Three-dimensional viscous flows with large secondary velocity

A new system of approximation equations is derived for three-dimensional steady viscous compressible flows in which a primary-flow direction is present, but in which both transverse velocity components can be large. Previous approaches which address simplification of the steady Navier-Stokes equations are discussed, and a new approach is proposed. The transverse velocity vector which corrects a given potential flow has been decomposed into potential and rotational components. It is found that the potential-velocity vector may be assumed small, whereas the rotational-velocity vector may be assumed small, whereas the rotational velocity vector and hence the composite secondary flow can be of order unity. This assumption leads to a system of governing equations whose characteristic polynomial has a non-elliptic form for arbitrary Mach numbers. The resulting non-elliptic approximation equations can be solved as an initial/boundary-value problem. Computed results confirm the small scalar-potential approximation.