Modeling the response of turbulence subjected to cyclic irrotational strain

Using a second moment closure, analytical solutions for homogeneous turbule nce subjected to periodic compression-dilatation strains show that both the characteristic turbulence frequency and turbulence kinetic energy eventual ly decay, irrespective of the initial turbulence level, anisotropy of the s tress field, or Reynolds number. The eddy-viscosity models give erroneous r esults because of the artificial positive generation of turbulence energy d uring both the compression and expansion phase. The first observation resul ts from the phase lag between periodic strain rate and stresses introduced by the exact production term in the second moment closure, whereas the eddy -viscosity model synchronizes the stresses with the strain rate, resulting in an overestimation of turbulence generation. The above findings are illus trated by analytical solutions, as well as by numerical solutions of in-cyl inder turbulence, using the k-epsilon eddy-viscosity and the second-moment closure models. The analysis and simulations support the conjecture that tu rbulence submitted to cyclic strains should always finally decay. (C) 2001 American Institute of Physics.