Instability in Fully Developed Turbulence

Abstract

The direct‐interaction approximation is used to examine the growth and propagation of the energy spectrum of the point‐to‐point velocity difference between two isotropic turbulent flows which are statistically identical. If the two systems are driven by identical stirring forces, the question of whether an initial velocity‐difference spectrum grows or decays is found to be similar to that of growth or decay of magnetic seed fields in a turbulent fluid. Numerical calculations appear to be necessary to decide whether deviations between the two systems at high wavenumbers are swept out, to be destroyed by viscosity, or propagate down to make the velocity field in the energy‐containing range unpredictable in detail. The analysis is principally for three‐dimensional turbulence, but the direct‐interaction equations for the two‐dimensional case are stated also.