# Velocity profile in the viscothermal boundary layer

13 december 2018
###### Presentatie Nederlands Akoestisch Genootschap 2019
10 april 2019

Close to a wall, acoustic wave propagation is influenced by viscous and thermal dissipation losses. These losses result in the damping of acoustic waves and also influence the phase relationship between force and the acoustic particle velocity. The animation below shows what happens for a wave that is grazing parallel to a wall. At the wall, due to the no-slip condition, the particle velocity is zero. The further away from the wall the more the flow behaves inertial, where the acceleration is directly proportional to the driving force. Close to the wall, the movement of particles are controlled by both viscous shear and the driving force. Below you see what the velocity does close to a parallel wall:

The driving force is a sinusoidal force $\hat{K}(t) = cos(\omega t)$, and a proper scaling has been used to have a boundary layer thickness in the order of magnitude as the domain size (\$~1~). For more information, see the code in the repository, or the small documentation for the implemented differential equation and numerical solution scheme. Using the two Python scripts, you can see the solution for yourself!