A streamline coordinate system for distorted two-dimensional shear flows

Abstract

A function ϕ is derived which is constant along the orthogonal trajectories of streamlines in two-dimensional flow. In irrotational flows, ϕ reduces to the velocity potential. The pair of functions ϕ and ψ, where ψ is the stream function, are used to define a coordinate system in rotational fluid flows. Tensor methods are used to transform the equations of motion of a turbulent fluid and the equations for second moments of turbulent fluctuations to this coordinate system. Explicit extra terms appear in the transformed equations embodying the effects of streamline curvature and mean flow acceleration. These extra terms are characterized by two lengthscales which arise naturally from the transformation: the local radius of curvature of the streamline and the ‘e-folding’ distance of the mean streamwise velocity.