ABSTRACT
The most common generalization of the non-relativistic conservation laws of fluid dynamics to include viscosity are called the Navier-Stokes equations, which are used in a wide range of applications of fluid dynamics, from water flows and weather prediction to medical fluid dynamic. The stronger the viscosity of the fluid, the more momentum is converted to heating and transferred between fluid parcels due to shearing and compression. Fluids that depend quadratically on velocity gradients are called Stokesian fluids. The first-order terms can be decomposed into two effects, bulk viscosity and shear viscosity. Under realistic conditions, viscosity can often not be ignored and Euler's equations need to be augmented with terms describing its impact. The continuity equation is not affected by fluid viscosity. Viscosity is a consequence of friction, in turn produced by local velocity differences within the fluid. In general, viscosity is not of importance in areas of astrophysical modelling where the gases are dilute, although there are notable exceptions.
