Boundary layers in turbulent vertical convection at high Prandtl number

Abstract

Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with differentially heated walls to investigate such convective, turbulent boundary layers. Through the implementation of a multiple-resolution technique, we are able to perform simulations at a wide range of Prandtl numbers ${Pr}$ . This allows us to distinguish the parameter dependences of the horizontal heat flux and the boundary layer widths in terms of the Rayleigh number $\mbox {{Ra}}$ and Prandtl number ${Pr}$ . For the considered parameter range $1\leq {Pr} \leq 100$ , $10^{6} \leq \mbox {{Ra}} \leq 10^{9}$ , we find the flow to be consistent with a ‘buoyancy-controlled’ regime where the heat flux is independent of the wall separation. For given ${Pr}$ , the heat flux is found to scale linearly with the friction velocity $V_\ast$ . Finally, we discuss the implications of our results for the parameterisation of heat and salt fluxes at vertical ice–ocean interfaces.

Double-diffusive transport in multicomponent vertical convection

“…In this case, the Nusselt number ratio is R ∼ Le 1/3 . Since this scaling argument is consistent with the single-component VC results of [22], it should be valid at Le = 1, where we know that R = 1. For the scaling's range of validity, there should therefore be no pre-factor and we get R = Le 1/3 .…”

“…This can be explained by our previous finding in [22] that the scalar flux in vertical convection at moderate Rayleigh number and high Schmidt number is consistent with N u C ∼ Re τ Sc 1/3 . Such a scaling with Sc is more widely applicable in high Schmidt number turbulent boundary layers [31], where the Sc 1/3 factor arises due to the scalar boundary layer being nested within the viscous sublayer [32].…”

“…Here g is gravitational acceleration, which acts in the z-direction, ν is the kinematic viscosity, and κ T and κ C are the molecular diffusivities of heat and salt respectively. We consider a domain of length 8H in the vertical direction (z) and 4H in the spanwise direction (y), and impose periodic boundary conditions along these axes, as in our previous single component study [22].…”

“…Rather than fixing the fluid properties to realistic values, in order to better understand the physical mechanisms, we vary the Schmidt number and Lewis number and systematically investigate how the fluxes depend on the dimensionless control parameters of the system. This study builds on our previous work on VC at high Prandtl number [22]. As in that study, we use a multiple-resolution technique to perform large threedimensional simulations with low-diffusivity scalars at a reduced computational cost.…”

Interaction of Vertical Convection with an Electromagnetically Forced Flow

“…The main interest of his work was in studying heat transport through double layer windows. Later, a number of works on the VC topic mainly for air or water was done [5,[11][12][13][14][15][16][17][18].…”