Morino Method”, the flow field around the propeller is represented by an unknown potential. The majority of the flow field is governed by the potential theory while the viscosity is assumed to be largely confined to thin shear layer on the propeller surface. The boundary layer calculations are performed by using Cebeci-Smith two dimensional model and the local skin friction coefficients and blowing velocities are obtained along the pre-computed on-body streamlines. It is shown that the prediction of torque of the propeller is improved when the boundary layer calculations are used instead of the boundary layer corrections based on the formulae established for the flat plates.     

北太平洋海洋带状流的正压特性

海洋中包含着多种时空尺度的运动过程,海洋带状流是近年来发现的一种新的流动形式。这种流动现象介于地转湍流和准定常流之间。上层海洋中大尺度运动的强度远大于海洋带状流而将其遮盖,因而带状流需要借助滤波方法提取出来。本研究基于纬向速度数据,通过切比雪夫高通滤波提取了北太平洋海洋带状流的三维结构,定义了“流向稳定度”指数,量化分析了北太平洋海域带状流的正压特性,从而进一步加深了对北太平洋海洋带状流结构特征的认识。     

Barotropic Response of the Sea of Okhotsk to Wind Forcing

We have examined wind-induced circulation in the Sea of Okhotsk using a barotropic model that contains realistic topography with a resolution of 9.25 km. The monthly wind stress field calculated from daily European Centre for Medium-Range Weather Forecasting (ECMWF) Re-Analysis data is used as the forcing, and the integration is carried out for 20 days until the circulation attains an almost steady state. In the case of November (a representative for the winter season from October to March), southward currents of velocity 0.1–0.3 m s⁻¹ occur along the bottom contours off the east of Sakhalin Island. The currents are mostly confined to the shelf (shallower than 200 m) and extend as far south as the Hokkaido coast. In the July case (a representative for the summer season from April to September), significant currents do not occur, even in the shallow shelves. The simulated southward current over the east Sakhalin shelf appears to correspond to the near-shore branch of the East Sakhalin Current (ESC), which was observed with the surface drifters. These seasonal variations simulated in our experiments are consistent with the observations of the ESC. Dynamically, the simulated ESC is interpreted as the arrested topographic wave (ATW), which is the coastally trapped flow driven by steady alongshore wind stress. The volume transport of the simulated ESC over the shelf reaches about 1.0 Sv (1 Sv = 10⁶ m³s⁻¹) in the winter season, which is determined by the integrated onshore Ekman transport in the direction from which shelf waves propagate. This revised version was published online in July 2006 with corrections to the Cover Date.     

Investigation of Barotropic and Baroclinic Seiches in Bounded Sea Basins

We present a survey of works carried out at the Wave-Theory Department of the Marine Hydrophysical Institute of the National Academy of Sciences of Ukraine for the last ten years and devoted to investigation of free and forced waves in bounded basins. Our attention is focused on the results of investigation of internal waves in basins of variable depth for the case of three-layer stratification of the liquid. The profiles of the bottom of the basin and interfaces are regarded as parabolic. Analytic solutions are obtained and the periods of oscillations of the free surface and interfaces for the first and second modes are determined. The dependences of the characteristics of baroclinic waves on the geometry of the basin and parameters of stratification are analyzed.     

Unsteady Chains of Wave Structures and Anomalous Transport of Passive Admixture in a Barotropic Jet Flow

Izvestiya, Atmospheric and Oceanic Physics - The anomalous transport of passive admixture is studied when unsteady chains of wave structures with closed streamlines are excited in a barotropic jet...     

Transformation of the Level of Barotropic Ocean under an Elliptic Region of Disturbances of a Baric Field

We study elevations of the level of a homogeneous ocean caused by a large-scale elliptic anomaly of the field of atmospheric pressure and determine the conditions under which Earth's rotation and the asymmetry of the region of disturbances of the baric field lead to significant deviations of the ocean level from its values given by the law of inverted barometer. Our investigation is based on the numerical analysis of the integral solution of the linear problem. It is shown that the deviations from the law of inverted barometer are especially pronounced in shallow-water regions, at high latitudes, and for strongly asymmetric regions of disturbances of atmospheric pressure.     

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.     

Barotropic tidal mixing effects in a coupled climate model: Oceanic conditions in the Northern Atlantic

Impacts of mixing driven by barotropic tides in a coupled climate model are investigated by using an atmosphere–ocean–ice–land coupled climate model, the GFDL CM2.0. We focus on oceanic conditions of the Northern Atlantic. Barotropic tidal mixing effects increase the surface salinity and density in the Northern Atlantic and decrease the RMS error of the model surface salinity and temperature fields related to the observational data.     

无结构网格二维海洋模式的正压梯度力算法改进

基于一套自主研制的无结构网格二维河口海洋数值模式A2D,在大圆湖理想模型下,通过与解析解进行比较分析,采用不同架构配置,改进设计正压梯度力计算方法。改进后的算法中引入了从算架构的配置,以配合主算架构,得到更佳的稳定性。通过水位场平面分布与单点过程线可以发现,三组试验的算法均获得了较好的精度和比原算法更好的稳定性,其中TSNS配置算法(中心点计算水位、边中点计算流速的主算架构,配合节点计算水位、边中点计算流速的从算架构)由于其主算架构更接近结构网格下的C网格,在守恒性、移动潮滩边界处理等方面具有一定优势和便利性,有利于在实际海洋中的计算。将TSNS配置算法在江浙沿海进行试算,水位验证结果与实测基本符合,与原A2D模式计算水位之间无显著差异。TSNS算法在稳定性方面的改进,有助于提升模式升级为三维后的稳定性,为今后模式成功升级为三维打下基础。     

Results of a known seafloor instability event

A submarine sediment instability event (landslide) occurred at Kitimat, British Columbia, in 1975. Recent high-resolution surveys provide details of the resulting seafloor morphology. The effects of the slide include modification of the fjord head delta-front slopes, transport of delta sediments into deep water and mixing with deep water, fjord bottom clays. Distinctive features include the results of shallow rotational sliding, tearing and shearing, compressional folding and long distance block gliding at the downslope slide terminus.     

Numerical simulation of viscous cavitating flow around a ship propeller

In the present study, cavitation and a ship propeller wake are reported by computed fluid dynamics based on viscous multiphase flow theory. Some recent validation results with a hybrid grid based on unsteady Navier-Stokes (N-S) and bubble dynamics equations are presented to predict velocity, pressure and vapor volume fraction in propeller wake in a uniform inflow. Numerical predictions of sheet cavitation, tip vortex cavitation and hub vortex cavitation are in agreement with the experimental data, same as numerical predictions of longitudinal and transversal evolution of the axial velocity. Blade and shaft rate frequency of propeller is well predicted by the computed results of pressure, and tip vortex is the most important to generate the pressure field within the near wake. The overall results indicate that the present approach is reliable for prediction of cavitation and propeller wake on the condition of uniform inflow.     

Simulation of a 3D submerged jet flow around a pile

The submerged 3D turbulent jet flow behavior around a pile on a rigid bed and on a scoured bed was studied experimentally and numerically. ADV was used to obtain the jet velocity distributions and Realizable k–ε turbulence model was used for the prediction of flow field around a pile. The jet flow area was three-dimensional and thus numerical model was a three-dimensional model. The numerical results were used to predict the velocity close to the pile and bed shear stress on the bed. In general, the results indicated that the flow field was also in agreement with the findings of previous experiments in literature and the related principles in the subject area. The experimental results demonstrated that Acoustic Doppler Velocimeter (ADV) measurements were almost identical with the Realizable k–ε turbulence model results for turbulence intensity I=10%.     

Data Assimilation Modeling of the Barotropic Tides in the Korea/Tsushima Strait

During 1999–2000, 13 bottom mounted acoustic Doppler current profilers (ADCPs) and 12 wave/tide gauges were deployed along two lines across the Korea/Tsushima Strait, providing long-term measurements of currents and bottom pressure. Tidally analyzed velocity and pressure data from the moorings are used in conjunction with other moored ADCPs, coastal tide gauge measurements, and altimeter measurements in a linear barotropic data assimilation model. The model fits the vertically averaged data to the linear shallow water equations in a least-squares sense by only adjusting the incoming gravity waves along the boundaries. Model predictions are made for the O₁, P₁, K₁, μ₂, N₂, M₂, S₂, and K₂ tides. An extensive analysis of the accuracy of the M₂ surface-height predictions suggests that for broad regions near the mooring lines and in the Jeju Strait the amplitude prediction errors are less than 0.5 cm. Elsewhere, the analysis suggests that errors range from 1 to 4 cm with the exception of small regions where the tides are not well determined by the dataset. The errors in the model predictions are primarily caused by bias error in the model’s physics, numerics, and/or parameterization as opposed to random errors in the observational data. In the model predictions, the highest ranges in sea level height occur for tidal constituents M₂, S₂, K₁, O₁, and N₂, with the highest magnitudes of tidal velocities occurring for M₂, K₁, S₂, and O₁. The tides exhibit a complex structure in which diurnal constituents have higher currents relative to their sea level height ranges than semi-diurnal constituents.     

Wave-induced seabed instability in front of a breakwater

The wave-induced soil response in a porous seabed has become an important factor for the stability of offshore facilities, because many marine structures may have failed due to seabed instability and concomitant subsidence. An analytical solution is presented for the wave-induced soil response under the action of a three-dimensional wave system. Based on this general solution, the mechanism of seabed instability is then investigated. The general solutions for pore pressure and effective stresses are readily reducible to two dimensions for progressive waves, and are compared to theoretical and experimental work available. Some dominant factors affecting the wave-induced seabed instability are discussed; including permeability, seabed thickness and degree of saturation.