Y. D. Afanasyev

Horizontal jets and vortex dipoles in a stratified fluid

When a horizontal force is applied locally to some volume of a viscous densitystratified fluid, flows with high concentration of vertically oriented vorticity (vortex dipoles) are generated. The processes of generation and evolution with time of these unsteady flows in a stratified fluid are studied. A convenient way to produce and study these flows in the laboratory is to use a submerged horizontal jet as a ‘point’ source of momentum. The main governing parameter (the ‘force’) is easily controlled in this case. Two regimes were studied: starting jets with dipolar vortex fronts (the force acts continuously) and impulsive vortex dipoles (the force acts for a short period of time). A conductivity microprobe, aluminium powder, shadowgraph, thymol-blue and other techniques have been used to measure the velocity and density distributions in the flows. It is found that in both regimes the flows are self-similar: the lengthscale of the flows increases with time as t ½ for starting jets and as t 1/3 for vortex dipoles. Detailed information about the generation mechanism, kinematics and dynamics of the flows is obtained. On the basis of similarity principles a theoretical explanation of the experimental results is given. The theory is in good agreement with the results obtained.

Two-dimensional vortex-dipole interactions in a stratified fluid

Planar motion produced when a viscous fluid is forced from an initial state of rest is studied. We consider a vortex dipole produced by the action of a point force (Cantwell 1986), and a vortex quadrupole produced by the action of two equal forces of opposite direction. We also present results from an experimental investigation into the dynamics of the interactions between vortex dipoles as well as between vortex dipoles and a vertical wall in a stratified fluid. Theoretical consideration reveals that the dynamics of two-dimensional vortex-dipole interactions are determined by two main governing parameters: the dipolar intensity of the vorticity distribution (momentum) and the quadrupolar intensity of the vorticity distribution of the flow. We document details of different basic types of interactions and present a physical interpretation of the results obtained in terms of vortex multipoles: dipoles, quadrupoles and their combinations.

Quasi-two-dimensional turbulence on the polar beta-plane: laboratory experiments

Results from a new series of experiments on turbulent flows decaying in a thin layer of water with a free surface in a rotating circular container are presented. The flows are generated electromagnetically using a regular array of permanent magnets. The Particle Image Velocimetry method is used to determine the velocity and vorticity fields in the flow. The experimental results demonstrate the formation of a polar vortex and jets perturbed by stationary Rossby waves in experiments with higher values of the beta parameter. Blocking events similar to those occurring in the Earths atmosphere were observed in the laboratory flows. The Two-dimensional energy spectra of the flow demonstrate anisotropy in the space of the azimuthal and total wavenumbers. The One-dimensional energy spectra are characterized by a peak at the Rhines wavenumber.

On breaking internal waves over the sill in Knight Inlet

This paper describes a new series of numerical simulations of stratified flow over localized topography which has been designed to address issues arising from a recently published sequence of detailed observations from a coastal oceanographic setting. Results demonstrate that the numerically simulated flow is very similar to that which develops in Knight Inlet, British Columbia, a fjord which is subject to periodic tidal forcing, and that the detailed dynamical characteristics of this flow are also strikingly similar to those of severe downslope windstorms that often occur in the atmosphere. A typical sequence of events observed in such flows includes the ‘breaking‘ of a forced stationary internal wave induced by the topography, which results in irreversible mixing and the formation, through wave–mean flow interaction, of a decelerated mixed layer that extends downstream from the level of breaking. The formation of this mixed layer is a necessary precondition for transition of the flow into a supercritical hydraulic regime in which a low–level high–velocity jet develops in the lee of the topographic maximum. Simulations with both fixed inflow velocity and harmonically varying inflow velocity are performed and intercomparison of the results clearly demonstrates that flow evolution in the unsteady forcing case can be described, to reasonable approximation, by the results of the corresponding quasi–steady simulations, at least during the accelerating stage when inflow velocity is slowly increasing. At later times of flow evolution, however, the well–mixed fluid accumulates and the flow enters a statistically steady hydraulic–like regime which is characterized by a constant mean drag exerted by the topography on the flow even while the inflow velocity slowly decreases.

Starting vortex dipoles in a viscous fluid: Asymptotic theory, numerical simulations, and laboratory experiments

Translational velocity of the starting vortex dipoles generated by the continuous or impulsive action of a localized force is obtained theoretically on simple physical grounds. Solutions of the diffusion equation for vorticity which take into account the translational motion of fluid particles are then obtained and compared with the results of direct numerical simulations of vortex dipoles as well as with the laboratory experiments. The comparison shows good quantitative agreement in both cases. Theoretical results for the translational velocity of the three-dimensional (axisymmetric) flows such as starting jets or vortex rings are discussed as well.

On the origin of jets in the ocean

We show a mechanism whereby the jets result during the development of β-plumes (i.e., low-frequency Rossby waves that establish gyre circulations) in a model of ocean-basin circulation. The energy originates in baroclinic meanders of circulation at the eastern boundary of the ocean. Eddies are intimately related and occur as a result of the instability of this process. This mechanism does not rely on the existence of the small-scale turbulence to establish zonal flows. Zonal jets can then be amplified by eddies arranged in certain order in the flow. The underlying dynamics include the propagation of linear and nonlinear basin scale Rossby waves. The related barotropic theory for these waves is developed here. We demonstrate the radiative development of jets and β-plumes in a laboratory experiment using a rotating fluid with a paraboloidal free surface. The dynamical fields are measured by the laboratory analog of the satellite altimetry.

Experiments on the evolution of gravitational instability of an overturned, initially stably stratified fluid

Unstable density stratifications were created in the laboratory by rapid overturning of a narrow tank containing an initially stable density structure. The experiments were carried out for two different initial density distributions: (i) a two‐layer (steplike) and (ii) a linear stratification. For the former case the depth of the mixing layer was found to increase linearly with time. The number of convective elements (thermal‐like flow structures) present at the front of the mixing layer was observed to decrease with time, through the mechanism of subsequent pairing. In the case of an initially linear stratification the flow evolution is characterized by a number of distinct stages: different modes of instability emerge subsequently through the entire fluid column, leading to the formation of horizontal layers, which finally break up into thermal‐like convective flow structures.

Wakes behind towed and self-propelled bodies: Asymptotic theory

Solutions for the (steady or unsteady) wake flows induced by a localized single force or a force doublet in a uniform stream are obtained in Oseen approximation for two-dimensional (planar) as well as for three-dimensional (axisymmetric) flows. These solutions are compared with the steady solutions obtained previously by other authors in boundary layer approximation. The straightforward approach to the general problem of the flow induced by any distribution of localized forces which was developed here, can be used to obtain the vorticity and stream function distributions for the flows generated by forcing of more complicated spatial symmetry in both two and three dimensions.

Formation of vortex dipoles

Evolution of a two-dimensional flow induced by a jet ejected from a nozzle of finite size is studied experimentally. Vortex dipole forms at the front of the developing flow while a trailing jet establishes behind the dipole. The dynamics of the flow is discussed on the basis of detailed measurements of vorticity and velocity fields which are obtained using particle image velocimetry. It is found that dipoles do not separate (pinch-off) from the trailing jet for values of the stroke ratio up to 15, which fact can be contrasted with the behavior of vortex rings reported previously by other authors. A characteristic time scale that is defined differently from the formation time of vortex rings can be introduced. This time scale (startup time) indicates the moment when the dipole starts translating after an initial period when it mainly grows absorbing the jet from the nozzle. A simple model that considers the competing effects of expansion and translation is developed to obtain an estimate of the dimensionle...

Three-dimensional instability of anticyclonic swirling flow in rotating fluid: Laboratory experiments and related theoretical predictions

We present results from a new series of experiments on the geophysically important issue of the instability of anticyclonic columnar vortices in a rotating fluid in circumstances such that the Rossby number exeeds unity. The core of the vortex is modeled as a solid cylinder rotating in a fluid that is itself initially in a state of solid-body rotation. When the cylinder rotates cyclonically the flow induced by the differential rotation is stable except for a brief initial period. When the cylinder rotates anticyclonically, however, intense perturbations spontaneously appear and amplify in the flow. The experimental results demonstrate that secondary motions appear in an annular region of finite width surrounding the cylinder (in accord with the prediction of the generalized Rayleigh criterion) and are governed by the process of three-dimensional centrifugal instability. These motions are characterized by a definite wave number in the coordinate direction parallel to the axis of the cylinder. Both the widt...