Spectral transform simulations of finite amplitude double-diffusive instabilities in two dimensions
Simulations of double-diffusion with a two-dimensional, vertical plane spectral transform model reveal details of finite amplitude behavior in salt finger, interleaving and diffusive instabilities. Within the range of fluid parameters studied (3 < σ < 10, .1 < r < .5), infinite, fastest-growing fingers are unstable to Holyer's (1984) nonoscillatory instability and are completely disrupted by it. Finite fingers localized on density steps are also disrupted. Initialized density steps are eroded (the gradients reduced). Fluxes and other diagnostic quantities were determined for salt finger fields at statistical stationarity. These fields contain transitory, irregular finger structures. Fluxes decline steeply as Rfp increases. A single point of comparison of buoyancy flux with ocean measurement yielded good agreement. The dependence of flux ratio on the stability parameter is similar to the linear theory prediction for fastest-growing, infinite fingers and does not increase as Rfp approaches 1, in contrast to laboratory measurements. Holyer's (1984) Floquet theory is extended to the case of nonzero, density compensating, horizontal gradients, and, together with the simulation results, encourages the interpretation of the interleaving instability as being sloping salt fingers. A few preliminary simulations of the diffusive regime indicate very complex behavior. A growing oscillatory perturbation can lead to subcritical convective instability. Such motions sharpen initialized density steps. In the presence of a step, unstable motions are supported even when the fluid is linearly stable to both convection and the diffusive mode.
Whitfield, D. W., G. Holloway, and J. Y. Holyer. 1989. "Spectral transform simulations of finite amplitude double-diffusive instabilities in two dimensions." Journal of Marine Research 47, (2). https://elischolar.library.yale.edu/journal_of_marine_research/1929