  The shallow water equations without shear effects are similar to the gas
dynamics equations with a polytropic equation of state. When the shear effects
are taken into account, the equations contain additional evolution equations
mathematically analogous to those of the Reynolds stresses in turbulent flows
of compressible fluids when the source terms are neglected (ideal turbulence).
We show that the non-dissipative model of shear shallow water flows and the
model of ideal turbulence admit a similar variational formulation where, in the
both cases, the equations for the Reynolds stress tensor evolution are
considered as non-holonomic constraints.
