The rapid formation of a new proton radiation belt at L •_ 2.5 following the March 24, 1991 Storm Sudden Commencement (SSC) observed at the CRRES satellite is modelled using a relativistic guiding center test particle code. The SSC is modelled by a bipolar electric field and associated compression and relaxation in the magnetic field, superimposed on a dipole magnetic field. The source population consists of both solar and trapped inner zone protons. The simulations show that while both populations contribute to drift echoes in the 20-80 MeV range, primary contribution is from the solar protons. Proton acceleration by the SSC differs from relativistic electron acceleration in that different source populations contribute and nonrelativistic conservation of the first adiabatic invariant leads to greater energization of protons for a given decrease in L. Model drift echoes and flux distribution in L at the time of injection compare well with CRRES observations.

The Richtmyer–Meshkov instability in an incompressible and compressible stratified two-dimensional ideal flow is studied analytically and numerically. For the incompressible problem, we initialize a single small-amplitude sinusoidal perturbation of wavelength λ, we compute a series expansion for the amplitude a in powers of t up to t(11) with the MuPAD computer algebra environment. This involves harmonics up to eleven. The simulations are performed with two codes: incompressible, a vortex-in- cell numerical technique which tracks a single discontinuous density interface; and compressible, PPM for a shock-accelerated case with a finite interfacial transition layer (ITL). We identify properties of the interface at time t = tM at which it first becomes ‘multivalued’. Here, we find the normalized width of the ‘spike’ is related to the Atwood number by (wm/λ)−0.5 = −0.33A. A high-order Pad approximation is applied to the analytical series during early time and gives excellent results for the interface growth rate a˙. However, at intermediate times, t > tM, the agreement between numerical results and different-order Padé approximants depends on the Atwood number. During this phase, our numerical solutions give a˙∝O(t−1) for small A and a˙∝O(t−0.4) for A = 0.9. Experimental data of Prasad et al. (2000) for SF6 (post shock Atwood number = 0.74) shows an exponent between −0.68 and −0.72 and we obtain −0.683 for the compressible simulation. For this case, we illustrate the important growth of vortex-accelerated (secondary) circulation deposition of both signs of vorticity and the complex nature of the roll-up region.

We examine the vortex dynamics and interfacial evolution of “reacceleration” and “reshock” for single interface density-stratified fluid (Richtmyer–Meshkov) environments. In the former case, we simulate, visualize, and quantify the parameter range of the free falling tank laboratory experiment of J. Jacobs and C. F. Niederhaus, where the impulsive subsequent acceleration of the interface occurs after several rolls from the initial impulsive acceleration. We interpret the rapid onset of chaotic motion in the roll-up region as due to the formation of intertwined close-laying layers of opposite-signed vorticity. In the latter case, we make compressible simulations at low Mach number (M=1.2) and compare with incompressible simulations. We juxtapose the results and find an excellent agreement in large and intermediate size features and their magnitudes before the “reshock.” At the “reshock,” discrepancies arise due to highly compressible regime. The simulations were made with incompressible vorticity-based methods, vortex-in-cell (VIC) and vortex blob (VB), and compressible second-order Godunov codes.

Numerical simulation is used to study the turbulence generated by the passage of strong shocks (typical Mach number 7.3) through an inhomogeneous fluid at moderate Reynolds numbers. Before passage of the shock, the material consists of mass-density inhomogeneities embedded in a background fluid. The entire system is initially at uniform temperature, pressure, and number density, with the nonuniform mass density resulting from differing mass species in different regions. In the present application, the substances are treated as ideal gases, though in the motivating physical problems they are more complex materials. The shock retains its identity and a sharp front, but leaves behind it a turbulent state whose locally averaged properties only slowly become spatially uniform. The shock acquires a turbulent “thickness” (the linear dimension of the nonuniform region behind the shock front) that seems ultimately damped by viscous and thermally conducting properties that are dependent on transport coefficients and (highly uncertain) Reynolds numbers. Typically, the turbulence is highly compressible, with comparable mean divergences and curls in the velocity field, and fractional rms density fluctuations of the order of 0.25 in the parameter ranges studied. The rms vorticity generated can be estimated reasonably well from dimensional considerations. The effect of the high density inhomogeneities is primarily to create a wide region of compressible turbulence behind the shock. The inhomogeneities create both a succession of reflected shocks and considerable vorticity.

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