Orthogonal, solenoidal, three-dimensional vector fields for no-slip boundary conditions

Numerical calculations of turbulence, as well as theoretical turbulence closure techniques, often depend upon a spectral decomposition of the flow fields. Viscous fluid dynamical calculations generally assume no-slip boundary conditions. However, for incompressible flows, such spectral decompositions have been limited to two-dimensional situations. Here we present a method that yields orthogonal decompositions of incompressible, three-dimensional flow fields and apply it to periodic cylindrical and spherical no-slip boundaries.