Propagating high-frequency shear waves in simple fluids

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.