Negative-viscosity phenomena in three-dimensional flows

The paper treats the stability of a periodic unidirectional three-dimensional flow. It is shown that at sufficiently high Reynolds numbers a flow of this type is unstable to long-wavelength disturbances. This instability can be interpreted in terms of negative effective viscosity of the corresponding large-scale flow. The problem is solved using the mode-elimination methods of field theory. It is shown that the results are exact in the limit k→0 for any finite Reynolds number. Also discussed is long-wavelength instability of the flow generated by an unidirectional force field which varies randomly with respect to both the space coordinates and time.