A stochastic wavevector approach is formulated to accurately represent compressible turbulence subject to rapid deformations. This approach is inspired by the incompressible particle representation model of Kassinos & Reynolds (1994), and preserves the exact nature of compressible rapid distortion theory (RDT). The adoption of a stochastic – rather than Fourier – perspective simplifies the transformation of statistics to physical space and serves as a starting point for the development of practical turbulence models. We assume small density fluctuations and isentropic flow to obtain a transport equation for the pressure fluctuation. This results in four fewer transport equations compared with the compressible RDT model of Yu & Girimaji (Phys. Fluids, vol. 19, 2007, 041702). The final formulation is closed in spectral space and only requires numerical approximation for the transformation integrals. The use of Monte Carlo for unit wavevector integration motivates the representation of the moments as stochastic variables. Consistency between the Fourier and stochastic representation is demonstrated by showing equivalency between the evolution equations for the velocity spectrum tensor in both representations. Sample clustering with respect to orientation allows for different techniques to be used for the wavevector magnitude integration. The performance of the stochastic model is evaluated for axially compressed turbulence, serving as a simplified model for shock–turbulence interaction, and is compared with linear interaction approximations and direct numerical simulation (DNS). Pure and compressed sheared turbulence at different distortion Mach numbers are also computed and compared with RDT/DNS data. Finally, two additional deformations are applied and compared with solenoidal and pressure-released limits to demonstrate the modelling capability for generic rapid deformations.

Travelling wave charges lying on the insulating walls of an electrolyte-filled capillary give rise to oscillatory modes which vanish when averaged over the period of oscillation. They also give rise to a zero mode (a unidirectional, time-independent velocity component) which does not vanish. The latter is a nonlinear effect caused by continuous symmetry breaking due to the quadratic nonlinearity associated with the electric body force in the time-dependent Stokes equations. In this paper, we provide a unified view of the effects arising in boundary-driven electrokinetic flows (travelling wave electroosmosis) and establish the universal behaviour exhibited by the observables. We show that the incipient velocity profiles are self-similar implying that those obtained with a single experimental configuration can be employed again to attain further insights without the need of repeating the experiment. Certain results from the literature are recovered as special cases of our formulation and we resolve certain paradoxes having appeared in the past. We present simple theoretical expressions, depending on a single-fit parameter, that reproduce these profiles, which could thus provide a rapid test of consistency between our theory and future experiment. The effect becomes more pronounced when reducing the transverse dimension of the system, relative to the velocity direction, and increasing the excitation wavelength, and can therefore be employed for unidirectional transport of electrolytes in thin and long capillaries. General relations, expressing the zero mode velocity in terms of the electric potential and the geometry of the system only, can thus be easily adapted to alternative experimental settings.

Large-eddy simulation (LES) is performed to study the tip vortex flow in a ducted propulsor geometry replicating the experiments of Chesnakas & Jessup (2003, pp. 257–267), Oweis et al. (2006a J. Fluids Engng 128, 751–764) and Oweis et al. (2006b J. Fluids Engng 128, 751–764). Inception of cavitation in these marine propulsion systems is closely tied to the unsteady interactions between multiple vortices in the tip region. Here LES is used to shed insight into the structure of the tip vortex flow. Simulation results are able to predict experimental propeller loads and show agreement with laser Doppler velocimetry measurements in the blade wake at design advance ratio, $J=0.98$. Results show the pressure differential across the blade produces a leakage vortex which separates off the suction side blade tip upstream of the trailing edge. The separation sheet aft of the primary vortex separation point is shown to take the form of a skewed shear layer which produces a complex arrangement of unsteady vortices corotating and counter-rotating with the primary vortex. Blade tip boundary layer vortices are reoriented to align with the leakage flow and produce instantaneous low-pressure regions wrapping helically around the primary vortex core. Such low-pressure regions are seen both upstream and downstream of the propeller blade trailing edge. The trailing edge wake is found to only rarely have a low-pressure vortex core. Statistics of instantaneous low pressures below the minimum mean pressure are found to be concentrated downstream of the blade’s trailing edge wake crossing over the primary vortex core and continue in excess of 40 % chord length behind the trailing edge. The rollup of the leakage flow duct boundary layer behind the trailing edge is also seen to produce counter-rotating vortices which interact with the primary leakage vortex and contribute to strong stretching events.

In this study, the propagation behaviour of detonation waves in a channel filled with stratified media is analysed using a detailed chemical reaction model. Two symmetrical layers of non-reactive gas are introduced near the upper and lower walls to encapsulate a stoichiometric premixed H2–air mixture. The effects of gas temperature and molecular weight of the non-reactive layers on the detonation wave’s propagation mode and velocity are examined thoroughly. The results reveal that as the non-reactive gas temperature increases, the detonation wave front transitions from a ‘convex’ to a ‘concave’ shape, accompanied by an increase in wave velocity. Notably, the concave wave front comprises detached shocks, oblique shocks and detonation waves, with the overall wave system propagating at a velocity exceeding the theoretical Chapman–Jouguet speed, indicating the emergence of a strong detonation wave. Furthermore, when the molecular weight of non-reactive layers varies, the results qualitatively align with those obtained from temperature variations. To elucidate the formation mechanism of different detonation wave front shapes, a dimensionless parameter $\eta$ (defined as a function of the specific heat ratio and sound speed) is proposed. This parameter unifies the effects of temperature and molecular weight, confirming that the specific heat ratio and sound speed of non-reactive layers are the primary factors governing the detonation wave propagation mode. Additionally, considering the effect of mixture inhomogeneity on the detonation reaction zone, the stream tube contraction theory is proposed, successfully explaining why strong detonation waves form in stratified mixtures. Numerical results show good agreement with theoretical predictions, validating the proposed model.

The flow behind impulsively started circular and polygonal plates is investigated experimentally, using particle image velocimetry at several azimuthal angles. Observing plates accelerating up to a steady Reynolds number $Re=27\,000$, the three invariants of the motion, circulation $\Gamma$, hydrodynamic impulse $I$ and kinetic energy $E$, were scaled against four candidate lengths: the hydraulic diameter, perimeter, circumscribed diameter and the square root of the area. Of these, the square root of the area was found to best collapse all the data. Investigating the three-dimensionality of the flow, it is found that, while a single-plane measurement can provide a reasonable approximation for $\Gamma$ behind plates, multiple planes are necessary to accurately estimate $E$ and $I$.