City Research Online

Abstract

For decades there has been considerable interest in flows which can become convectively unstable due to differential diffusion in thermohaline convection. We consider the stability of the steady motion of a stably stratified fluid in an infinite vertical slot generated by a temperature difference across the boundaries. In particular, we are interested in the case where the instabilities are affected by a vertical salt gradient, where salt diffuses more slowly than heat.

The disturbances at marginal instability when a salinity gradient in a slot was subject to differential heating were previously examined by Thangam, Zebib & Chen (1981). We attempt to re-produce their results for the stability boundary using two independent numerical approaches, the Runge-Kutta scheme and the Galerkin method. Our results indicate there are various instability regimes in the linear analyses and most are stationary except for one small curved section on the stability boundary that gives oscillatory solutions. Our results also show that the oscillatory solutions reported by Thangam et al. are erroneous. This is confirmed by Young & Rosner (1998) in their recent paper.

We have identified four different asymptotic regimes on the stability boundary. One of these, the limit of a strong salinity gradient, has previously been analysed by Thorpe, Hutt & Soulsby (1969). Other asymptotic regimes including the limits of small wave number, large thermal Rayleigh number and weak salinity gradient are also analysed. These four cases represent almost the entire boundary that separates the stable and unstable modes for double- diffusive instabilities in a vertical slot.

Publication Type:	Thesis (Doctoral)
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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