The Secret of Flow Separation Uncovered

Real flow as potential flow modified by vortical slip separation with point stagnation.

The flow around a body moving through a slightly viscous incompressible fluid like water or air at subsonic speeds, attaches at the front as fluid particles approach the body and separates in the back as fluid particles part from the body.

In slightly viscous flow fluid particles glide along the surface with small skin friction which can be approximated as a slip boundary condition.

Observation shows laminar attachment and turbulent separation, with the flow being close to potential flow (inviscid irrotational flow with slip) prior to separation. In potential flow the separation is simply reverse attachment and thus real flow differs from potential flow at separation.

Ever since the basic mathematics of fluid mechanics was formulated by Euler and d'Alembert in the mid 18th century, a prime goal has been to describe slightly viscous flow around a body as potential flow subject to some modification at separation:

• Prandtl as the father of modern fluid mechanics described the modification as a boundary layer effect from a no-slip boundary condition.
• Kutta and Zhukovsky as fathers of modern flight mechanics described the modification as large scale circulation around a wing section.

In the new article Analysis of Separation in Turbulent Incompressible Flow together with Johan Hoffman (submitted), we show that the answer is neither boundary layer nor circulation, but instead

• vortical slip separation with point stagnation.

We give evidence in the form of

• mathematical analysis of basic instability of potential flow at separation
• computational solution of Navier-Stokes equations
• experimental observation.

We thus present strong evidence that the dream of Euler and d'Alembert can be fulfilled by describing slightly viscous flow around a body as

• potential flow modified by vortical slip separation with point stagnation.

The article gives the details.

As an application we uncover The Secret of Flight (upcoming book) and The Mathematical Secret of Flight (article and talk).