Abstract
A complex dynamics of a shear wave decay, defined as an initial value problem u(y,0)=U sin(ky)i, where i is a unit vector in the x-direction, is investigated in the entire range of the Weissenberg–Knudsen number (Wi=τνk2=τ2c2k2) variation 0≤Wi≤∞, where τ and c are the fluid relaxation time and speed of sound in the vicinity of thermodynamic equilibrium, respectively. It is shown that in the limit Wi⪡1, the shear wave decay is a purely viscous process obeying a parabolic diffusion equation. When Wi⪢1, a completely new regime emerges, the flow behaves as a dissipative transverse traveling wave. This transition is theoretically predicted as a solution to the Boltzmann–Bhatnagar–Gross–Krook equation and confirmed by the lattice Boltzmann numerical simulations. In the limit Wi=τνk2⪢1 the observed slowing down of the shear wave decay can be interpreted as a high-frequency drag reduction.
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