On the variational problem for the upper bounds of solute transport in double-diffusive convection

TL;DR

This paper discusses variational formulations for bounding solute transport in double-diffusive convection, showing how a generalized functional improves bounds at moderate Rayleigh numbers and converges to Strauss's approximation at large Rayleigh numbers.

Contribution

It introduces a generalized variational functional that provides more accurate upper bounds for solute transport at small and intermediate Rayleigh numbers, extending previous Strauss's approach.

Findings

General functional yields accurate bounds at small/intermediate Rayleigh numbers.

Functional converges to Strauss's approximation at large Rayleigh numbers.

Guidelines for choosing the appropriate functional based on Rayleigh number.

Abstract

The formulation of the variational problems for the solute transport in a fluid layer in presence of double-diffusive thermal convection is discussed. It is shown that the variational functional obtained by Strauss can be generalized and the general functional leads to accurate upper bounds on the solute transport for the case of small and intermediate values of the Rayleigh number. The general functional however is a non-homogeneous one but for asymptotically large Rayleigh numbers it converges to the Strauss approximation. Thus for small and intermediate values of the Rayleigh numbers one should use the general functional and for vary large values of the Rayleigh numbers one can use the functional of Strauss.