Zonal flows,Rossby waves,and vortex transport in laboratory experiments with rotating annular channel

Results of experiments are considered for flows generated by different sources-sinks of mass in the rotating annular channel with beta-effect simulation using the inclined bottom. Diagrams of regimes are presented in parameters of the dimensionless angular velocity of the zonal flow averaged over the channel width and the dimensionless angular velocity of transport of vortex perturbations of cyclonic and anticyclonic types. In experiments and the simplest linear theories, most attention is paid to diagram regions with a slow motion of vortices relative to the rotating coordinate system near the parameters for stationary Rossby waves.     

Emergence of sub(super)-rotation and jet streams from small-scale quasi-two-dimensional vortices in laboratory experiments

This paper presents the results of experiments in a circular stationary and rotating channels with thin layers of conductive fluid for configurations consisting of a large number of permanent magnets and providing the MHD generation of small-scale velocity fields. The alternating radial configurations of magnets were chosen in such a way as to ensure the conservation of a discrete symmetry of their mutual arrangement relative to rotations of the circular channel around a central axis and were formed on the basis of numerical calculations with the shallow-water equations. Both in numerical and laboratory experiments, large-scale nearly circular vortices were obtained as a result of the energy transfer from the system of externally generated small-scale vortices to large-scale velocity fields (inverse cascade) under the influence of the Coriolis force in the rotating case. Single large-scale vortices and wide jet streams appear in subrotation and superrotation modes relative to external rotation, depending on its angular velocity. Rotation in a nearly circular vortex has a differential character with a decrease in the angular velocity of rotation with the radius in most area of the channel.     

淤泥质潮流深槽最大冲刷深度的一个概念模型

以概念模式方法计算了淤泥质潮流深槽的最大深度,探讨了涨落潮流速、涨落潮历时、深槽淤泥质物质粒径、深槽顶底部原始深度、水道长度等因素对潮流深槽最大深度的影响。概念模式的假设条件是:(1)深槽形态为长方体,底部纵向坡度为0;(2)沉积物粒径无垂向变化;(3)只考虑潮流作用的影响,涨、落潮流速在时间序列上呈正弦分布;(4)不考虑细颗粒物质的粘性和絮凝作用。模拟结果显示:(1)涨、落潮历时对深槽最大深度的影响很小。(2)优势潮流流速与最大深槽深度之间存在着幂函数关系。(3)深槽的底质粒径、深槽的长度均与最大冲刷深度呈正相关关系。(4)深槽顶部水深与最大深度呈负相关关系。(5)由于潮汐水道深度与潮流流速和沉积物侵蚀强度之间具有负反馈关系,因此水道冲刷存在着一个极限,即最终可以达到均衡状态。潮流深槽的均衡态特征和达到均衡态所需的时间可运用沉积动力学方法来确定;同时,若应用深槽的真实参数,进一步减少模型的假设条件,可望使该模型具有实际的应用价值。     

2016下半年安达曼海潮、余流观测分析

The characteristics of currents and tidal currents in the Andaman Sea(AS) are studied during the second half of2016 using observed data from a moored acoustic Doppler current profiler(ADCP) deployed at 8.6°N, 95.6°E.During the observation period, the mean flow is 5–10 cm/s and largely southward. The root mean square and kinetic energies of the low and high frequency flows, which are divided by a cutoff period of 5 d, are at the same level, indicating their identical importance to the total current. A power spectrum analysis shows that intraseasonal oscillations, a tidal-related semilunar month signal, a semidiurnal tidal signal and periods of 3–4 d are prominent. The barocliny of an eddy kinetic energy is stronger than the mean kinetic energy, both of which are the strongest on the bottom and the weakest at 70 m depth. Residual currents are largely southward(northward) during the summer(winter) monsoon season. Two striking peaks of the southward flow cause the 80 d period of meridional currents. The first peak is part of a large-scale circulation, which enters the AS through the northern channel and exits through the southern channel, and the second peak is part of a local vortex. The 40 d oscillation of the zonal current is forced by geostrophic variations attributed to local and equatorial remote forcing. The tidal current is dominated by semidiurnal constituents, and among these, M2 and N2 are the top two largest major axes. Moreover, astronomical tidal constituents MM and MSF are also significant. Diurnal constituents are weak and shallow water tides are ignorable. The aims are to introduce the new current data observed in the AS and to provide initial insights for the tidal and residual currents in the Andaman Sea.     

Baroclinic seiches in rotating basins of variable depth in the case of two-layer density stratification

We solve a plane problem of linear baroclinic seiches in closed rotating basins of variable depth with two-layer density stratification. In the long-wave approximation, we get a boundary-value problem for a system of ordinary differential equations and propose a numerical procedure for finding internal seiches. The analytic solutions of the problem are obtained for a basin of constant depth. The numerical analysis of seiches is performed for the distributions of depth corresponding to the zonal and meridional sections of the Black Sea and model basins including the cases of a shelf zone and an underwater ridge. It is shown that the baroclinic seiches become more intense in shallow-water regions and that the intense longshore currents caused by Earth’s rotation are formed in the shelf zones and over the underwater ridges.     

VORTEX SHEDDING FROM A CIRCULAR CYLINDER IN OSCILLATORY FAR FLOW

By using a process of successive approximations, the Boundary-Layer equations are solved to determine the separation points of a circular cylinder in oscillatory flow under the conditions of vortex existing. Combining with the discrete vortex model, the separation points and the fluid force coefficients are calculated at different KC numbers and Re numbers, A modified Morison equation is used in calculating the inline forces, and good agreements are obtained between the calculated results and those from other's experiments.     

Self-localization of planetary wave structures in the ionosphere upon interaction with nonuniform geomagnetic field and zonal wind

The generation and further linear and nonlinear dynamics of planetary magnetized Rossby waves (MRWs) in the rotating dissipative ionosphere are studied in the presence of a zonal wind (shear flow). MRWs are caused by interaction with the spatially nonuniform geomagnetic field and are ionospheric manifestations of ordinary tropospheric Rossby waves. A simplified self-consistent set of model equations describing MRW-shear flow interaction is derived on the basis of complete equations of ionospheric magnetohydrodynamics. Based on an analysis of an exact analytical solution to the derived dynamic equations, an effective linear mechanism of MRW amplification in the interaction with nonuniform zonal wind is ascertained. It is shown that operators of linear problems are non-self-adjoint in the case of shear flows, and the corresponding eigenfunctions are nonorthogonal; therefore, the canonically modal approach is of little use when studying such flows; a so-called nonmodal mathematical analysis is required. It is ascertained that MRWs effectively get shear flow energy during the linear stage of evolution and significantly increase (by several orders of magnitude) their energy and amplitude. The necessary and sufficient condition of shear flow instability in an ionospheric medium is derived. Nonlinear self-localization begins with the development of shear instability and an increase in the amplitude, and the process ends with the self-organization of strongly localized isolated large-scale nonlinear vortex structures. Thus, a new degree of freedom and a way for perturbation evolution to occur appear in medium with shear flow. The nonlinear systems can be a pure monopole vortex, a vortex streets, or vortex chains depending of the shape of the sheared flow velocity profile. The accumulation of such vortices in the ionospheric medium can produce a strongly turbulent state.     

Formulation of a continuously stratified sea model with three-dimensional representation of the upper layer

A two-layered model is considered in which the upper layer is continuously stratified and the lower layer is homogeneous. The system is driven by atmospheric forces. Bottom stress and topography are included in the model. The linear three-dimensional hydrodynamical equations are used to describe the system. Taking the eddy viscosity in the upper layer as inversely proportional to the static stability, the dependent variables are expanded in terms of continuous functions in the vertical (eigenfunctions). Using this method it is possible to compute currents and internal displacements at any depth in the upper layer. The three-dimensional structure of the lower layer is not considered in this model. The equations describing the lower layer are integrated over depth to give depth mean currents. Using a staggered finite-difference grid in the horizontal and a forward time-stepping procedure, numerical test experiments are carried out for a cross section and for a closed rectangular basin.     

Hydrodynamic coefficients for vertical circular cylinders at finite depth

Hydrodynamics coefficients for vertical circular cylinders at finite water depth are obtained and presented for different depth to radius and draft to radius ratios. A summary of equations for computer application is presented. Limiting values for heave added mass for zero frequency are discussed. A matching technique is used to satisfy the continuity of pressure and normal velocities.     

Effects of mass and damping ratios on VIV of a circular cylinder

In this study the basic characteristics of the dynamic response and vortex shedding from an elastically mounted circular cylinder in laminar flow is numerically investigated. The Reynolds number ranges from 80 to 160, a regime that is fully laminar. The governing equations of fluid flow are cast in terms of vorticity. The two-dimensional vorticity transport equation is solved using a vortex method. Effects of important parameters on the system response and vortex shedding are investigated; these include: mass ratio, damping ratio, Reynolds number and reduced velocity. The numerical results show that a decrease in either the mass ratio or damping ratio of the system can lead to an increase in both the oscillation amplitude and the reduced velocity range over which lock-in occurs. The results also suggest that the mass-damping parameter may characterize the system response adequately, although the effect of changing mass ratio appears to be a little more profound compared to damping ratio. Vorticity contour plots suggest that the vortex shedding occurs in the 2S mode, although a wake structure similar to the C(2S) mode appears at distances 15–20 diameters downstream in the lock-in region. The simulation results are in good agreement with previously published data.     

Stream-wise and cross-flow vortex induced vibrations of single tapered circular cylinders: An experimental study

Tapered circular cylinders are employed in a variety of ocean engineering applications. While being geometrically simple, this configuration creates a complex flow pattern in the near wake of the structure. Most previous experimental studies on tapered circular cylinders were dealing with stationary cylinders to explore the wake flow field and vortex shedding patterns past the cylinder. Few studies paid attentions to the vortex induced vibration of the tapered cylinders. This paper reports some results from in-water towing-tank experiments on the vortex-excited vibrations of tapered circular cylinders in a uniform flow. Cylinders with different mean diameters (28 and 78 mm), mass ratios (6.1 and 2.27) and tapers (5–20), along with their equivalent uniform cylinders, have been examined. The single degree of freedom vibrating system has a low mass-damping parameter (m*ξ = 0.0084–0.0279). The Reynolds number, based on mean diameter of the cylinders, ranges from 1400 to 70,200. The reduced velocities vary from 1.5 to 22. Effects of variations in the taper and mass ratios on the lock-in range, the reduced response amplitude, the reduced velocity for the peak vibration response and other stream-wise and cross-flow VIV parameters are reported and discussed.     

Asymptotic analysis of transition to turbulence and chaotic advection in shear zonal flows on a beta-plane

The generation of narrow-band Rossby wave packets and the modulated vortex chains induced by them in a weakly-dissipative zonal flow on the beta-plane with a velocity profile in the form of a shear layer is studied. The analysis is performed within the framework of the asymptotic approach based on the distinguishing a thin critical layer inside of which the vortex chains are formed. The evolution equations, describing the simultaneous development of a wave packet envelope and vorticity perturbations in a nonlinear critical layer, are derived for a weakly supercritical flow. A transition to the complex dynamics of a wave packet (low-mode turbulence) is studied within the framework of a numerical solution of the derived equations and its mechanism is revealed. The onset of chaotic advection and anomalous diffusion of passive scalar in the critical layer is considered, and the exponent of the diffusion law is calculated.     

Vortex shedding suppression for flow over a circular cylinder near a plane boundary

In this study, the Navier-Stokes equations and the pressure Poisson equation for two-dimensional time-dependent viscous flows are solved with a finite difference method in a curvilinear coordinate system. With this numerical procedure, the vortex shedding flow past a circular cylinder near a wall is investigated. The flow is calculated for a broad range of gap ratios for different Reynolds numbers ranging from 80 to 1000. Based on the numerical solutions, the vortex shedding is observed using various methods, and the mechanism for the vortex shedding suppression at small gap ratios is analyzed. The critical gap ratio at which the vortex shedding is suppressed is identified at different Reynolds numbers.     

The asymptotic theory of the generation of long-wave structures in critical layers of weakly dissipative jet flows

The mechanisms of the large-scale vortex structures formation in zonal jet flows (atmospheric blockings, cyclonic, and anticyclonic vortices) is investigated. Nonlinear perturbations formed during the onset of barotropic instability of a long-wave mode in weakly-dissipative and weakly supercritical jet flows with a symmetric velocity profile are considered in the β-plane approximation. This analysis is performed within the framework of the asymptotic theory based on the concept of a nonlinear critical layer. The equations describing the interaction of a wave with vorticity perturbations in a critical layer are derived. The regimes of a quasi-stationary and nonstationary nonlinear critical layer are considered separately. Combined equations of evolution covering the principle regimes of instability development are proposed. The existence of autowave-type structures characterized by a balance between the energy receipt to the wave and its dissipation are obtained within the framework of a numerical simulation. The dependence of the parameters of generated autowave structures on the shape of the zonal jet profile and the flow supercriticality level is studied.     

波生流对海岸污染物输移的影响

通过物理模型实验对海岸波浪作用下污染物运动特性进行了分析,重点分析了质量输移流、沿岸流、沿岸流不稳定运动及破波带内旋涡运动等海岸水动力因素的影响.实验中坡度分别取为1:100和1:40,实验中采用CCD摄像机记录墨水的运动轨迹,同步测量流体质点速度以及波面升高.实验表明,在破碎带外污染物主要受波浪非线性引起的质量输移流的影响;在破碎带内主要受沿岸流的影响,同时还受沿岸流不稳定运动及大尺度旋涡运动的影响.     

The surge motion of a circular cylinder containing a concentric cylindrical hole in finite depth

This paper deals with hydrodynamic forces of a single semisubmerged circular cylinder containing a concentric cylindrical hole constrained to move in a water domain of finite depth. The fluid domain is divided into inner and outer regions. The Laplace equations governing velocity potentials for the three regions are solved by separation of variables and expressed in terms of eigenfunctions of the resulting equations which satisfy appropriate boundary conditions. Continuity of pressure and velocity at the interface of the regions provides the necessary equations from which the velocity potentials, pressures and forces are obtained. Numerical results are plotted for added mass and damping coefficients for different draft-to-depth and radius-to-depth values and for various wave amplitudes.     

Cyclostrophic adjustment and nonlinear oscillations in the core of an intense atmospheric vortex

Intense atmospheric vortices are characterized by a regime of cyclostrophic balance, i.e., the balance between the pressure gradient and centrifugal force. To describe motions in the core of an axisymmetrical vortex, a class of exact solutions to the equations of gas dynamics with a linear dependence on radius is derived for the velocity components and with a quadratic dependence for temperature. It is shown that small deviations from the balance state give rise to oscillations of the hydrothermodynamic fields in the vortex core with a frequency proportional to the angular velocity of the rotation of the core. For fairly large initial deviations, oscillations are clearly anharmonic and, under the conditions of the prevailing centrifugal force, result in a significant temperature decrease on the vortex axis. The application of this class of solutions to describing the Ranque vortex effect (the intense cooling of gas during rapid rotations) and the acoustic radiation from tornadoes is discussed.     

Flow past a circular cylinder between parallel walls at low Reynolds numbers

The flow about a circular cylinder placed centrally inside a channel is studied numerically with an unstructured collocated grid finite volume method based on the primitive variable formulation. The distance between the channel walls is allowed to vary to change the blockage ratio. Simulations are carried out over a range of Reynolds numbers that are consistent with the two-dimensional assumption. The study confirms that transition to vortex shedding regime is delayed when the channel walls are close to the cylinder because of the interaction between the vortices from the channel wall and cylinder wake. In the unsteady vortex shedding regime, the wake pattern is opposite to the classic Karman street in respect of the positions of the shed vortices. The cylinder drag coefficient and Strouhal number are considerably increased at smaller gaps while the root-mean-squared lift coefficient is significantly decreased. Several important flow parameters are correlated with the input parameters, namely Reynolds number and blockage ratio.     

Experimental and numerical investigation of local scour around a submerged vertical circular cylinder in steady currents

Local scour around a submerged vertical circular cylinder in steady currents was studied both experimentally and numerically. The physical experiments were conducted for two different cylinder diameters with a range of cylinder height-to-diameter ratios. Transient scour depth at the stagnation point (upstream edge) of the cylinder was measured using the so-called conductivity scour probes. Three-dimensional (3D) seabed topography around each model cylinder was measured using a laser profiler. The effect of the height-to-diameter ratio on the scour depth was investigated. The experimental results show that the scour depth at the stagnation point is independent on cylinder height-to-diameter ratio when the later is smaller than 2. The increase rate of equilibrium scour depth with cylinder height increases with an increase in Shields parameter.