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Abstract: The Leray-$\alpha$ model reduces the range of active scales of theNavier-Stokes equations by smoothing the advective transport. Here we assessthe potential of the Leray-$\alpha$ model in its standard formulation tosimulate wall-bounded flows. Three flow cases are considered: plane channelflow at $\Re \tau=590$, Rayleigh-B\-{e}nard convection at $\Ra=10^7$ and$\Pr=1$, and a side-heated vertical channel at $\Ra=5 \times 10^6$ and$\Pr=0.7$. The simulations are compared to results from a well resolved andcoarse DNS. It is found that for all three flow cases, the variance in thevelocity field increases as the filter width parameter $a$ is increased, where$a$ is connected to the filter width as $\alpha i = a \Delta x i$, with $\Deltax i$ the local grid size. Furthermore, the viscous and diffusive wall regionstend to thicken relative to the coarse DNS results as a function of $a$. In thecases where coarse DNS overpredicts wall gradients as for Rayleigh-B\-{e}nardconvection and the side-heated vertical channel, the thickening is beneficial.However, for the plane channel flow, coarse DNS underpredicts the wall-shearvelocity, and increasing $a$ only degrades the results. It is shown thatbuoyancy effects need to be included with care, because of the close relationof turbulent heat flux and the production of turbulent kinetic energy.

Author: Maarten van Reeuwijk, Harm J.J. Jonker, Kemo Hanjalic

Source: https://arxiv.org/

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