This development is a description of the transport of mass, energy and momentum in flowing viscous fluids at the molecular level; and results in: • A thermostatistical link between Reynolds’ number and momentum and free energy, • A wave characterization of the behavior of flowing fluids using the forces of attraction between molecules as a basis, • Calculation of the velocity components in flowing fluids for all Reynolds’ numbers greater than 535; thus defining a mathematical theory of turbulence, • An analytic solution of the Navier-Stokes equations for incompressible fluids in 3-dimensions. The following steps lead to the solution: • Definition of the fluid Model, • A re-characterization of Reynolds’ number in terms of momentum and free energy, • Calculation of the shear and circulatory components of velocity, • Transformation of the Navier-Stokes equations into the curvilinear coordinates of the intermolecular force waves, • Using the transformed equations to calculate the velocity components and Pressure-wave front resulting from the current, • Corroboration of the theoretical results with: a) wave fronts as manifest in the behavior of sails in uniform flow, b) boundary layer definition/behavior compared to theoretical and empirical developments of Schlichting and others, and c) empirical results for forces measured in the OCEANIC/DeepStar high Re beam-tow tests.

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