Yakov D. Afanasyev

SPONTANEOUS EMISSION OF GRAVITY WAVES BY INTERACTING VORTEX DIPOLES IN A STRATIFIED FLUID: LABORATORY EXPERIMENTS

Results from a new series of experiments on the geophysically important issue of spontaneous emission of internal gravity waves during unsteady interactions of vortical structures are presented. Vortex dipoles are a common element of a quasi-two-dimensional turbulent flow. Vortex dipoles perform translational motion and can collide with other vortices. During collision events the flow is unsteady and unbalanced and a further adjustment process associated with these events can therefore result in the spontaneous emission of gravity waves. Our laboratory experiments demonstrate that gravity waves are emitted when two translating vortex dipoles interact (collide) in a layered fluid, in accord with the current theoretical results. The emission was evident both in a two-layer system and in a fluid with a linear distribution of density with depth. The waves were generated during the period of deceleration of the secondary dipoles which constitute a vortex quadrupole emerging immediately after the collision of the primary dipoles.

Rotating dipolar gyres on a γ-plane

Nonlinear dipolar vortices/gyres on a γ-plane are investigated both experimentally and theoretically. The solutions describe a fundamental dipolar mode of large scale barotropic motion of the polar ocean or atmosphere on the rotating planet. The entire dipolar gyre is predicted to rotate anticyclonically with a specific angular velocity. The existence and stability of the theoretically predicted flow are confirmed in a laboratory experiment on a rotating platform. The laboratory flows are induced by an electromagnetic method and are observed using the nonintrusive optical method of altimetric imaging velocimetry. The rotation rate of the experimental flow is in good agreement with that predicted theoretically. Detailed measurements of the velocity field and surface elevation demonstrate that an assumption of linearity of the relation between the relative vorticity and the stream function is valid.

Vortices and Rossby waves in cylinder wakes on a parabolic β-plane observed by altimetric imaging velocimetry

Intense vortices in the wake of a circular cylinder are investigated in a rotating parabolic (polar) β-plane fluid. This system has a background potential vorticity (PV) field that supports Rossby waves and causes vortices to migrate and radiate. A method for imaging rotating flows, which we call “altimetric imaging velocimetry” is employed. Optical color coding of slopes of the free-surface elevation field yields the pressure, geostrophic and gradient wind velocity, and potential vorticity fields with very high spatial resolution, limited largely by the pixel resolution of the available imaging sensors. Cylinder wakes on the polar β-plane exhibit strikingly different regimes as it is translated azimuthally, eastward or westward. Self-arrangement of vortices after the cylinder was stopped drives an intense eastward jet formed by the rows of anticyclones and cyclones on its flanks. In agreement with the idea of a PV staircase, this jet has a strong PV gradient at its center, while PV is homogenized by the ...

Flight in a viscous fluid: Asymptotic theory of the vortex wake

Solutions for the three-dimensional distributions of vorticity in the wake behind localized forces moving in a viscous fluid are obtained. The forces simulate the drag, thrust, and lift forces applied on the fluid by a flying animal such as a small insect. Concentrated vortex tubes in the wake are also illustrated in a visualization experiment where a “virtual” insect is modeled using the electromagnetic method of forcing.

Buoyancy storms in a zonal stream on the polar beta-plane: Experiments with altimetry

Results from a new series of experiments on flows generated by localized heating in the presence of a background zonal current on the polar β-plane are presented. The flow induced by a heater without the background zonal flow is in the form of a β-plume. Zonal jets of alternating directions are formed within the plume. The westward transport velocity in the plume is proportional to the upwelling velocity above the heater in agreement with linear theory. When the background flow in the form of the eastward zonal current is present, the β-plume can be overwhelmed by the eastward current. The main control parameters of the experiment are the strength of the heater and strength of the sink which is used to create the background flow. The regime diagram shows the area where a β-plume can exist in the parameter space. The critical value of the velocity of the zonal flow below which the β-plume can exist is obtained by considering barotropic Rossby waves emitted by the baroclinic eddies in the heated area.

Dipolar gyres generated by continuous forcing on a polar β-plane

Dipolar vortices generated by a force applied to an area of finite size are investigated in a rotating, polar β-plane fluid. The laboratory polar β-plane is dynamically equivalent to the polar regions of the ocean or the atmosphere where the Coriolis parameter varies quadratically with latitude. Both forced and unforced evolution of the flow is observed. The altimetric imaging velocimetry method is employed for imaging the rotating flows and measuring the velocity and surface elevation fields. The forced dipoles were observed to rotate in the anticyclonic direction from their initial orientation where the axis of the dipole is aligned with the direction of the force toward some steady state where the axis of the dipole is at an angle to the direction of the force. The theoretical prediction of the rotation angle is found to be in good agreement with the experimental results. Asymptotic solutions for limiting cases when forced dipoles are affected either by the Ekman-type bottom friction or by the γ-effect...

INTERACTIONS OF GRAVITY WAVES GENERATED BY A MOVING SOURCE WITH THE SHELF: LABORATORY EXPERIMENT

Rapidly moving storm crossing the shelf from shallow water to deep water can generate tsunami-like waves which can cause local flooding and damage to docks when the waves hit the coast. We report on laboratory experiments to examine the reflection of waves generated by a moving disturbance from the shelf. Experiments are performed in a two-layer fluid consisting of a layer of oil based ferrofluid lying on top of a layer of water with step bottom. The disturbance is generated by a permanent magnet moving above the surface of ferrofluid. Digital images of the flow are analyzed to obtain the evolution of the wave field. The experimental flows demonstrate two distinct regimes, namely subcritical when the speed of the magnet is less than the phase speed of the wave, and supercritical when the speed of the magnet is greater than the phase speed of the wave. In subcritical regime the disturbance is localized and its size is determined by the spatial extent of the forcing. In supercritical regime the waves form two beams extending at “Mach angle” with respect to the direction of motion. Oblique wave incident on the shelf can experience total reflection if the angle between the wave front and the shelf is greater than a critical value.Copyright