Shear stress ($\tau$)

Shear stress is the tangential component of traction on a surface. For leading unidirectional flow $u(y)$ in a Newtonian fluid, $\tau =\mu du/dy$.

A horizontally compressive force per width $F$, carried uniformly through thickness $a$, gives additional horizontal stress $F/a$. Resolving its traction on a fault dipping at angle $\delta$ gives the displayed mean shear stress. An isotropic background pressure adds only normal traction. The integrated force alone does not determine the actual depth-dependent stress distribution or whether a fault fails.

The shear velocity is the velocity scale $u_{\ast }=\sqrt{|\tau |/\rho }$ associated with a shear stress $\tau$ in a fluid of mass density $\rho$. It is a stress scale, not automatically the actual local fluid velocity at a grain.