EXACT NONLINEAR FORCED PERIODIC-SOLUTIONS OF THE NAVIER-STOKES EQUATION

Two-dimensional flow with the vector potential exp(A1x + A2y + A3z)cos(B3z - omega-t)k, is self-superposable, in the sense that the curl to the Lamb vector vanishes. In addition, superposing a steady flow in the z-direction gives a non-linear exact solution for the Navier-Stokes equation with an eigenvalue condition or dispersion equation involving the coefficients of the variables. Scaling relations are developed between the Reynolds number, the Strouhal number, and dimensionless numbers based on the wavelengths and the damping lengths. As are acoustic waves, this flow is 'forced'; in other words, driven by some source. Theory agrees well with Rayleigh's empirical formula for the "edge tone". A possible explanation for the onset of turbulence in this flow is advanced.