In the video link above describing Prandtl Meyer Waves, lecturer stated (at 22:40) a very important fact on which he based his first half of the lecture. "Mach wave (mach lines) deflect the flow through an infinitely small angle".

Now, lets look at the flow over the airfoil. First the flow over the top surface will accelerate to supersonic speeds(and above) until it reaches the point(roughly) of maximum camber. Due to acceleration, mach lines will diverge and of course no shock wave will form. But, after the point of maximum camber, where adverse pressure gradient will be introduced and decelerate the airflow than mach lines will start to converge (coalesce). Once they do it the shock wave will form above an airfoil (picture below). If aircraft countinues to accelerate, the mach lines would intersect each other more lower and lower to the airfoil bringing a shock wave down, until it meets the airframe (this sentence is my assumption and I would like confirmation if it is correct). At that point(once it touches the airframe) the boundary layer will always separate and cause a shock stall(also my assumtion, will it happen always?). My question is:

Is boundary layer separation caused by the extreme instantaneous pressure increase on the airfoil surface, or because of the convergence of mach lines and deflecting the airflow regardless of the pressure(and density) change? Or is it combination of both? Also if the statement from the lecturer is correct, shouldn't the mach lines deflect the airflow sooner and not only at the point when they all merge together?

Shock wave formation above airfoil


1 Answer 1


The simplest answer is that a shock wave for a boundary layer means a sharp adverse pressure gradient. You probably know already that adverse pressure gradient will thicken a boundary layer and thick boundary layers are more prone to separation. Also, if the adverse pressure grad. is so strong, it can immediately produce a detachment of the flow from the wall.

Shock wave/Boundary layer interaction simulated with LES. Source: Argonne Leadership Computing Facility, Argonne National Laboratory, U.S. DOE

Add to this that a separation bubble forms in the near region and this interacts with the shock. All these phenomena are quite complicated and to explore their underlying physics Large-Eddy Simulations (LES) are used for the Navier-Stokes equations. This is a topic of Ph.D level research. If you want an introduction you can check this source and discover further on your own.


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