Double-Diffusive Interleaving. Part I: Linear Stability Analysis

Abstract

Quasi-horizontal interleaving between water masses is frequently observed in the frontal regions between different water masses where there are significant compensating isopycnal gradients of temperature and salinity. It is believed that these intrusions are driven by double-diffusive convection which transports salt, heat and density across sharp, quasi-horizontal interfaces (i.e., across regions of large vertical property gradients). Stern and other investigators have parameterized the vertical flux of salt in these intrusions by an eddy diffusivity multiplied by the vertical gradient of salinity, whereas laboratory experiments show that sharp interfaces tend to occur by double-diffusive convection and that the vertical fluxes of properties depend on the property contrasts across the interfaces. In this paper it is assumed that the vertical fluxes of double-diffusive convection are proportional to the salinity contrast across the sharp interfaces that occur between the quasi-horizontal intrusions. The previous approaches had the fluxes proportional to this salinity difference divided by the height of the intrusions. It is shown that the results of the linear stability analysis are the same as those found by Toole and Georgi if their nondimensional vertical wavenumber is simply reinterpreted. In addition to finding the three wavenumbers of the fastest growing linear instability, the ratios of several of the growing perturbation quantities are also derived. It is shown that the fastest growing intrusions move directly across the front with zero velocity component in the alongfront direction. The only effect of rotation is to introduce an alongfront tilt to he instrusions: the wavenumbers, velocity components and the growth rate are all shown to be independent of the rotation rate. The instantaneous (synoptic) ratio of the changes of potential temperature and salinity along any particular intrusion is also derived and is found to be much nearer to 1 (with a typical value of 0.9) than to the buoyancy flux ratio γf of salt fingers. The ratios of the exponentially growing quantities provide further quantities to be compared with oceanographic and laboratory observations and so test the model.