On the variational problem for the upper bounds of solute transport in   double-diffusive convection
  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. 
Nikolay Vitanov and Zlatinka Dimitrova
physics.flu-dyn