An analytical turbulence modeling based on the double-Lagrangian formalism

Abstract

An analytical approach to turbulence modeling based on the double-Lagrangian formalism is applied to turbulence modeling. Extending a selfconsistent closure theory of homogeneous turbulence, current approach allows us to derive a quadratic nonlinear viscosity form of the Reynolds stress without relying on empirical parameters. To examine the future possibility of the present methodology as practical modeling approach, a simple non-linear K -ε model is constructed, which is then applied to turbulent channel flow at a medium Reynolds number (Re = 590). With the help of conventional modeled equations for K and ε, the channel turbulence is stably calculated yielding reasonable agreements with a DNS.

Keywords

• turbulence shear flow
• homogeneous turbulence
• renormalization
• lagrangian formalism
• turbulence modeling