Two-space, two-time similarity solution for decaying homogeneous turbulence

Abstract

A two-point, two-time similarity solution is derived for homogeneous decaying turbulence. This is the first known solution which includes the temporal decay at two-different times. It assumes that the turbulence is homogeneous in all three space dimensions, and finds that homogeneity holds across time. The solutions show that time is logarithmically “stretched” while the homogeneous spatial scales grow. This solution reduces to the two point, single time equation when the two times are set equal. The turbulence initially decays exponentially, then asymptotically as t−n where n≥1 and equality is possible only if the initial energy is infinite. The methodology should be applicable to other non-equilibrium homogeneous turbulent flows.