A method for large eddy simulation (LES) is presented in which the sub-grid-scale modeling is achieved by filtering procedures alone. The procedure derives from a deconvolution model, and provides a mathematically consistent approximation of unresolved terms arising from any type of nonlinearity. The formal steps of primary filtering to obtain LES equations, approximate deconvolution to construct the subgrid model term and regularization are combined into an equivalent filter. This filter should be an almost perfect low pass filter below a cut-off wavenumber and then fall off smoothly. The procedure has been applied to a pressure-velocity-entropy formulation of the Navier–Stokes equations for compressible flow to perform LES of two fully developed, turbulent, supersonic channel flows and has been assessed by comparison against direct numerical simulation (DNS) data. Mach numbers are 1.5 and 3.0, and Reynolds numbers are 3000 and 6000, respectively. Effects of filter cut-off location, choice of differentiation scheme (a fifth-order compact upwind formula and a symmetric sixth-order compact formula were used), and grid refinement are examined. The effects are consistent with, and are readily understood by reference to, filtering characteristics of the differentiation and the LES filter. All simulations demonstrate a uniform convergence towards their respective DNS solutions.

Over the last 30 years, turbulent entrainment has come to be viewed as a large-scale process, directed by coherent structures, and described as engulfing. With turbulence simulations, we examined the process of entrainment directly, as growth of vorticity and concentration along fluid particle pathlines which were computed simultaneously. Our results indicate that the process is more often small scale. Growth occurs close to the turbulence boundary, within small radial displacements, and in times which are smaller than local large-scale times. These observations can be cast into a model to show that overall rates can be predicted by large-scale quantities even though the process occurs at small scales; the only requirement is a fixed relationship across scales as in fully developed turbulent flows. So it is not inconsistent that engulfment can be a successful, and accepted, model for fully developed flows even if it is not the more frequent process.

Experimental investigations of laminar swirling jets had revealed a new form of vortex breakdown, named conical vortex breakdown, in addition to the commonly observed bubble form. The present study explores these breakdown states that develop for the Maxworthy profile (a model of swirling jets) at inflow, from streamwise-invariant initial conditions, with direct numerical simulations. For a constant Reynolds number based on jet radius and a centreline velocity of 200, various flow states were observed as the inflow profile’s swirl parameter $S$ (scaled centreline radial derivative of azimuthal velocity) was varied up to 2. At low swirl ( $S=1$ ) a helical mode of azimuthal wavenumber $m=-2$ (co-winding, counter-rotating mode) was observed. A ‘swelling’ appeared at $S=1.38$ , and a steady bubble breakdown at $S=1.4$ . On further increase to $S=1.5$ , a helical, self-excited global mode ( $m=+1$ , counter-winding and co-rotating) was observed, originating in the bubble’s wake but with little effect on the bubble itself – a bubble vortex breakdown with a spiral tail. Local and global stability analyses revealed this to arise from a linear instability mechanism, distinct from that for the spiral breakdown which has been studied using Grabowski profile (a model of wing-tip vortices). At still higher swirl ( $S=1.55$ ), a pulsating type of bubble breakdown occurred, followed by conical breakdown at 1.6. The latter consists of a large toroidal vortex confined by a radially expanding conical sheet, and a weaker vortex core downstream. For the highest swirls, the sheet was no longer conical, but curved away from the axis as a wide-open breakdown. The applicability of two classical inviscid theories for vortex breakdown – transition to a conjugate state, and the dominance of negative azimuthal vorticity – was assessed for the conical form. As required by the former, the flow transitioned from a supercritical to subcritical state in the vicinity of the stagnation point. The deviations from the predictions of the latter model were considerable.

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An analysis is presented for the production of weakly ionized plasmas by electron beams, with an emphasis on the production of broad, planar plasmas capable of reflecting X-band microwaves. Considered first in the analysis is the ability of weakly ionized plasmas to absorb, emit and reflect electromagnetic radiation. Following that is a determination of the electron beam parameters needed to produce plasmas, based on considerations of beam ionization, range, and stability. The results of the analysis are then compared with a series of experiments performed using a sheet electron beam to produce plasmas up to 0.6 m square by 2 cm thick. The electron beam in the experiments was generated using a long hollow-cathode discharge operating in an enhanced-glow mode. That mode has only recently been recognized, and a brief analysis of it is given for completeness. The conclusion of the study is that electron beams can produce large-area, planar plasmas with high efficiency, minimal gas heating, low electron temperature, high uniformity, and high microwave reflectivity, as compared with plasmas produced by other sources.