# Turbulent force as a diffusive field with vortical sources

## Abstract

In Reynolds-average Navier-Stokes equation it is the divergence of Reynolds stress tensor, i.e., the turbulent force, rather than the tensor itself, is to be simulated and partially modeled. Thus, directly working on turbulent force could bring significant simplification. In this paper a novel exact equation for incompressible turbulent force f is derived: (∂l∂t - ν∇2)f=∇·S, where ν is the molecular viscosity and all source terms in tensor S to be modeled are vortical. The dominant mechanism is the advection and stretching (with an opposite sign) of a "pseudo-Lamb vector" by fluctuating velocity field. No coupling with pressure is involved. The equation follows from a study of the mean fluctuating Lamb vector and kinetic energy, which constitute the turbulent force. Both constituents are governed by the same kind of equations as f. This innovative turbulent-force equation is similar to Lighthill's acoustic analogy and naturally calls one's attention to studying the vortical sources of turbulent force. The methodology described here may lead to turbulence models which provide more complete treatment than that of two-equation models, but relatively easier computation than that of second-order closures. © 1999 American Institute of Physics.