Exact solution of the wave-resistance problem for a submerged cylinder. I: Linearized theory (Q1968697)

The authors consider two-dimensional fluid in an infinite channel with free surface and a submerged obstacle of finite length and small thickness. Looking for a steady, inviscid and irrotational flow, the authors expand the nonlinear problem in powers of the thickness of the obstacle. To leading order, they derive a linear elliptic equation in a strip, cut along a horizontal line segment in the interior, and equipped with certain (linear) boundary conditions on both sides of the cut and on the top and bottom of the strip. Subtracting a harmonic function which satisfies the given boundary conditions, the authors reduce the original problem to a Dirichlet problem in an infinite strip without cut. This problem is then solved using a variational characterization of the solution. The result is an essential ingredient to the solution of the nonlinear problem examined in part II [see the following entry].