Camilla Nobili University of Surrey

Scaling laws in turbulent convection


Scaling laws are a useful tool in studying and characterizing geo-physical flows as they may indicate their behaviour in extreme parameter regimes which are unapproachable by experiments. In particular, the challenge of finding scaling laws requires synergetic efforts involving laboratory, computational, and theoretical studies. In fact, deducing and calibrating scaling laws requires physical arguments, analytical bounding arguments, numerical simulations and experiments. We will focus on convection problems as they are a relevant in a multitude of natural phenomena in meteorology, oceanography and industrial applications. In this seminar we are interested in rigorously proving power law scalings for the heat transport, as measured by the nondimensional Nusselt number Nu for the Rayleigh-Bénard convection problem. In this specific case the scaling laws have the functional form Nu ∼ Raα, where Ra is the thermal driving of the system. We will present the latest rigorous upper bounds on the Nusselt number for flows subject to various boundary conditions (no-slip, free-slip and Navier-slip) in flat and rough domains. In particular we will show how to substantially simplify arguments used in the seminal works of Doering and Constantin in the 90's and improve bounds.