Abstract
Turbulent flows in which all mean (time-averaged) values of functions of the fluctuating velocity field are independent of orientation are said to be “statistically isotropic” (Taylor [1]). The macroscopic motion of turbulent flows in which the turbulence is approximately isotropic seem to be well predicted by the so-called k-ε theory, in which the turbulent fluid at the macroscopic scale is assumed to obey the usual Navier-Stokes equations but the viscosity is allowed to vary as a function of the additional “turbulence variables” k and ε. Here, k denotes the “turbulent kinetic energy” per unit mass and ε denotes the “rate of turbulent energy dissipation.” Additional transport equations for k and ε are posed, both of which are similar in form to the usual energy conservation equation. Alternative, but similar, theories of isotropic turbulence have been constructed using the “mixing length” ℓ (Launder and Spalding [2]) or a microscopic “vorticity” scalar ω (Saffman [3]) instead of ε, where these variables are related to k and ε according to ω∝ ε/k and ℓ ∝k 3/2 /ε.
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Dedicated to Paul M. Naghdi on the occasion of his 70th birthday
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© 1995 Birkhäuser Verlag Basel/Switzerland
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Marshall, J.S. (1995). A structural theory of anisotropic turbulence. In: Casey, J., Crochet, M.J. (eds) Theoretical, Experimental, and Numerical Contributions to the Mechanics of Fluids and Solids. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9229-2_38
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DOI: https://doi.org/10.1007/978-3-0348-9229-2_38
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