Nonlinear Interactions in Turbulence with Strong Irrotational Straining

The rate of growth of the nonlinear terms in the vorticity equation are analysed for a turbulent flow with r.m.s. velocity u0 and integral length scale L subjected to a strong uniform irrotational plane strain S, where (u0/L)/S = ε ≪ 1. The Rapid Distortion Theory (RDT) solution is the zeroth order term of the perturbation series solution in terms of ε. We use the asymptotic form of the convolution integrals for the zeroth order nonlinear terms when exp(St) ≫ 1 to determine when (in wavenumber k and time t) the perturbation series in ε fails, and hence estimate precisely the domain of validity of inviscid and viscous RDT.