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A theory for the evolution of a metric $g$ driven by the equations ofthree-dimensional continuum mechanics is developed. This metric in turn allowsfor the local existence of an evolving three-dimensional Riemannian manifoldimmersed in the six-dimensional Euclidean space. The Nash-Kuiper theorem isthen applied to this Riemannian manifold to produce a wild evolving $C^{1}$manifold. The theory is applied to the incompressible Euler and Navier-Stokesequations. One practical outcome of the theory is a computation of criticalprofile initial data for what may be interpreted as the onset of turbulence forthe classical incompressible Navier-Stokes equations.

Fluids, Geometry, and the Onset of Navier-Stokes Turbulence in Three Space Dimensions