Double-Diffusive Interleaving in the Presence of Turbulence: The Effect of a Nonconstant Flux Ratio

Abstract

The influence of turbulent mixing on double-diffusively driven thermohaline interleaving is investigated. The problem is formulated using a turbulence-modified flux ratio to link the fluxes of T and S; the addition of turbulence changes the way in which the effective flux ratio varies with the density ratio R?. Formulation of the problem maps onto past interleaving studies, except that the flux ratio is a function of R? in the present work. Posing the problem in this way allows the effects of turbulence and intrinsic variations in the salt-finger flux ratio to be studied within the same theoretical framework. Turbulence modifies the slope, wavelength, and growth rate of the fastest-growing intrusions, decreasing the range of slopes and wavenumbers that can grow. However, analysis shows that growing solutions exist for any finite value of the turbulent diffusivity Kt, suggesting that double-diffusively driven intrusions can exist in the ocean even when double-diffusive fluxes are much weaker than turbulent fluxes. If the flux ratio is a decreasing function of R? (as suggested by some models of salt finger convection) a different instability occurs, which has unbounded growth rates in the high wavenumber limit (a ?UV catastrophe?). In most cases, the instability can be suppressed by the addition of sufficiently strong turbulent mixing. The threshold for this instability depends upon variation of the T/S flux ratio with R?, and hence on the relative strengths of turbulent and double-diffusive mixing. The instability is shown to be nonintrusive in nature, as it does not rely upon lateral advection across a front; it is found to be closely related to the one-dimensional double-diffusive instability investigated by Huppert.