Numerical study of nonlinear streaming inside a standing wave resonator

The acoustic streaming associated to standing waves in a cylindrical resonator is studied for increasing nonlinear Reynolds numbers by numerically solving the compressible Navier-Stokes equations, using a high resolution finite difference scheme. The resonator is excited by shaking it along the axis at imposed frequency, corresponding to the fundamental resonance frequency of the waveguide. For sufficiently large acoustic velocities, shocks are visible. The mean field is computed by time-averaging over the main acoustic period. When the nonlinear Reynolds number increases, the center of the outer streaming cells are pushed toward the acoustic velocity nodes and two additional vortices per quarter-wavelength are generated on the axis, near the velocity anti-nodes. This result differs from linear models and is in agreement with several recent experimental measurement performed in the nonlinear regime. The mean temperature field evolution within the resonator is also investigated.