Solitary flexural-gravity waves in three dimensions.

The focus of this work is on three-dimensional nonlinear flexural-gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis, presented in (Plotnikov & Toland. 2011 , 2942-2956 (doi:10.

Korteweg-de Vries solitons on electrified liquid jets.

The propagation of axisymmetric waves on the surface of a liquid jet under the action of a radial electric field is considered. The jet is assumed to be inviscid and perfectly conducting, and a field is set up by placing the jet concentrically inside a perfectly cylindrical tube whose wall is maintained at a constant potential. A nontrivial interaction arises between the hydrodynamics and the electric field in the annulus, resulting in the formation of electrocapillary waves.

Numerical study of interfacial solitary waves propagating under an elastic sheet.

Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model.

Hybrid free-surface flows in a two-dimensional channel.

Hybrid free-surface flows past disturbances in a two-dimensional channel are identified and studied. The fluid is assumed to be inviscid and incompressible, and the flow to be steady and irrotational. The disturbances consist of a step in the bottom of the channel and a flat object lying on the free-surface (e.

Three-dimensional waves beneath an ice sheet due to a steadily moving pressure.

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.

Two-dimensional generalized solitary waves and periodic waves under an ice sheet.

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.

The mathematical challenges and modelling of hydroelasticity.

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, including physically and mathematically elaborated models and the techniques used in their analysis.

Gravity capillary waves in fluid layers under normal electric fields.

We study the formation and dynamics of interfacial waves on a perfect dielectric ideal fluid layer of finite depth, wetting a solid wall, when the region above the fluid is hydrodynamically passive but has constant permittivity, for example, air. The wall is held at a constant electric potential and a second electrode having a different potential is placed parallel to the wall and infinitely far from it. In the unperturbed state the interface is flat and the normal horizontally uniform electric field is piecewise constant in the liquid and air.

Monte Carlo simulation of an inhomogeneous dielectric continuum model for B-DNA.

Thermodynamic and structural properties of the counterion atmosphere surrounding B-DNA are calculated by Monte Carlo simulation in a spatially inhomogeneous, but piecewise uniform, dielectric continuum cell model - the "barbarous" model. A boundary element formulation is implemented to study the sensitivity of these properties with respect to perturbations in the location of discontinuous dielectric boundaries relative to fixed and mobile charges. High concentrations are considered corresponding to the liquid crystalline hexagonally ordered phase of DNA.

Steady two-layer flows over an obstacle.

Nonlinear waves in a forced channel flow of two contiguous homogeneous fluids of different densities are considered. Each fluid layer is of finite depth. The forcing is due to an obstruction lying on the bottom.