  In the laminar mode interactions among molecules generate friction between
layers of water that slide with respect to each other. This friction triggers
the shear stress, which is traditionally presumed to be linearly proportional
to the velocity gradient. The proportionality coefficient characterizes the
viscosity of water. Remarkably, the standard Navier-Stokes model surmises that
materials never fail - the transition to turbulence can only be triggered by
some kinematic instability of the flow. This premise is probably the reason why
the Navier-Stokes theory fails to explain the so-called subcritical transition
to turbulence with the help of the linear instability analysis. When linear
instability analysis fails, nonlinear instability analysis is often resorted
to, but, despite the occasional uses of this approach, it is intrinsically
biased to require finite flow perturbations which do not necessarily exist.
  In the present work we relax the traditional restriction on the perfectly
intact material and introduce the parameter of fluid viscous strength, which
enforces the breakdown of internal friction. We develop a generalized
Navier-Stokes constitutive model which includes a material failure description,
and use it to analyze the Couette flow between two parallel plates to find that
the lateral infinitesimal perturbations can destabilize the laminar flow.
Furthermore, we use the results of the recent experiments on the onset of
turbulence in pipe flow to calibrate the viscous strength of water.
Specifically, we find that the maximal shear stress that water can sustain in
the laminar flow is about one Pascal. We note also that the introduction of the
fluid strength uncovers new prospects in the explanation of the remarkable
phenomenon of the delay of the transition to turbulence due to an addition of a
small amount of long polymer molecules to water.

Fluid Dynamics