Hydrodynamic forces on two moving discs. (English) Zbl 1106.76015

The authors study the motion of ideal fluid around two rigid circular discs moving in the plane. The authors present an explicit construction of complex potentials for irrotational incompressible fluid flows by means of elliptic functions. The exponential and conformal mappings are used to relate elliptic functions with meromorphic functions in the annular complex region and in the region in the plane outside two discs. First-order poles in the annular region correspond to vortices outside the discs. Inflows are incorporated by putting a second-order pole at the point in the annulus that corresponds to infinity. Both stationary two-disc configurations and configurations in which the discs move relative to each other, are considered.


76B47 Vortex flows for incompressible inviscid fluids
76M40 Complex variables methods applied to problems in fluid mechanics
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