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Cusp behind shock?

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Old   July 3, 2008, 15:36
Default Cusp behind shock?
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Frank
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Hi Guys, I am studying steady, 2D transonic flow. I am concerned with subsonic freestream which have a Mach number above the critical Mach number (and therefore give rise to an embedded supersonic bubble on top of the airfoil).

I am reading that the foot of the shock is normal to the surface of the airfoil, I understand this to be necessary in order to ensure that the flow behind the shock is tangential to the airfoil surface. I have read, however, that the Rankine Hugoniot equations require that the shock has an infinite curvature at its foot. This is referred to as a Zierep cusp.

I am unsure what is meant by this statement. Could someone please explain to me what is meant by "infinite curvature"; I'd also be very happy if someone could explain why this cusp forms?

I have a working knowledge of the RH conditions but do not know why they would impose any condition upon the curvature of the shock.

Could someone please advise? Frank
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