10.8 Geometric Fluid Dynamics

Abstract

The material realm flow is extended to continuum mechanics, establishing pure geometric fluid dynamics and aerodynamics. Core results: the geometric Reynolds number is determined by the spectral ratio of the Birkhoff Hessian; the boundary layer thickness mm; the Kolmogorov scale μm; the geometric lift coefficient and drag coefficient . All are derived from existing geometric intrinsic quantities, with no experimental input. **Keywords:** geometric fluid dynamics; aerodynamics; Navier-Stokes mapping; Reynolds number; boundary layer; turbulence; Kolmogorov scale; lift; drag; Mach number