  We present a phenomenological fluid dynamics model for a dilatant fluid, i.e.
a severe shear thickening fluid, by introducing a state variable. The
Navier-Stokes equation is coupled with the state variable field, which evolves
in response to the local shear stress as the fluid is sheared. The viscosity is
assumed to depend upon the state variable and to diverge at a certain value due
to jamming. We demonstrate that the coupling of the fluid dynamics with the
shear thickening leads to an oscillatory instability in the shear flow. The
model also shows a peculiar response of the fluid to a strong external impact.
