  Low-frequency molecular fluctuations in the translational nonequilibrium zone
of one-dimensional strong shock waves are characterised for the first time in a
kinetic collisional framework in the Mach number range $2\le M\le 10$. Our
analysis draws upon the well-known bimodal nature of the probability density
function (PDF) of gas particles in the shock, as opposed to their Maxwellian
distribution in the freestream, the latter exhibiting an order of magnitude
higher dominant frequencies than the former. Inside the (finite-thickness)
shock region, the strong correlation between perturbations in the bimodal PDF
and fluctuations in the normal stress suggests introducing a novel two-bin
model to describe the reduced-order dynamics of a large number of collision
interactions of gas particles. Our model correctly predicts the
order-of-magnitude difference in fluctuation frequencies in the shock versus
those in the freestream and is consistent with the small-amplitude fluctuations
obtained from the highly resolved Direct Simulation Monte Carlo (DSMC)
computations of the same configuration. The variation of low-frequency
fluctuations with changes in the conditions upstream of the shock revealed that
these fluctuations can be described by a Strouhal number, based on the bulk
velocity upstream of the shock and the shock-thickness based on the maximum
density-gradient inside the shock, that remains practically independent of Mach
number in the range examined. Our results are expected to have far-reaching
implications for boundary conditions employed in the vicinity of shocks in the
framework of flow instability and laminar-turbulent transition studies of flows
containing both unsteady and nominally stationary shocks.
