Effect of sheared flow on the growth rate and turbulence decorrelation

The effect of a large scale flow shear on a linearly unstable turbulent system is considered. A cubic equation describing the effective growth rate is obtained, which is shown to reduce to well-known forms in weak and strong shear limits. A shear suppression rule is derived which corresponds to the point where the effective growth rate becomes negative. The effect of flow shear on nonlinear mode coupling of drift or Rossby waves is also considered, and it is shown that the resonance manifold shrinks and weakens as the vortices are sheared. This leads to a reduction of the efficiency of three-wave interactions. Tilted eddies can then only couple to the large scale sheared flows, because the resonance condition for that interaction is trivially satisfied. It is argued that this leads to absorbtion of the sheared vortices by large scale flow structures. Studying the form of the effective growth rate for weak shear, it was shown that in addition to reducing the overall growth rate, a weak flow shear also reduces the wave number where the fluctuations are most unstable.