Double-Diffusive Interleaving: The Influence of Nonconstant Diffusivities

Abstract

The influence of nonconstant diffusivity and viscosity on double-diffusive interleaving is examined using a simple model. The analysis allows a prediction of the slope, vertical wavenumber, and growth rate of the fastest-growing interleaving mode for specified background gradients of salinity and temperature. Allowing the salt diffusivity to be a function of the density ratio Rp leads to a larger growth rate and a lower vertical wavenumber than in the constant diffusivity case considered by Toole and Georgi, while the cross-front slope of the intrusions is essentially unaffected. The nonconstant viscosity included in the model formulation is found to have no effect on the form of the solutions. The larger vertical scales and growth rates predicted by the model can be traced to an enhanced ?effective diffusivity? resulting from the diffusivity gradients associated with the growing intrusions. A transformation is found that converts the system with generalized diffusivities examined here to the simpler system considered by Toole and Georgi.