ABSTRACT
The effect of a rigid plane wall on the potential flow due to a source/sink is equivalent (Section 16.1) to the introduction of an identical image, leading to tangential velocity at the wall, and doubling of the velocity at large distance; in the case a vortex (Section 16.2) the condition of tangential velocity at the wall, leads to an image with opposite circulation; the flow at large distance appears like due to a dipole perpendicular to the wall, and decays faster than it would for the isolated vortex. For a monopole seen in the far-field, the source/sink part is doubled by the wall effect, and unless absent, dominates the vortex part that decays faster as a dipole (Section 16.3). For a dipole (multipole) the effect (Section 16.4) in the far-field is similar, doubling the real part and causing the imaginary part to decay faster as a quadrupole (multipole one order higher). In the case of a source/sink (Section 16.5) [vortex (Section 16.6)], at any position in a rectangular corner there are three identical (alternating) images, so that in the far-field the strength is multiplied by four [is reduced to a quadrupole]. The superposition of the preceding specifies the flow field due to a monopole in a rectangular corner (Section 16.7), for example, along the diagonal. A source/sink in a corner of angle β = 2π/n is multiplied in strength by n in the far-field (Section 16.8), whereas a vortex in a corner of angle β = π/n becomes (Section 16.9) a multipole of order n in the far-field. The representation of wall effects by images applies not only to potential flows (Chapters 16, 28, 34, 36, 38) but also to electrostatic (Chapter 24) and magnetostatic (Chapter 26) fields and various types of waves.
