Journal
JOURNAL OF FLUID MECHANICS
Volume 823, Issue -, Pages -Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2017.348
Keywords
compressible boundary layers; turbulence modelling; turbulent boundary layers
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Funding
- Netherlands Organisation for Scientific Research (NWO) [SSH-223-13]
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We derive an alternative formulation of the turbulent kinetic energy equation for flows with strong near-wall density and viscosity gradients. The derivation is based on a scaling transformation of the Navier-Stokes equations using semi-local quantities. A budget analysis of the semi-locally scaled turbulent kinetic energy equation shows that, for several variable property low-Mach-number channel flows, the 'leading-order effect' of variable density and viscosity on turbulence in wall bounded flows can effectively be characterized by the semi-local Reynolds number. Moreover, if a turbulence model is solved in its semi-locally scaled form, we show that an excellent agreement with direct numerical simulations is obtained for both low- and high-Mach-number flows, where conventional modelling approaches fail.
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