Thermoviscous dissipation of nonlinear acoustic waves in channels with wavy walls

We derive a nonlinear acoustic wave propagation model for analyzing the thermoviscous dissipation of nonlinear acoustic waves in narrow pores with wavy walls using the boundary layer theory. As a nonlinear acoustic wave propagates in a pore, the wave-steepening effect competes with the bulk dissipation, as well as the thermoviscous heat transfer and shear from the pore walls. Due to thermoviscous dissipation, the wave thickness increases beyond the weak shock thickness scale. Using the weak shock thickness scale, we obtain dimensionless linear and nonlinear model wave equations governing the shock-wall interactions. We also perform two-dimensional shock-resolved direct numerical simulation of the wave propagation inside the pores and compare the results with model equations. The direct numerical simulation and model calculations show that, for flat walls and shock strength parameter ϵ, the dimensional wall heat-flux and shear scale as ϵ. For wavy walls, the scaling becomes ϵ3/2-n(k) where k is the wall-waviness wavenumber and the exponent n increases from 0.5 for k = 0 to n(k)≈0.65 for k = 10, n(k)≈0.75 for k = 20, and n(k)≈0.85 for k = 40. Furthermore, we show that both the dimensionless scaled wall shear and wall heat-flux decrease with increasing k.