Propagation of Strong Blast in an Atmosphere of Varying Density (Classic Reprint) - Brossura

Austern, Norman

 
9781330188927: Propagation of Strong Blast in an Atmosphere of Varying Density (Classic Reprint)

Sinossi

Excerpt from Propagation of Strong Blast in an Atmosphere of Varying Density

The parameter S first was introduced in equation and entered the differential equations through the similarity transformation It measures the distortion of shape of the shock surface. In some fashion S must be determined by a requirement that the solutions be consistent at y O.

The requirement we actually use is that S be chosen so that the solution is as regular as possible at y 0.

Physically, the reasonableness of determining the shock shape by a condition at the center may be understood in the following way: The hydrodynamical equations are local equations, so an approximate integration which proceeds inwards from a small region of the shock surface can only determine the properties of the volume behind the shock with respect to the properties of that surface region from which the integration has started. To determine the overall shock shape and velocity the various different surface elements must communicate with each other, by way of signals trans mitted through the interior. This communication is equivalent mathematically to the requirement of the consistency with each other of the solutions which emanate from the different points of the shock surface. In the present problem.

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