ENERGY STABILITY BOUNDS ON CONVECTIVE HEAT-TRANSPORT - NUMERICAL STUDY

The concept of nonlinear energy stability has recently been extended t o deduce bounds on energy dissipation and transport in incompressible flows, even for turbulent flows. In this approach an effective stabili ty condition on ''background'' flow or temperature profiles is derived , which when satisfied ensures that the profile produces a rigorous up per estimate to the bulk dissipation. Optimization of the test backgro und profiles in search of the lowest upper bounds leads to nonlinear E uler-Lagrange equations for the extremal profile. In this paper, in th e context of convective heat transport in the Boussinesq equations, we describe numerical solutions of the Euler-Lagrange equations for the optimal background temperature and present the numerical computation o f the implied bounds.