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Figure 4. Sketch of the uniform flow (speed = 1, Mach number >1) past the aerofoil
everywhere.) The non-dimensional version of the physical configuration is
shown in figure 4. Finally, the boundary conditions are
and
where the first, (3.23), ensures that, upstream, we have only the given uniform flow
with and the second, (3.24), states that the surface of the aerofoil is
a streamline of the flow.
Equation (3.22), with and is predominantly a wave equation (but
here expressed in spatial variables, x and y); the form of this equation suggests that we
seek an asymptotic solution
and then we obtain
and so on. Correspondingly, the boundary conditions give
and
