Interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex

Abstract

This paper focuses on the nonlinear interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a sub-surface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in Kelvin-Helmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective 'self'-energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs -termed "cooperative" and "adverse" shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive.

Interaction between a Quasi-Geostrophic Buoyancy Filament and a Heton

“…The billows are more regular in case 6.4 since the filament here is twice as intense. The appearance of approximately five billows is one less than expected from the linear stability analysis of a strip in isolation [23]. A monochromatic wave with wavenumber k = 5 (corresponding to ka = 0.625) has a growth rate σ 0.085b * m /a, while wavenumber k = 6 (corresponding to ka = 0.75) has a slightly large growth rate, σ 0.088b * m /a.…”

“…This rotates the direction of propagation of the heton by more than 90 • , and causes it to reverse direction but not before it has crossed below the original location of the filament. Notably, as the heton passes below the filament, it traps part of it and extends the trailing filament, which then is even more unstable [23,32]. This results in the formation of a string of small but intense billows trailing behind the heton.…”

“…Besides the vortex separation effect studied above, now the external velocity field of the heton deforms the surface filament. The buoyancy filament is known to be unstable, see [20][21][22][23]32]. In particular, Reinaud et al (2016) have shown that the fastest growing mode for a filament having a basic-state buoyancy profile b * (x) = b * m √ 1 − x 2 /a 2 occurs at the dimensionless longitudinal wavenumber ka = 0.729 with growth rate σ = 0.089b * m /a.…”

“…Conversely, for a heton moving away from the filament, the vortex nearer the surface must be in cooperative horizontal shear. Previous studies have shown that adverse horizontal shear is significantly more disruptive than cooperative shear [23,34,35]. Hence, a heton which moves towards a surface filament is likely to undergo significant deformation and, in some cases, even partial destruction.…”

“…This distribution induces a uniform horizontal shear, λ = b * m /a, at the surface for −a < x < a, (see [23]). Next, a heton is placed in the interior of the computation domain.…”