The exponential decay of homogeneous turbulence

Abstract

Similarity equations of the spectral equations for decaying homogeneous turbulence are considered for which the similarity length scale is not allowed to grow. Two types of solutions are found: an inviscid solution and one involving viscosity. For the former, the energy decays asymptotically as t−2, while for the latter the energy decays exponentially and the ratio of integral scale to Taylor microscale is constant. For both the spectra for fixed initial conditions collapse during decay with simply the energy and a single length scale. The exponentially decaying solution appears to provide an excellent description of the turbulence generated in recent space-filling fractal grid experiments.