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Bénard convection; boundary layer structure; turbulent convection
Abstract:
The kinetic energy balance in Rayleigh–Bénard convection is investigated by means
of direct numerical simulations for the Prandtl number range 0.01 <= Pr <= 150 and for
fixed Rayleigh number
Ra 5x10^6. The kinetic energy balance is divided into a
dissipation, a production and a flux term. We discuss the profiles of all the terms and
find that the different contributions to the energy balance can be spatially separated
into regions where kinetic energy is produced and where kinetic energy is dissipated.
By analysing the Prandtl number dependence of the kinetic energy balance, we show
that the height dependence of the mean viscous dissipation is closely related to
the flux of kinetic energy. We show that the flux of kinetic energy can be divided
into four additive contributions, each representing a different elementary physical
process (advection, buoyancy, normal viscous stresses and viscous shear stresses).
The behaviour of these individual flux contributions is found to be surprisingly rich
and exhibits a pronounced Prandtl number dependence. Different flux contributions
dominate the kinetic energy transport at different depths, such that a comprehensive
discussion requires a decomposition of the domain into a considerable number of
sublayers. On a less detailed level, our results reveal that advective kinetic energy
fluxes play a key role in balancing the near-wall dissipation at low Prandtl number,
whereas normal viscous stresses are particularly important at high Prandtl number.
Finally, our work reveals that classical velocity boundary layers are deeply connected
to the kinetic energy transport, but fail to correctly represent regions of enhanced
viscous dissipation.
