The background method is a widely used technique to bound mean properties of turbulent
flows rigorously. This work reviews recent advances in the theoretical formulation and …

The calculus of variations is employed to find steady divergence-free velocity fields that
maximize transport of a tracer between two parallel walls held at fixed concentration for one …

This paper presents a research for Marangoni convection driven by a power-law
temperature gradient. It is assumed that the surface tension is quadratic functions of the …

We study the melting dynamics of a phase change material by the action of thermocapillary
driving. The geometry corresponds to squares and rectangles with a top free flat surface. We …

The background method has been a successful tool in obtaining strict bounds on global
quantities such as the rate of energy dissipation and heat transfer in turbulent flows …

The vertical heat transfer in Bénard–Marangoni convection of a fluid layer with infinite
Prandtl number is studied by means of upper bounds on the Nusselt number is optimal …

In this paper, we use the well-known background method to obtain a rigorous lower bound
on the volume flow rate through a helical pipe driven by a pressure differential in the limit of …

We introduce an innovative numerical technique based on convex optimization to solve a
range of infinite-dimensional variational problems arising from the application of the …

Turbulence is ever-present: from flows in engineering, such as a wake behind a submarine,
the boundary layer over an aircraft wing, and the swirl in an internal combustion engine, to …

We prove a new rigorous upper bound on the vertical heat transport for Bénard–Marangoni
convection of a two-or three-dimensional fluid layer with infinite Prandtl number. Precisely …