Potential/complex-lamellar velocity decomposition and its relevance to turbulence

I n discussing turbulent shear layers, experimentalists have divided the flow into a turbulent region, which is vortical, and a non-turbulent region, which is irrotational but unsteady. This paper introduces a theoretical method of decomposing the velocity field into potential and vortical components that is compatible with the experi-mentalists ’ viewpoint. Specifically, only potential motions will exist in the non-turbulent region, while the decomposition shows that the turbulent region consists of both potential and vortical motions. The kinematic decomposition used is called a potential/complex-lamellar decomposition. Compared with the standard Helmholtz decomposition, the complex-lamellar decomposition is not widely known, and this article includes a discussion of its properties and characteristics. The vector com-ponents in this decomposition may be represented by three scalar potentials: 4, @ and x, One of the important physical interpretations of the potentials concerns vortex lines. Vortex lines are defined by the intersection of a surface @ = constant with a surface x = constant. Since these surfaces are a function of time, this establishes a sound kinematic theory for following the history of vortex lines in a turbulent or viscous flow. 1