A large-Reynolds-number asymptotic theory is presented for the problem of a vortex tube of finite circulation [Gcy ] subjected to uniform non-axisymmetric irrotational strain, and aligned along an axis of positive rate of strain. It is shown that at leading order the vorticity field is determined by a solvability condition at first-order in ε = 1/R[Gcy ] where R[gcy ] = [gcy ]/ν. The first-order problem is solved completely, and contours of constant rate of energy dissipation are obtained and compared with the family of contour maps obtained in a previous numerical study of the problem. It is found that the region of large dissipation does not overlap the region of large enstrophy; in fact, the dissipation rate is maximal at a distance from the vortex axis at which the enstrophy has fallen to only 2.8% of its maximum value. The correlation between enstrophy and dissipation fields is found to be 0.19 + O(ε2). The solution reveals that the stretched vortex can survive for a long time even when two of the principal rates of strain are positive, provided R[gcy ] is large enough. The manner in which the theory may be extended to higher orders in ε is indicated. The results are discussed in relation to the high-vorticity regions (here described as ‘sinews’) observed in many direct numerical simulations of turbulence.

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329Energy cascade process is investigated numerically on a scalar model of fully-developed threedimensional turbulence. It is found that energy propagates through the inertial range intermittently like bursts which are separated by quiescent periods (Siggia's view revisited). During the activated phase the first local Lyapunov exponent oscillates violently, and the support of the first Lyapunov vector spreads over the inertial subrange.

The growth of the gradient of a scalar temperature in a quasigeostrophic 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 inviscid problem, we propose a completely different interpretation of the growth, that is, the temperature gradient can be fitted equally well by a double-exponential function of time rather than an algebraic blowup. It seems impossible to distinguish whether the flow blows up or not on the basis of the inviscid computations at hand. In the viscous case, a comparison is made between a series of computations with different Reynolds numbers. The critical time at which the temperature gradient attains the first local maximum is found to depend double logarithmically on the Reynolds number, which suggests the global regularity of the inviscid flow.

Three-dimensional Euler equations are studied numerically and analytically to characterize intense vortex stretching in an inviscid fluid. Emphasis is put on the nonlocal effects stemming from the pressure term. The purpose of this paper is twofold. One is to give numerically a detailed characterization of vortex structures on the basis of previously proposed two eigenvalue problems associated with vorticity. The other is to give some mathematical analyses which highlight the role of the pressure Hessian in vortex dynamics, especially in connection with a possible singularity. Also discussed are the differences in local and global (possible) blowups. The blowup problem is not directly discussed by the present numerics at moderate resolution.