Camilla Nobili University of Surrey
Scaling laws in turbulent convection
Abstract:
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.