We consider the propagation of a plane front separating a turbulent region of fluid from a quiescent region. Initially, the turbulent-energy distribution as a function of z, the displacement normal to the front, is assumed to be localized, and after a time t, general renormalization-group arguments show that there is a similarity solution of the form q(z,t)t-(2/3+2i)f (zt-(2/3+), ), where i and are -dependent anomalous dimensions, satisfying the scaling law i+=0 and is a measure of the dissipation. Using perturbation theory, we calculate values of i and o O(), which are in good agreement with numerical calculations, and we explicitly verify the above scaling law and find the form of the scaling function f.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics