Volume viscosity

Volume viscosity (also called bulk viscosity) appears in the Navier-Stokes equation if it is written for compressible fluid, as described in the most books on general hydrodynamics ^[1], ^[2], and the acoustics ^[3],^[4].

$\rho \left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v}\right) = -\nabla p + \mu \nabla^2 \mathbf{v} + \mathbf{f} +(4\mu /3 + \mu^v) \nabla (\nabla \cdot \mathbf{v})$