Evolution of homogeneous turbulence in a density-stratified medium. 1. Analysis in far field

The equations presented in [1] for the evolution of homogeneous turbulence in a density-stratified medium are investigated analytically. The problem involves the small parameter ε = Fr². Applying variants of the small-parameter method, it is possible to calculate the frequency of internal waves and a number of asymptotic regimes in the development of turbulent velocity and scalar fields over time. The so-called far field of evolution, i.e., the field of large values of τ (τ ≫ 1, is considered, in which the differential order of the initial system of equations is lowered. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 1, pp. 30–39, January–February, 1997.