TY - CONF
T1 - The interaction of turbulence with shock waves: a basic model
AU - Zank, Gary P.
AU - Zhou, Ye
AU - Matthaeus, William H.
AU - Rice, W. K. M.
PY - 2001/10/1
Y1 - 2001/10/1
N2 - Analytic work addressing the interaction of turbulence with a shock wave
has concentrated on investigating the generation of sound by jet
engines. Hydrodynamic modes (acoustic, vortical, and entropic) can
experience considerable amplification on passage through a shock [Moore,
1954; Ribner, 1954, 1987; McKenzie & Westphal, 1968; Mahesh et al.,
1995], while downstream of a shock there exists a critical angle for
incident acoustic modes where the reflection coefficient is 1. The
analytic studies cited assume that the incident, radiated and resulting
perturbations, including the shock front distortion, is of small
amplitude, allowing a linearized description. Not addressed in this
approach is the nonlinear response of the shock wave to the incident
turbulence, nor the conversion of mean shock wave momentum and energy to
the amplification of the incident turbulence. However, upstream
turbulence can affect significantly the mean flow variables of a shock
wave. Instead, the classical Rankine-Hugoniot (R-H) conditions, which
relate the upstream and downstream states of a shock wave, are no longer
exact for the mean flow. The mean R-H conditions are modified by
contributions to the mass, momentum, and energy fluxes from turbulent
fluctuations. To properly understand the interaction of turbulence with
shocks, one must incorporate the back reaction of the shock-turbulence
interaction. One must therefore incorporate statistically variation in
ram pressure, energy, and mass flux in the mean R-H conditions and then
determine the mean position, velocity, and strength of the shock. This
is an entirely different perspective from that developed in previous
analytic studies, although captured in principle by numerical studies.
We present initial results for a highly simplified system that goes some
way towards addressing the non-linear interaction of fully developed
turbulence with shock waves.
AB - Analytic work addressing the interaction of turbulence with a shock wave
has concentrated on investigating the generation of sound by jet
engines. Hydrodynamic modes (acoustic, vortical, and entropic) can
experience considerable amplification on passage through a shock [Moore,
1954; Ribner, 1954, 1987; McKenzie & Westphal, 1968; Mahesh et al.,
1995], while downstream of a shock there exists a critical angle for
incident acoustic modes where the reflection coefficient is 1. The
analytic studies cited assume that the incident, radiated and resulting
perturbations, including the shock front distortion, is of small
amplitude, allowing a linearized description. Not addressed in this
approach is the nonlinear response of the shock wave to the incident
turbulence, nor the conversion of mean shock wave momentum and energy to
the amplification of the incident turbulence. However, upstream
turbulence can affect significantly the mean flow variables of a shock
wave. Instead, the classical Rankine-Hugoniot (R-H) conditions, which
relate the upstream and downstream states of a shock wave, are no longer
exact for the mean flow. The mean R-H conditions are modified by
contributions to the mass, momentum, and energy fluxes from turbulent
fluctuations. To properly understand the interaction of turbulence with
shocks, one must incorporate the back reaction of the shock-turbulence
interaction. One must therefore incorporate statistically variation in
ram pressure, energy, and mass flux in the mean R-H conditions and then
determine the mean position, velocity, and strength of the shock. This
is an entirely different perspective from that developed in previous
analytic studies, although captured in principle by numerical studies.
We present initial results for a highly simplified system that goes some
way towards addressing the non-linear interaction of fully developed
turbulence with shock waves.
M3 - Paper
SP - 1004
ER -