SLOW-DOWN OF NONLINEARITY IN 2-D NAVIER-STOKES FLOW

The equations governing the dynamics of large-scale perturbations supe rimposed on incompressible small-scale flow driven by a force have, un der suitable conditions, the same structure as Navier-Stokes equations . The breaking of Galilean invariance due to the presence of the small -scale flow will, in general, induce a 'vertex renormalization': the c onstant a in front of the advective nonlinearity does not remain equal to unity. A class of basic flows where the calculation of a can be pe rformed analytically is discussed. For finite Reynolds numbers, the co nstant a can indeed be very different from unity and can also vanish. The Reynolds number and the dynamics of a large-scale flow can then be quite different than predicted by setting a = 1.