- Full text PDF available (10)
Solutions of the nonlinear water wave equations under an ice sheet are computed using a boundary integral equation method. The ice sheet is modelled as a thin elastic plate and the fluid equations are nonlinear. Depending on the velocity of the moving disturbance generating the flow, different types of responses of the floating ice sheet are discussed.
Stirling's formula, the asymptotic expansion of n! for n large, or of Γ(z) for z → ∞, is derived directly from the recursion equationΓ(z + 1) = zΓ(s) and the normalization condition Γ 1 2 = √ π.
Two-dimensional gravity waves travelling under an ice sheet are studied. The flow is assumed to be potential. Weakly nonlinear solutions are derived and fully nonlinear solutions are calculated numerically. Periodic waves and generalized solitary waves are studied.
Hydroelasticity brings together hydrodynamics and elastic theories. It is concerned with deformations of elastic bodies responding to hydrodynamic excitations, which themselves depend on elastic deformation. This Theme Issue is intended to identify and to outline mathematical problems of modern hydroelasticity and to review recent developments in this area,… (More)
Two different physical problems are considered: the magnetic shaping of a liquid metal column and the distortion of a bubble in a corner vortex flow. It is shown that the two problems can be modeled with a virtually identical set of equations. These equations are solved numerically using a conformal mapping and a series truncation method, which permits fast… (More)
This study considers the nonlinear dynamics of stratified immiscible fluids when an electric field acts perpendicular to the direction of gravity. A particular setup is investigated in detail, namely, two stratified fluids inside a horizontal channel of infinite extent. The fluids are taken to be perfect dielectrics, and a constant horizontal field is… (More)
Recently developed techniques in exponential asymptotics beyond all orders are employed on the problem of potential flows with a free surface and small surface tension, in the absence of gravity. Exponentially small capillary waves are found to be generated on the free surface where the equipotentials from singularities in the flow (for example, stagnation… (More)