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Dynamic roughness model for large-eddy simulation of turbulent flow over multiscale, fractal-like rough surfaces

Published online by Cambridge University Press:  03 May 2011

W. ANDERSON  and
C. MENEVEAU
W. ANDERSON
Affiliation:
Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, the Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
C. MENEVEAU*
Affiliation:
Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, the Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
*
†Email address for correspondence: meneveau@jhu.edu
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Abstract

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Many flows especially in geophysics involve turbulent boundary layers forming over rough surfaces with multiscale height distribution. Such surfaces pose special challenges for large-eddy simulation (LES) when the filter scale is such that only part of the roughness elements of the surface can be resolved. Here we consider LES of flows over rough surfaces with power-law height spectra Eh(k) ~ kβs (−3 ≤ βs < −1), as often encountered in natural terrains. The surface is decomposed into resolved and subgrid-scale height contributions. The effects of the unresolved small-scale height fluctuations are modelled using a local equilibrium wall model (log-law or Monin–Obukhov similarity), but the required hydrodynamic roughness length must be specified. It is expressed as the product of the subgrid-scale root-mean-square of the height distribution and an unknown dimensionless quantity, α, the roughness parameter. Instead of specifying this parameter in an ad hoc empirical fashion, a dynamic methodology is proposed based on test-filtering the surface forces and requiring that the total drag force be independent of filter scale or resolution. This dynamic surface roughness (DSR) model is inspired by the Germano identity traditionally used to determine model parameters for closing subgrid-scale stresses in the bulk of a turbulent flow. A series of LES of fully developed flow over rough surfaces are performed, with surfaces built using random-phase Fourier modes with prescribed power-law spectra. Results show that the DSR model yields well-defined, rapidly converging, values of α. Effects of spatial resolution and spectral slopes are investigated. The accuracy of the DSR model is tested by showing that predicted mean velocity profiles are approximately independent of resolution for the dynamically computed values of α, whereas resolution-dependent results are obtained when using other, incorrect, α values. Also, strong dependence of α on βs is found, where α ranges from α ~ 0.1 for βs = −1.2 to α ~ 10−5 for βs = −3.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 679 , 25 July 2011 , pp. 288 - 314
Copyright
Copyright © Cambridge University Press 2011

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