Sergey I. Voropayev

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.

Grain sorting on sand ripples in heterogeneous sediments

Sand ripples are commonly observed coastal benthic features that form under the action of waves/currents. In most previous studies of ripple dynamics homogeneous sand was used (see, e.g., Testik et al., 2005 and references herein)(1). In nature, sands are mostly heterogeneous. In the figures above we give an example of typical grain sorting as observed in a bimodal sand mixture under steady oscillatory flow in a water channel. The mixture consists of 34 % of fine sand (d = 0.3 mm, blue) and 66 % of course sand (d = 0.6 mm, brown). Initially flat (Fig. 1), sand mixture is subject to oscillatory flow (from left to right). With time, established ripples are formed (Figs. 2 and 3) with typical sediment segregation pattern: fine grains (blue) are mostly seen on the ripple troughs with very narrow strips on the tops of the crests; coarse grains (brown) are seen mostly on the ripple crests.

HORIZONTAL JETS IN A ROTATING STRATIFIED FLUID

A horizontal jet emerging continuously from a small round nozzle (concentrated source of momentum) in a rotaing stratified fluid is investigated using laboratory experiments. The jet either (i) deflects from the direction of injection, forming an anticyclonic spiral monopole (monopole regime), or (ii) propagates along the injection direction, forming a dipolar structure (dipole regime). Which of these characteristic flows occurs depends on the system parameters, the Reynolds number Re, and the buoyancy frequency to Coriolis parameter ratio N/f; a flow regime diagram is developed for the parameter ranges 40≲ Re≲200 and 0≲N/f≲35, respectively. A theoretical analysis is advanced to explain the conditions under which the monopole and dipole regimes occur, including the transition curve between the two regimes. The theory is supported by laboratory experiments. Some geophysical examples of the considered flows are discussed.

Formation of vorticity fronts in shear flow

When a cylindrical laminar jet flowing into a resting fluid of the same density has its transport increased to another steady value, an axisymmetric convergence forms between the fast and slow streams. The free boundary surrounding the jet deforms with time, and a steeply sloping vorticity front forms at the nose of the convergent region. This propagates with a speed equal to the average signal velocity (for infinitesimal amplitude disturbances) associated with the laminar flow on either side of the convergence, according to a locally consistent ‘‘shock’’ joining condition which supplements a previous long‐wave theory. The prediction is verified by observations of a dyed jet issuing from a round nozzle at Reynolds numbers of approximately 102. It is suggested that the vorticity frontogenesis effect is also important in the turbulent flow over a flat plate.

On the frontal collision of two round jets in water

In our experiment two laminar round jets collide in water forming a zero-momentum toroidal vortex and this flow is modeled theoretically. First, the linearized time dependent basic solution for the starting round jet is derived in a straightforward manner. Then a superposition of these solutions is used to model the frontal collision of two round jets. The resulting flow patterns are calculated and compared with the experiments. The comparison shows good qualitative agreement.

Evolution of a confined turbulent jet in a long cylindrical cavity: Homogeneous fluids

The flow induced in a long cylinder by an axially discharging round turbulent jet was investigated experimentally with applications to crude oil storage in the U.S. strategic petroleum reserves (SPR). It was found that the flow does not reach a true steady state, but vacillates periodically. Digital video recordings and particle image velocimetry were used to map the flow structures and velocity/vorticity fields, from which the frequency of jet switching, jet stopping distance, mean flow, turbulence characteristics, and the influence of end-wall boundary conditions were inferred. The results were parameterized using the characteristic length D and velocity J1/2/D scales based on the jet kinematic momentum flux J and cylinder width D. The scaling laws so developed could be used to extrapolate laboratory observations to SPR flows.

Experiment on the Self-Propagating Quasi-Monopolar Vortex

Abstract The aim of this contribution is to present the results of laboratory experiments on the dynamics of basic self-propagating vortices generated in a large volume of fluid when a linear (P) and an angular (M) momentum are applied locally to a fluid. Using the method proposed, it is possible to generate a whole family of isolated (net vorticity is equal to zero) vortices with different values of the nondimensional parameter e, which is proportional to the ratio of linear to angular momentum (e ∝ RP/M, R is the eddy size). Typical examples include monopole (e = 0), quasi monopole (e = 0.1–0.3), quasi dipole (e ≈ 1), and dipole (e = ∞). One of the possible applications is the dynamics of oceanic eddies. Recently, Stern and Radko considered theoretically and numerically a symmetric barotropic eddy, which is subject to a relatively small amplitude disturbance of unit azimuthal wavenumber on an f plane. This case corresponds to a self-propagating quasi monopole. They analyzed the structure of the eddy and...

Flat Vortex Structures in a Stratified Fluid

Abstract When a horizontal force is applied locally to some volume of a viscous, density stratified fluid, three-dimensional flows with high concentration of vertically oriented vorticity are easily generated. A convenient way to produce and to study such flows in the laboratory is to use a submerged horizontal round jet as a “point” source of momentum. The main governing parameter (the force) is easily controlled in this case. The results of such experiments are presented. Two regimes are studied: developing jets with vortex front (the force acts continuously) and isolated vortex couples (the force acts for a short period of time). It is found that in both, regimes the flows are self-similar; the fluid “forgets” the initial details of motion near the origin and the length scale of the flows increases with time as t 1/2 for developing jets and as t 1/3 for vortex couples. Detailed information on these flows is presented. Some qualitative experiments were made to study the interactions between vortex couples. It is found that vortex couples can split and penetrate each other in a soliton-like manner. Theoretical explanations of the experimental results are given. The theory is in a good agreement both with the results of the laboratory experiments and with ocean data obtained through remote sensing of the upper ocean.

Thermal surface signatures of ship propeller wakes in stratified waters

When a ship moves in temperature stratified water, e.g., in the ocean diurnal thermocline, the propeller(s) as well as the turbulent boundary layer of the hull mix the surface water with underlying colder fluid. As a result, when observed from above, a temperature “wake signature” of ∼1–2 °C may be detected at the water surface. To quantify this phenomenon, theoretical modeling and physical experiments were conducted. The dominant processes responsible for thermal wake generation were identified and parameterized. Most important similarity parameters were derived and estimates for wake signature contrast were made. To verify model predictions, scaled experiments were conducted, with the water surface temperature measured using a sensitive infrared camera. Comparison of laboratory measurements with model estimates has shown satisfactory agreement, both qualitative and quantitatively. Estimates for ocean ship-wake scenarios are also given, which are supported by available field observations.