This paper explains hysteretic transitions in swirling jets and models external flows of vortex suction devices. Toward this goal, the steady rotationally symmetric motion of a viscous incompressible fluid above an infinite conical stream surface of a half-angle θc is studied. The flows analysed are generalizations of Long's vortex. They correspond to the conically similar solutions of the Navier-Stokes equations and are characterized by circulation Γc given at the surface and axial flow force J1. Asymptotic analysis and numerical calculations show that four (for θc ≤ 90°) or five (for θc > 90°) solutions exist in some range of Γc and J1.The solution branches form hysteresis loops which are related to jump transitions between various flow regimes. Four kinds of jump are found: (i) vortex breakdown which transforms a near-axis jet into a two-cell flow with a reverse flow near the axis and an annular jet fanning out along conical surface θ = θs < θc (ii) vortex consolidation causing a reversal of (i); (iii) jump flow separation from surface θ = θc and (iv) jump attachment of the swirling jet to the surface. As Γc and/or J1 decrease, the hysteresis loops disappear through a cusp catastrophe. The physical reasons for the solution non-uniqueness are revealed and the results are discussed in the context of vortex breakdown theories. Vortex breakdown is viewed as a fold catastrophe. Two new striking effects are found: (i) there is a pressure peak of O(Γ2c) inside the annular swirling jet; and (ii) a consolidated swirling jet forms with a reversed (‘anti-rocket’) flow force.

Four high-frequency-response pressure transducers with 10 viscous units resolution each have been used to obtain simultaneously the fluctuating pressure gradients at the wall of a zero-pressure-gradient boundary layer and then to compute the vorticity flux away from the wall. Since the viscous force on an element of incompressible fluid is determined by the local vorticity gradients, understanding of their dynamical characteristics is essential in identifying the turbulent structure. Extremely high and low amplitudes of both vorticity gradients have been observed which contribute significantly to their statistics although they have low probability of appearance. The r.m.s. of the vorticity flux when scaled with inner wall variables depends very strongly on the Reynolds number, indicating a breakdown of this type of scaling. The application of a small threshold to the data indicated two preferential directions of the vorticity flux vector. An attempt has been made to identify these high- and low-amplitude signals with physical phenomena associated with bursting-sweep processes. Vortical structures carrying bipolar vorticity are the dominant wall structures which are associated with the violent events characterized by large fluctuations of vorticity flux.

Numerical simulations are employed in a detailed test of the statistical mechanical description of topographic turbulence. Predictions of steady flows correlated with topography are given particular attention. Agreement between numerical and statistical mechanical results is demonstrated for a large range of parameter values, and over an ensemble of random choices of topography and initial conditions.

This paper examines a supersonic multi-jet interaction problem that we believe is likely to be important for mixing enhancement and noise reduction in supersonic mixer-ejector nozzles. We demonstrate that it is possible to synchronize the screech instability of four rectangular jets by precisely adjusting the inter-jet spacing. Our experimental data agree with a theory that assumes that the phase-locking of adjacent jets occurs through a coupling at the jet lip. Although synchronization does not change the frequency of the screech tone, its amplitude is augmented. The synchronized multi- jets exhibit higher spreading than the unsynchronized jets, with the single jet spreading the least. We compare the near-field noise of the four jets with synchronized screech to the noise of the sum of four jets operated individually. Our noise measurements reveal that the more rapid mixing of the synchronized multi-jets causes the peak jet noise source to move upstream and to radiate noise at larger angles to the flow direction. Based on our results, we have grounds to believe that screech synchronization is advantageous for noise reduction internal to a mixer-ejector nozzle, since the noise can now be suppressed by a shorter acoustically lined ejector.

The fundamental hypotheses underlying Kolmogorov-Oboukhov (1962) turbulence theory (K62) are examined directly and quantitutivezy by using high-resolution numerical turbulence fields. With the use of massively parallel Connection Machine-5, we have performed direct Navier-Stokes simulations (DNS) at 5123 resolution with Taylor microscale Reynolds number up to 195. Three very different types of flow are considered: free-decaying turbulence, stationary turbulence forced at a few large scales, and a 2563 large-eddy simulation (LES) flow field. Both the forced DNS and LES flow fields show realistic inertial-subrange dynamics. The Kolmogorov constant for the k−5/3 energy spectrum obtained from the 5123 DNS flow is 1.68 ±.15. The probability distribution of the locally averaged disspation rate εr, over a length scale r is nearly log-normal in the inertial subrange, but significant departures are observed for high-order moments. The intermittency parameter p, appearing in Kolmogorov's third hypothesis for the variance of the logarithmic dissipation, is found to be in the range of 0.20 to 0.28. The scaling exponents over both εr, and r for the conditionally averaged velocity increments $\overline{\delta_ru|\epsilon_r}$ are quantified, and the direction of their variations conforms with the refined similarity theory. The dimensionless averaged velocity increments $(\overline{\delta_ru^n|\epsilon_r})/(\epsilon_rr)^{n/3}$ are found to depend on the local Reynolds number Reεr = ε1/3rr4/3/ν in a manner consistent with the refined similarity hypotheses. In the inertial subrange, the probability distribution of δru/(εrr)1/3 is found to be universal. Because the local Reynolds number of K62, Rεr = ε1/3rr4/3/ν, spans a finite range at a given scale r as compared to a single value for the local Reynolds number Rr = ε−1/3r4/3/ν in Kolmogorov's (1941a,b) original theory (K41), the inertial range in the K62 context can be better realized than that in K41 for a given turbulence field at moderate Taylor microscale (global) Reynolds number Rλ. Consequently universal constants in the second refined similarity hypothesis can be determined quite accurately, showing a faster-than-exponential growth of the constants with order n. Finally, some consideration is given to the use of pseudo-dissipation in the context of the K62 theory where it is found that the probability distribution of locally averaged pseudo-dissipation ε′r deviates more from a log-normal model than the full dissipation εr. The velocity increments conditioned on ε′r do not follow the refined similarity hypotheses to the same degree as those conditioned on εr.

Experiments carried out recently on a family of axisymmetric coflowing turbulent jets with different nozzle to free-stream velocity ratios are described. Special care was taken to ensure top-hat velocity profiles at the nozzle exit so as to reduce the number of parameters associated with the initial conditions. This results in a collapse of the data without the need to introduce different effective origins for the streamwise coordinate. The mean flow behaviour is compared to self-preserving asymptotic forms and stresses are also examined to investigate the possibility of self-preservation. Comparisons are made with measurements of other workers in coflowing jets and axisymmetric wakes. Further information on the structure of the coflowing jet is found by examining the spectral Reynolds shear stress correlation coefficient, the premultiplied spectra and the high-wavenumber forms of the spectra. An analysis was carried out to see if the mean flow, Reynolds stress distributions and spectra are consistent with an inviscid ‘double-roller’ vortex structure for the representative large-scale energy-containing motions. Results show support for such a model.

Two-dimensional simulations of gas cavity responses to both weak shocks (p ≤ 30 MPa) and strong shocks (p ranging from 500 to 2000 MPa) are performed using a finite volume method. An artificial viscosity to capture the shock and a simple, stable, and adaptive mesh generation technique have been developed for the computations. The details of the shock propagation, rarefaction, transmission and bubble wall motions are obtained from the numerical computations. A weak shock is defined in the present context as one that does not cause liquid jet formation upon impact with the bubble. For this case, a large pressure is created within the gas upon collapse due to rapid compression of the gas, ultimately causing the re-expansion of the bubble. The bubble collapse and re-expansion time predicted by this model agree well with spherically symmetric computations. When impacted by strong shock waves, the bubble will collapse and a liquid jet is formed that propagates through the bubble to the opposite bubble wall. Jet speeds as high as 2000 m s−1 are predicted by this model.

In the absence of Brownian motion, inertia and inter-particle forces, two smooth spheres collide in a simple shear flow in a reversible way returning to their initial streamlines. Because the minimum separation during the collision can be less than 10−4 of the radius, quite a small surface roughness can have a significant irreversible effect on the collision. We calculate the change between the initial and final streamlines caused by roughness. Repeated random collisions in a dilute suspension lead to a diffusion of the particles across the streamlines. We calculate the shear-induced diffusivity for both self-diffusion and down-gradient diffusion.

We present an asymptotic theory for the dynamics of detonation when the radius of curvature of the detonation shock is large compared to the one-dimensional, steady, Chapman-Jouguet (CJ) detonation reaction-zone thickness. The analysis considers additional time-dependence in the slowly varying reaction zone to that considered ill previous works. The detonation is assumed to have a sonic point in the reaction- zone structure behind the shock, and is referred to as an eigenvalue detonation. A new, iterative method is used to calculate the eigenvalue relation, which ultimately is expressed as an intrinsic, partial differential equation (PDE) for the motion of the shock surface. Two cases are considered for an ideal equation of state. The first corresponds to a model of a condensed-phase explosive, with modest reaction rate sensitivity, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity, Dn, the first normal time derivative of the normal shock velocity, Dn, and the shock curvature, K. The second case corresponds to a gaseous explosive mixture, with the large reaction rate sensitivity of Arrhenius kinetics, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity, Dn, its first and second normal time derivatives of the normal shock velocity, Dn, Dn, and the shock curvature, K, and its first normal time derivative of the curvature, k. For the second case, one obtains a one-dimensional theory of pulsations of plane CJ detonation and a theory that predicts the evolution of self-sustained cellular detonation. Versions of the theory include the limits of near-CJ detonation, and when the normal detonation velocity is significantly below its CJ value. The curvature of the detonation can also be of either sign, corresponding to both diverging and converging geometries.

In this paper the evolution of a free liquid filament of arbitrary viscosity, contracting under the action of surface tension forces, is studied by numerical means. A finite- element discretization procedure is used to obtain approximate solutions to the Navier-Stokes equations. A Lagrangian approach is employed to deal with the large domain deformations which occur during the evolution of the filament. Typically we find that during the contraction a bulbous region forms at the end of the filament. The character of the evolution of the filament is found to be crucially dependent on the value of the Ohnesorge number Oh (a measure of viscous and surface tension forces). For large Ohnesorge numbers (Oh [Gt ] O(1)) it is found that the liquid filament remains stable during contraction, even when the initial length of the filament is much longer than the Rayleigh stability limit. The bulbous end becomes more localized with decreasing Ohnesorge number while at the same time a clear neck forms in front of the bulbous end. In addition we find that the region in which the pressure is minimum moves towards the neck. For sufficiently small Ohnesorge numbers (Oh [Lt ] O(0.01)) the filament becomes unstable with the radius of the neck decreasing and, eventually, the bulbous end breaking away from the filament.

A process of generation and convergence of shock waves of arbitrary form and strength in a confined chamber is investigated theoretically. The chamber is a cylinder with a specifically chosen form of boundary. Numerical calculations of reflection and convergence of cylindrical shock waves in such a chamber filled with fluid are performed. The numerical scheme is similar to the numerical procedure introduced by Henshaw et al. (1986) and is based on a modified form of Whitham's theory of geometrical shock dynamics (1957, 1959). The technique used in Whitham (1968) for treating a shock advancing into a uniform flow is modified to account for non-uniform conditions ahead of the advancing wave front. A new result, that shocks of arbitrary polygonal shapes may be generated by reflection of cylindrical shocks off a suitably chosen reflecting boundary, is shown. A study is performed showing the evolution of the shock front's shape and Mach number distribution. Comparisons are made with a theory which does not account for the non-uniform conditions in front of the shock. The calculations provide details of both the reflection process and the shock focusing.

A laboratory study which simulates the dynamics of shallow sea fronts and the mixing across a tidal front is described. The experiments show, for the first time, that it is possible to simulate a stationary tidal front with the inclusion of buoyancy effects, Coriolis effects and turbulence in the laboratory. Experimental data obtained for the cross-front mixing rate are presented. The data analysis shows that the mixing rate increases with stratification and decreases with rotation. A theoretical model of the flow which collapses the experimental data is developed which shows that the cross-front mixing is controlled by baroclinic processes. The model enables an extrapolation of the laboratory results to oceanographic conditions. Estimates of the cross-front mixing velocity for oceanographic conditions give values consistent with estimates obtained from North Sea data.