ASYMPTOTIC ANALYSIS OF EQUILIBRIUM STATES FOR ROTATING TURBULENT FLOWS

The equilibrium states of homogeneous turbulence simultaneously subjec ted to a mean velocity gradient and a rotation are examined by using a symptotic analysis. The present work is concerned with the asymptotic behavior of quantities such as the turbulent kinetic energy and its di ssipation rate associated with the fixed point (epsilon/kS)(infinity) = 0, where S is the shear rate. The classical form of the model transp ort equation for epsilon (Hanjalic and Launder, 1972) is used. The pre sent analysis shows that, asymptotically, the turbulent kinetic energy (a) undergoes a power-law decay with time for (P/epsilon)(infinity) < 1, (b) is independent of time for (P/epsilon)(infinity) = 1, (c) unde rgoes a power-law growth with time for 1 < (P/epsilon)(infinity) < (C- epsilon 2 - 1)/(C-epsilon 1 - 1), and (d) is represented by an exponen tial law versus time for (P/epsilon)(infinity) = (C-epsilon 2 - 1)/(C- epsilon 1 - 1) and (epsilon/kS)(infinity) > 0 where P is the productio n rate. For the commonly used second-order models the equilibrium solu tions for P/epsilon, II, and III (where II and III are respectively th e second and third invariants of the anisotropy tensor) depend on the rotation number when (P/kS)(infinity) = (epsilon/kS)(infinity) = 0. Th e variation of (P/kS)(infinity) and IIinfinity versus R given by the s econd-order model of Yakhot and Orzag are compared with results of Rap id Distortion Theory corrected for decay (Townsend, 1970).