INVISCID AND INVISCID-LIMIT BEHAVIOR OF A SURFACE QUASI-GEOSTROPHIC FLOW

The growth of the gradient of a scalar temperature in a quasigeostroph ic flow is studied numerically in detail. We use a flow evolving from a simple initial condition which was regarded by Constantin et al. as a candidate for a singularity formation in a finite time. For the invi scid problem, we propose a completely different interpretation of the growth, that is, the temperature gradient can be fitted equally well b y a double-exponential function of time rather than an algebraic blowu p. It seems impossible to distinguish whether the flow blows up or not on the basis of the inviscid computations at hand. In the viscous cas e, a comparison is made between a series of computations with differen t Reynolds numbers. The critical time at which the temperature gradien t attains the first local maximum is found to depend double logarithmi cally on the Reynolds number, which suggests the global regularity of the inviscid flow. (C) 1997 American Institute of Physics.