The idealized interactions of shock waves with homogeneous and isotropic turbulence, homogeneous sheared turbulence, turbulent jets, shear layers, turbulent wake flows, and two-dimensional boundary layers have been reviewed. The interaction between a shock wave and turbulence is mutual. A shock wave exhibits substantial unsteadiness and deformation as a result of the interaction, whereas the characteristic velocity, timescales and length scales of turbulence change considerably. The outcomes of the interaction depend on the strength, orientation, location, and shape of the shock wave, as well as the flow geometry and boundary conditions. The state of turbulence and the compressibility of the incoming flow are two additional parameters that also affect the interaction. 310ANDREOPOULOS Ⅲ AGUI Ⅲ BRIASSULIS curvature, flow separation, dilatational effects, or longitudinal pressure gradients that may be present in flow before or after the interaction with the shock.The outcomes of the shock-turbulence interaction depend on (a) the characteristics of the interacting shock-wave-like strength, relative orientation to the incoming flow, and location and shape, (b) the state of turbulence of the incoming flow as it is characterized by the fluctuation levels of velocity, density, pressure, and entropy and length scales, (c) the level of compressibility of the incoming flow, and (d) the flow geometry and boundary conditions. Basic understanding of the physics of such complex interactions has been obtained through investigations of conveniently selected and reasonably simplified flow configurations. The flows to be considered here include shear free flows, shear layers, and wall-bounded flows. Most of the work in this review is confined to the following cases: (a) homogeneous and isotropic turbulence interactions with shock waves (see Figure 1a), (b) constant shear homogeneous turbulence interactions with shock waves (see Figure 1b), (c) circular jet flows interacting with shock waves (see Figure 1c), (d) plane shear layers interacting with oblique shock waves (see Figure 1d), (e) wake flows interacting with oblique or normal shock waves (see Figure 1e), and ( f ) boundary layer interactions with oblique shock waves (see Figure 1f). This classification of the interactions also reflects the level of increasing complexity from the first to the last flow configuration.We restrict our review to nominally two-dimensional interactions, albeit keeping in mind that all of these interactions are three-dimensional in nature because turbulence in all its complexity is characterized by instantaneous flow variables that exhibit a variation in time and space. Shock wave-boundary layer interactions have been reviewed in the past by Green (1970), Adamson & Messiter (1980), andDodson (1991). Compressibility effects of turbulence, including some shock wave interactions, have been recently reviewed by Lele (1994). Compressibility effects in turbulent boundary layers and shear layers in the absence of shock interactions have been reviewed by Sp...

The unsteady interaction of a moving shock wave with nearly homogeneous and isotropic decaying compressible turbulence has been studied experimentally in a large-scale shock tube facility. Rectangular grids of various mesh sizes were used to generate turbulence with Reynolds numbers based on Taylor's microscale ranging from 260 to 1300. The interaction has been investigated by measuring the three-dimensional velocity and vorticity vectors, the full velocity gradient and rate-of-strain tensors with instrumentation of high temporal and spatial resolution. This allowed estimates of dilatation, compressible dissipation and dilatational stretching to be obtained. The time-dependent signals of enstrophy, vortex stretching/tilting vector and dilatational stretching vector were found to exhibit a rather strong intermittent behaviour which is characterized by high-amplitude bursts with values up to 8 times their r.m.s. within periods of less violent and longer lived events. Several of these bursts are evident in all the signals, suggesting the existence of a dynamical flow phenomenon as a common cause. Fluctuations of all velocity gradients in the longitudinal direction are amplified significantly downstream of the interaction. Fluctuations of the velocity gradients in the lateral directions show no change or a minor reduction through the interaction. Root mean square values of the lateral vorticity components indicate a 25% amplification on average, which appears to be very weakly dependent on the shock strength. The transmission of the longitudinal vorticity fluctuations through the shock appears to be less affected by the interaction than the fluctuations of the lateral components. Non-dissipative vortex tubes and irrotational dissipative motions are more intense in the region downstream of the shock. There is also a significant increase in the number of events with intense rotational and dissipative motions. Integral length scales and Taylor's microscales were reduced after the interaction with the shock in all investigated flow cases. The integral length scales in the lateral direction increase at low Mach numbers and decrease during strong interactions. It appears that in the weakest of the present interactions, turbulent eddies are compressed drastically in the longitudinal direction while their extent in the normal direction remains relatively the same. As the shock strength increases the lateral integral length scales increase while the longitudinal ones decrease. At the strongest interaction of the present flow cases turbulent eddies are compressed in both directions. However, even at the highest Mach number the issue is more complicated since amplification of the lateral scales has been observed in flows with fine grids. Thus the outcome of the interaction strongly depends on the initial conditions.

A decaying compressible nearly homogeneous and nearly isotropic grid-generated turbulent flow has been set up in a large scale shock tube research facility. Experiments have been performed using instrumentation with spatial resolution of the order of 7 to 26 Kolmogorov viscous length scales. A variety of turbulence-generating grids provided a wide range of turbulence scales with bulk flow Mach numbers ranging from 0.3 to 0.6 and turbulent Reynolds numbers up to 700. The decay of Mach number fluctuations was found to follow a power law similar to that describing the decay of incompressible isotropic turbulence. It was also found that the decay coefficient and the decay exponent decrease with increasing Mach number while the virtual origin increases with increasing Mach number. A possible mechanism responsible for these effects appears to be the inherently low growth rate of compressible shear layers emanating from the cylindrical rods of the grid. Measurements of the time-dependent, three dimensional vorticity vectors were attempted for the first time with a 12-wire miniature probe. This also allowed estimates of dilatation, compressible dissipation and dilatational stretching to be obtained. It was found that the fluctuations of these quantities increase with increasing mean Mach number of the flow. The time-dependent signals of enstrophy, vortex stretching/tilting vector and dilatational stretching vector were found to exhibit a rather strong intermittent behaviour which is characterized by high-amplitude bursts with values up to 8 times their r.m.s. within periods of less violent and longer lived events. Several of these bursts are evident in all the signals, suggesting the existence of a dynamical flow phenomenon as a common cause.

Several techniques associated with the use of hot wire anemometry in compressible turbulence measurements are described and tested in shock tube flows. These techniques include 1. in-situ calibration of the hot-wire probe by firing several shock waves of different strengths in the shock tube; 2. on-line analog frequency compensation or off-line digital compensation of the temperature-wire; 3. simultaneous acquisition of time-dependent flow velocity and temperature of the flow without invoking Morkovin's hypothesis of strong Reynolds analogy. The techniques were tested in two different shock tube facilities, where a grid generated turbulent flow interacting with a moving shock was set up.1

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The unsteady interaction of a moving shock wave with nearly homogeneous and isotropic decaying compressible turbulence has been studied experimentally in a large-scale shock-tube facility by using rectangular grids of various sizes. The interaction has been investigated by measuring velocity, total pressure, and temperature inside the ow eld and static pressure at the wall of the shock tube with instrumentation of temporal and spatial resolution. Attenuation of the shock wave strength has been found to take place as a result of the interaction with the turbulent ow eld, which depends on the mesh size of the grid or its Reynolds number, the ow Mach number, and the initial Mach number of the shock wave. Finer grids produce turbulence, which attenuates the shock wave more than coarse grids at the same Mach number. Ampli cation of pressure uctuations after the interaction has been observed in all experiments, depending on grid size (initial turbulence level) and shock strength. Furthermore, this ampli cation is not the same through the whole range of wave numbers resolved.

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