The viscous stress tensor records momentum flux caused by velocity gradients. For a Newtonian compressible fluid it separates into shear and bulk contributions.
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The viscous stress tensor is a mathematical representation that describes the internal frictional forces in a fluid (or a deformable solid) due to its viscosity when it is subjected to deformation. It plays a critical role in fluid dynamics, especially in the study of Newtonian fluids, where the stress is linearly related to the strain rate.