The decay of turbulence

Solutions are given for the temporal decay of homogeneous turbulence and spatial decay of turbulence induced by a source of energy on a plane z = 0. In the latter case there may be a superimposed basic current W perpendicular to the plane. The initial energy spectrum function (at t = 0 or z = 0) for the idealized source is proportional to the wave number k. With increase of time or distance from the plane, the smaller eddies decay strongly and an energy peak develops. The energy in larger waves is permanent in the sense that the energy in a given wave number divided by the energy at that wave number in the original spectrum is a constant for k - or = k sub m. Thus the energy peak moves to larger and larger eddies containing smaller and smaller amounts of energy. The results agree with previous theories for turbulence caused by an oscillating grid and by flow in a wind tunnel past a fixed grid. There is also a comparison with experimental observations in the two cases.