A Potential-Flow Theory

The first part of this chapter is concerned largely with a specific prototype problem in which a stationary solid body is immersed in an unbounded, incompressible fluid that is undergoing a steady, uniform translational motion at large distances from the body ( at infinity ) For simplicity, we shall assume in most instances that the body is 2D namely, that it extends indefinitely in the third direction, z, without change of shape so that its geometry can be specified completely by its cross sectional shape in the xy plane. The streaming motion at infinity is then assumed to be parallel to the x y plane. 

To analyze streaming flow at high Reynolds number past a 2D body, the starting point is the full, steady-state Navier-Stokes and continuity equations, nondimensionalized by use of the streaming velocity Uoo as a characteristic velocity scale and a scalar length of the body in the xy plane, say, a, as the characteristic length scale, namely, 

Pressure has been nondimensionalized by use of pUf, as is appropriate for flow at large Reynolds number. 

A convenient way to discuss some aspects of flow at high Reynolds number is in terms of the transport of vorticity rather than directly in terms of velocity and pressure. We recall that the vorticity is defined as the curl of the velocity, 

physically, it represents the local rotational motion of the fluid. We obtain an equation for transport of vorticity directly by taking the curl of all terms in Eq. (10-1). Because 

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