Vortex generation by line plumes in a rotating stratified fluid

Abstract

We present the results of an experimental investigation of the generation of coherent vortical structures by buoyant line plumes in rotating fluids. Both uniform and stratified ambients are considered. By combining the scalings describing turbulent plumes and geostrophically balanced vortices, we develop a simple model which predicts the scale of the coherent vortical structures in excellent accord with laboratory experiments.

We examine the motion induced by a constant buoyancy flux per unit length B, released for a finite time t_s, from a source of length L into a fluid rotating with angular speed Ω = f/2. When the plume discharges into a uniformly stratified environment characterized by a constant Brunt–Väisälä frequency, N>f, the fluid rises to its level of neutral buoyancy unaffected by the system rotation before intruding as a gravity current. Rotation has a strong impact on the subsequent dynamics: shear develops across the spreading neutral cloud which eventually goes unstable, breaking into a chain of anticyclonic lenticular vortices. The number of vortices n emerging from the instability of the neutral cloud, n = (0.65±0.1)Lf^1/2/ (t^1/2_sB^1/3), is independent of the ambient stratification, which serves only to prescribe the intrusion height and aspect ratio of the resulting vortex structures. The experiments indicate that the Prandtl ratio characterizing the geostrophic vortices is given by P = Nh/(fR) = 0.47±0.12; where h and R are, respectively, the half-height and radius of the vortices. The lenticular vortices may merge soon after formation, but are generally stable and persist until they are spun-down by viscous effects.

When the fluid is homogeneous, the plume fluid rises until it impinges on a free surface. The nature of the flow depends critically on the relative magnitudes of the layer depth H and the rotational lengthscale L_f = B^1/3/f. For H>10L_f, the ascent phase of the plume is influenced by the system rotation and the line plume breaks into a series of unstable anticylonic columns of characteristic radius (5.3±1.0)B^1/3/f which typically interact and lose their coherence before surfacing. When H<10L_f, the system rotation does not influence the plume ascent, but does control the spreading of the gravity current at the free surface. In a manner analogous to that observed in the stratified ambient, shear develops across the surface current, which eventually becomes unstable and generates a series of anticyclonic surface eddies with characteristic radius (1.6±0.2)B^1/3t^1/3_s /f^2/3. These surface eddies are significantly more stable than their columnar counterparts, but less so than the lenticular eddies arising in the uniformly stratified ambient.

The relevance of the study to the formation of coherent vortical structures by leads in the polar ocean and hydrothermal venting is discussed.