Interaction of an ensemble of vortices in the β-plane

The evolution of an ensemble of intense vortices in the β-plane is numerically simulated. In the process of evolution, vortices interact either directly or by means of the Rossby waves emitted by them. We show that the mean displacements of vortices of the ensemble along the meridian and, as a result, their energy losses are lower than for the isolated vortices evolving in the β-plane. This means that they are more stable than the isolated vortices. In addition, for vortices in the ensemble, the theoretical dependence of the energy of a vortex on its displacement from the initial latitude obtained for the motion of an intense isolated vortex in the β-plane is in good agreement with the experimental data. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

On the stability of vortex streets in a stratified fluid

On the basis of the perturbation theory developed previously by the authors for localized hydrodynamic vortices, the influence of a specified jet flow and of the structure of individual vortices on the stability of the Karman street is investigated. It is shown that, for a street of vortices with a power law of decrease in the azimuthal velocity, the jet flow suppresses instability only with respect to perturbations with wavelengths from a certain range determined by the parameters of the flow. At the same time, for streets formed from vortices with a Gaussian profile of the azimuthal velocity, even in the absence of a specified flow, there is a certain region of the street’s parameters in which the street is stable against perturbations of all scales. Thus, for the purposes of modeling quasi-two-dimensional flows in a stratified fluid by a sequence of localized vortices, which is discussed in this study, vortices with a Gaussian profile of the azimuthal velocity turn out to be preferable. The results of this study are consistent with numerous experiments on the structure of a quasi-two-dimensional wake behind a body in a stratified fluid at large Reynolds and Froude numbers.     

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.     

海洋中长生命反气旋涡在地形上的演变以及涡旋的合并现象

通过对海洋中长生命反气旋涡在Ｇａｕｓｓ型孤立地形上演变的研究,发现地形对长生命反气旋涡的发展和传播有相当重要的影响。在无地形作用的情况下,仅有反气旋涡能够存在于向西的均匀基流中,这个涡是长生命的,并且在西移过程中有明显的向西倾斜。然而当其上游存在一个孤立地形时,可以发现这个涡有一个向东的倾斜,它的强度将增强且向西的移速会增加,其规迹象陀螺的运动。另一方面,当两个强度相同的反气旋涡同时存在时,这两个     

Structure of a pair of anticyclonic vortices in northern part of the South China Sea in autumn of 1994

A pair of remarkable meso-scale anticyclonic vortices, one formed closely to another, inthe northern part of the South China Sea during the period from the later August to early September of 1994 were documented by the in situ observation data. Their spatial structures were examined in detail from the horizontal and two nearly perpendicular/vertical angles of view. It was shown that the horizontal scales of these two vortices were around 100, 50 km, and their vertical scales were about 500, 1000 m, respectively. Two "warm core" structures associated with these two vortices were found in their horizontal and vertical analyses. The closer spacing of these two vortices (namely, 60 km), which was smaller than the Rossby radius of deformation, suggested that they might merge with each other during their next evolution stages and form into a larger vortex eventually.     

Taylor-Görtler vortices expected in the air flow on sea surface waves—II

The instability of Taylor-Görtler vortices which are expected in the air flow on water waves was studied in part I, under the assumption that the curvature around the crest or the trough of water waves, where the instability was expected to take place first, was constant, namely that the characteristics of the vortices were affected little by the local change of the curvature along the direction of the progress of water waves (the direction ofx-axis) However, the curvature actually varies from positive to negative, or vice versa. In order to study this effect, the instability of Taylor-Görtler vortices is examined with respect to the range of the part of a constant curvature, in the model in which the curvature is positive constant near the trough and negative constant near the crest, and zero in the intermediate regions, respectively. It is shown that as the region of the constant curvature becomes narrower, the instability tends to weaken. For the same example with part I, namely, when the wind of 12.2 m s^–1 is blowing over swells of 15 m in wavelength, if the range of constant curvature near the trough is taken as a quarter of one wave length, the critical wave height becomes 0.96 m instead of 0.50 m, and conversely, the wave length and the height of center of the vortex become 11.9 m and 2.1 m instead of 24 m and 3.7 m, respectively.Further, using the energy equations, quantitative estimates are performed of the intensity of the vortices which develop when the wave height of the swell is 1.05 m in the above described example, and also of the influence of the vortices upon the wind profile when the equilibrium state is reached. When the vortices are generated and grow to attain to an equilibrium state interacting with the mean flow, the maximumx-component of velocity in the vortices is about 1.04 m s^–1. Consequently, the wind profile undergoes a considerable distortion from the logarithmic one near the level of 2 m height. This distorted wind profile has a form similar to those sometimes observed above the sea surface.     

Taylor-Görtler vortices expected in the air flow on sea surface waves—I

Taylor-Grörtler vortices are longitudinal vortices resulting from a centrifugal instability. They are generated in the flow having a curved streamline with an increasing velocity in the direction of decreasing curvature.It is shown that the air flow above wind waves and swells also satisfies locally the condition of the centrifugal instability. Numerical calculations indicate the possibility of generation of Taylor-Görtler vortices on the trough of sea waves. For example, when a wind of about 12.2 m/s at 10-m level is blowing over sea waves of the wave length of 15 m like the swell, the critical water wave height beyond which the vortices may be generated is about 0.5 m, and the critical wave length and the height of center of the generated vortices are about 24 m and 3.7 m, respectively. Further, about the relations between the generation of vortices and wind waves, it is shown that the condition of their generation is satisfied at the trough of waves for early stages of the wave generation.In conclusion, it is expected that the Taylor-Görtler vortices change the wind profile along the sea surface, and also, play some part in the growth of wind waves, especially in the formation of their three dimensional structure.     

Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part I. Solitary waves

Interactions between a solitary wave and a submerged rectangular obstacle are investigated both experimentally and numerically. The Particle Image Velocimetry (PIV) technique is used to measure the velocity field in the vicinity of the obstacle. The generation and evolution of vortices due to flow separation at the corners of the obstacle are recorded and analyzed. It is found that although the size of the vortex at the weatherside of the obstacle is smaller than that at the leeside, the turbulence intensity is, however, stronger. A numerical model, based on the Reynolds Averaged Navier–Stokes (RANS) equations with a k–ϵ turbulence model, is first verified with the measurements. Overall, the agreement between the numerical results and laboratory velocity measurements is good. Using the RANS model, a series of additional numerical experiments with different wave heights and different heights of the rectangular obstacle are then performed to test the importance of the energy dissipation due to the generation of vortices. The corresponding wave transmission coefficient, the wave reflection coefficient and the energy dissipation coefficient are calculated and compared with solutions based on the potential flow theory. As the height of the obstacle increases to D/h=0.7, the energy dissipation inside the vortices can reach nearly 15% of the incoming wave energy.     

Two-layer quasi-geostrophic model of contour dynamics for a round basin

A quasi-geostrophic contour dynamics model permitting one to study flows induced by a system of vortex patches in a two-layer ocean with round shore boundaries in the presence of specified background flows caused by the bottom relief, the β effect, and sources and sinks at the boundaries is proposed. The principal relations of the model are presented and the algorithm of its numerical realization is described. Some experimental results of the study of the evolution of unstable two-layer vortices are demonstrated.     

Moving-Particle Semi-Implicit Method for Vortex Patterns and Roll Damping of 2D Ship Sections

A meshless method, Moving-Particle Semi-hnplicit Method （MPS） is presented in this paper to simulate the rolling of different 2D ship sections. Sections S. S. 0.5, S.S. 5.0 and S. S. 7.0 of series 60 with CB = 0.6 are chosen for the simulation. It shows that the result of MPS is very close to results of experiments or mesh-numerical simulations. In the simulation of MPS, vortices are found periodically in bilges of ship sections. In section S. S. 5.0 and section S. S. 7.0, which are close to the middle ship, two little vortices are found at different bilges of the section, in section S. S. 0.5, which is close to the bow, only one big vortex is found at the bottom of the section, these vortices patterns are consistent with the theory of Ikeda. The distribution of shear stress and pressure on the rolling hull of ship section is calculated. When vortices are in bilges of the section, the sign clmnge of pressure can be found, but in section S. S. 0.5, there is no sign change of pressure because only one vortex in the bottom of the section. With shear stress distribution, it can be found the shear stress in bilges is bigger than that at other part of the ship section. As the free surface is considered, the shear stress of both sides near the free surface is close to zero and even sign changed.     

Three-dimensional reversed horseshoe vortex structures under broken solitary waves

Turbulent vortical structures under broken solitary waves are studied using three-dimensional smoothed particle hydrodynamics (SPH) method. The numerical model predicts water surface evolution and horizontal velocity very well in comparison with the experimental results. The numerical results detect organized coherent structures characterized as reversed horseshoe (hairpin) vortices being generated at the back of the broken spilling wave and traveling downward. The counter rotating legs of the reversed horseshoe structures appear to be a continuous form of the previously found obliquely descending eddies. The reversed horseshoe structures are associated with the turbulence motion of sweep events (downwelling motion) and transport momentum and turbulent kinetic energy downward into the water column. Vortex turning play an important role on the generation and evolution of three dimensional reversed horseshoe structures from the spanwise breaking wave rollers.     

A numerical study on the formation and variation of a clockwise-circulation during winter in the Yellow Sea

In the Yellow Sea, the north-westerly wind dominates in winter and the existence of horizontal clockwise circulation has been suggested (Yanagi and Takahashi, 1993). The formation and variation mechanisms of this clockwise circulation is investigated using the wind forced numerical model which has a simplified basin configuration of the Yellow Sea. The model results show that two vortices (an anticlockwise vortex off Chinese coast and a clockwise vortex off Korean coast) are generated by the uniform north-westerly wind. Both vortices propagate along the shelf slope as the first mode shelf waves. An anti-clockwise vortex can not grow because it does not balance to the wind forcing. On the other hand, a clockwise vortex can grow and it reaches to the equilibrium condition at the northern part of the Yellow Sea, because this circulation can balance to the wind forcing. The time scale to become into the equilibrium condition is about 2 days. From this fact, it is ascertained that a clockwise circulation in the basin is generated periodically according to the variable wind forcing with 4 days period. The steady part of the current field exists with the fluctuating one which is induced by the periodical north-westerly wind.     

On the nature of oceanic eddies shed by the Island of Gran Canaria

We use hydrographic and buoy data to compare the initial temperature fields and Lagrangian evolution of water parcels in two vortices generated by the southward flowing Canary Current passing around the island of Gran Canaria Island. One vortex is anticyclonic, shed in June 1998 as the result of an incident current of about 0.05 m s⁻¹, and the second one is cyclonic, shed in June 2005 with the impinging current estimated as 0.03 m s⁻¹. The two vortices exhibit contrasting characteristics yet display some important similarities. The isopycnals are depressed in the core of the anticyclonic vortex, at least down to a depth of 700 m, whilst they dome up in the core of the cyclonic vortex but only down to 450 m. In the top 300 m the depression/doming of the isotherms is similar for both vortices, with a maximum vertical displacement of the isotherm of about 80 m, which correspond to temperature anomalies of some 2.5 °C at a given depth. A simple method is developed to obtain the initial orbital velocity field from the temperature data, from which we estimate peak values of 0.7 and 0.5 m s⁻¹ for the anticyclonic and cyclonic vortices, respectively. The buoys, three for the anticyclonic vortex and two for the cyclonic one, were drougued at 100 m depth, below the surface mixed layer, and their initial velocities are consistent with the above values. In both vortices, the buoys revolve either within a central core, where the rotation rate remains stable and large for several weeks, or in an outer ring, where the rotation rate is significantly smaller and displays large radial fluctuations. Within the inner core the anticyclonic vortex has significant inward radial velocity, while the cyclonic vortex has near-zero radial mean motions. The cyclonic vortex rotates more slowly than the anticyclonic, their initial periods being 4.5 and 2.5 days, respectively. A simple axisymmetric model with radial diffusion (coefficient K_h≅25 m² s⁻¹) and advection reproduces the observations reasonably well, the diffusive effect being more important than that resulting from the observed radial advection. The model also supports the hypothesis that the rotation rate of cyclonic vortices is less than that of anticyclonic vortices, as otherwise they would become inertially unstable. Both the buoys data and sea surface temperature images confirm that the vortices evolve from youth to maturity, as the cores shrink and the outer rings expands, and then to a decay stage, as the core rotation rates decrease, though frequent interactions with other mesoscale structures result in more accelerated aging. Despite these interaction they last many months as coherent structures south of the Canary Islands.     

内孤立波作用下半潜平台荷载及其周围流场数值模拟研究

内孤立波对海洋平台的安全运行存在一定的威胁,基于三维数值水槽对内孤立波传播引起的半潜平台受力及其周围流场的分布进行了数值模拟研究.通过与试验对比,分析了入射波幅和分层流体深度比对半潜平台上内孤立波荷载特性的影响规律,验证了数值模拟结果是准确可靠的.研究表明,内孤立波引起的平台荷载会随着内孤立波波幅的增加而增大,随着分层流体深度比的增加而减小.基于对平台周围剖面速度场和三维涡场的演化规律研究,发现在内孤立波传播过程中,平台周围会出现明显的速度减小区,平台周围会有大量的漩涡产生并发生脱落现象.     

Horseshow Vortices at Erodible Boundaries of Nonuniform Flows

The results of experimental studies of the interaction between the horseshoe vortices formed in nonuniform water flows and a sand surface are presented. The central part of the initial cylindrical vortex ascends, driven by the Kutta—Joukowski force. The vortex tails submerged into sand approach each other, grabbing the sand by their ends. Sharp bends are formed at the axes of the vortex tails. If the bends occlude, a ring vortex is formed above the bends. The ring approaches the surface at an angle of 40° and moves along the flow: the angle decreases, and the radius of the ring increases. When the whole vortex reaches the water surface, it breaks, loses the entrapped sand, and forms a ridge on the bottom.     

Scarifying and fingering surfaces of plunging jets

The local surface deformation resulting from the oblique impact of a columnar water jet has been computed, using a three-dimensional large eddy simulation, as a model of the overturning jet of a breaking wave. The emergence of the secondary jet from the front face of the initial jet has been examined and the organisation of the vortices within the jet characterised. As the secondary jet emerges, the vorticity field becomes unstable under the action of the strong shear beneath the jet surface and pairs of longitudinal counter-rotating vortices stretched along the direction of the jet projection are formed. The presence of these longitudinal vortex pairs creates convergent surface flows, resulting in the formation of longitudinal scars on the rear face of the projecting jet. Following significant growth of the scars on both its upper and lower surfaces, the jet decouples into fingers. The lateral widths of the longitudinal vortices provide a minimum measure of the finger size. A horizontal Froude number Fr_h, representing a measure of strength of horizontal shear in a gravity-dominated impacting flow is defined, which characterises the organisation of the longitudinal vortices occurring in the shear flow, and the resultant formation of scars and fingers. For higher Fr_h, stronger longitudinal vortices and deeper scars are formed at longer lateral intervals, enhancing the fingering process during the splashing event. Fundamental features of material transport in the vicinity of the surface of jets (e.g. gas transfer across a sea surface) are related to the entrainment of surface fluid by the longitudinal vortices, and is thus also characterised by Fr_h.     

Assessing New England's waterborne energy imports (1995–2004)

This paper tests four hypotheses relating to the waterborne commerce of New England's imported energy, by port of entry, from 1995 through 2004. It concludes that the region's ports engaged in this fossil fuel traffic are part of a hierarchical system of large, medium, and small ports; that such energy flows have increased over the study period; that localized demand for energy is the principal component leading to growth; and that regional inter-port competition was not stable.     

Numerical Simulation of Viscous Flow Around a Rolling Cylinder with Ship-Like Section

Two-dimensional unsteady incompressible viscous flow around a rolling cylinder with ship-like section is numerically simulated by employing the computational scheme previously developed by the authors, in which the continuity and momentum equations are satisfied simultaneously at each time step for oscillating flow. The numerical results show that the motion of vortices around a rolling ship hull is cyclical. It is found that the location of the vortices is very similar to the existing experimental result. Using these simulation results, we can calculate the roll damping of ships including viscous effects.     

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.     

Selective withdrawal from a rotating stratified current with applications to OTEC

The results of a simple theoretical model of axisymmetric withdrawal from a rotating stratified current are presented. A rotating stratified flume was used to test the validity of the theory. Good agreement was found and when the theory is applied to the fluid motion into an OTEC plant, it is found that when the current going by the plant is small, large vortices develop near the inlets. The torques on the plant due to these vortices and the degradation of temperature due to selective withdrawal processes are estimated to be potentially significant.