J. Fluid Mech. (2002), vol. 459, pp. 139–166. c  2002 Cambridge University Press DOI: 10.1017/S0022112002007905 Printed in the United Kingdom 139 A new approach to modelling near-wall turbulence energy and stress dissipation By S. JAKIRLI ´ C 1 AND K. HANJALI ´ C 2 1 Institute of Fluid Mechanics and Aerodynamics, Darmstadt University of Technology, Petersenstr. 30, 64287 Darmstadt, Germany 2 Faculty of Applied Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands (Received 1 August 2000 and in revised form 29 October 2001) A new model for the transport equation for the turbulence energy dissipation rate ε and for the anisotropy of the dissipation rate tensor ε ij , consistent with the near- wall limits, is derived following the term-by-term approach and using results of direct numerical simulations (DNS) for several generic wall-bounded flows. Based on the two-point velocity covariance analysis of Jovanovi´ c, Ye & Durst (1995) and reinterpretation of the viscous term, the transport equation is derived in terms of the ‘homogeneous’ part ε h of the energy dissipation rate. The algebraic expression for the components of ε ij was then reformulated in terms of ε h , which makes it possible to satisfy the exact wall limits without using any wall-configuration parameters. Each term in the new equation is modelled separately using DNS information. The rational vorticity transport theory of Bernard (1990) was used to close the mean curvature term appearing in the dissipation equation. A priori evaluation of ε ij , as well as solving the new dissipation equation as a whole using DNS data for quantities other than ε ij , for flows in a pipe, plane channel, constant-pressure boundary layer, behind a backward- facing step and in an axially rotating pipe, all show good near-wall behaviour of all terms. Computations of the same flows with the full model in conjunction with the low-Reynolds number transport equation for u i u j , using ε h instead of ε, agree well with the direct numerical simulations. 1. Introduction The transport equation for the turbulence energy dissipation rate ε = ν ∂u i ∂x k ∂u i ∂x k has been widely used to close single-point k − ε eddy-viscosity and second-moment (Reynolds stress transport) models.† Motivation for modelling and solving an equa- tion for ε comes from the fact that ε appears as the sole viscous sink in the transport equation for the turbulence kinetic energy, hence no need for modelling. Furthermore, the classic similarity theory (though valid only for equilibrium turbulence) suggests ε † Although ε does not represent the true dissipation rate τ ij s ij = 1 2 ν (∂u i /∂x j + ∂u j /∂x i ) 2 , where τ ij is the fluctuating viscous stress and s ij the fluctuating strain rate, in the viscous and inner turbulent region close to a smooth solid surface (and everywhere else) the difference term ν (∂ 2 u i u j /∂x i ∂x j ), representing an ‘extra’ viscous diffusion was found from DNS data for a channel flow to be less than 2% of the total dissipation, and hence, negligible (Bradshaw & Perot 1993).