Numerical solutions for laminar incompressible fluid flows past an abruptly started elliptic cylinder at 45° incidence are presented. Various finite-difference schemes for the stream-function/vorticity formulation are used and their merits briefly discussed. Almost steady-state solutions are obtained forRe= 15 and 30, whereas forRe= 200 a Kármán vortex street develops. The transient period from the start to the steady or quasi-steady state is investigated in terms of patterns of streamlines and lines of constant vorticity and drag, lift and moment coefficients.

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Numerical solutions for the irrotational flow of an incompressible fluid about a circular cylinder accelerated from rest below a free surface are presented. The usual restriction to linearized free-surface boundary conditions has been avoided. The transient period from the start to a local steady state or to the development of a very steep wave slope is investigated in terms of free-surface profiles and body-surface pressure distributions. Linear and nonlinear results are used to illustrate the transition from deep submergence when nonlinear effects are small to shallow submergence when linearized analysis is inaccurate.

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