My question refers to stokes's law of sound attenuation in viscous medium. At this point i don't try to understand the mathematical form of the law - i simply don't understand how viscosity effects planar waves - this law states that planar waves decay exponentially, and i don't understand how a shear stress emerges in the propogation of perfectly planar waves. So what do shear stresses and sound propogation have in common?
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Newton's law of viscosity, when properly extended using mathematical rigor to 3 dimensions, results in a linear relationship between the 3D stress tensor and the 3D rate of deformation tensor, and includes not only viscous shear stresses and shear rates, but also normal stresses and normal strain rates. These normal stresses and strains are operative in the situation(s) that you are describing. The relationship between the stress tensor and the rate of deformation tensor reduces to the usual equation relating shear stress to shear rate for the special case of pure shear (with only one velocity gradient).
Even for the case of pure shear, if the stresses and strains are resolved into their principal components (say by transforming using a coordinate system rotation), the only stress components present will be normal stresses and the only strain rate components present will be normal strain rates.
answered Sep 9, 2016 at 23:35