Small-scale chaos at low Reynolds numbers

A system of dissipative modes in an incompressible flow of space dimensions d>or=2 is considered. The self-induced phase chaos is shown to arise in the motions of very small scales, which are fed by the large-scale ones through repeated nonlinear interactions. This property is used to derive the equations for the Fourier amplitudes. Solutions similar to those derived previously for turbulent fluctuations in the dissipation range are obtained. Properties of the short-scale intermittency are analysed. The authors show that no coherence and intermittency can be built up at asymptotically high wavenumbers.