Sonically produced heat in a fluid with bulk viscosity and shear viscosity

In a viscous fluid, sound produces heat in a spatial pattern which, in general, depends on the relative magnitudes of the shear viscosity coefficient eta and the bulk viscosity coefficient B'. It is well known that when the particle velocity components ui relative to Cartesian coordinates xi are given for an arbitrary sound field, or any field of flow, the volume rate of heat production qv can be determined from a dissipation function in the form B'T1 + eta T2. Here, T1 and T2 are quadratic functions involving derivatives of the type delta ui/delta xj. In this paper, examples are discussed for continuous monofrequency sound fields, including crossed plane waves, as well as focused and unfocused fields. In these examples, spatial distributions of the time-averaged quantity [qv] for media in which the loss mechanism is primarily bulk viscosity are compared to those for media in which shear viscosity dominates.