Numerical study of interfacial solitary waves propagating under an ice 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. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches end with the free surface approaching the interface. On the other hand, the limiting configurations of long baroclinic (i.e. internal) solitary waves are characterized by an infinite broadening in the horizontal direction. Baroclinic wave-packet modes also exist for a large range of amplitudes and generalized solitary waves are computed in a case of a long internal mode in resonance with surface modes. In contrast to the pure gravity case (i.e without an elastic cover), these generalized solitary waves exhibit new Wilton-ripple-like periodic trains in the far field

The trajectory of slender curved liquid jets for small Rossby number

© The Author(s) 2018. Wallwork et al. (2002, The trajectory and stability of a spiralling liquid jet. Part 1. Inviscid theory. J. Fluid Mech., 459, 43-65) and Decent et al. (2002, Free jets spun from a prilling tower. J. Eng. Math., 42, 265-282) developed an asymptotic method for describing the trajectory and instability of slender curved liquid jets. Decent et al. (2018, On mathematical approaches to modelling slender liquid jets with a curved trajectory. J. FluidMech., 844, 905-916.) showed that this method is accurate for slender curved jets when the torsion of the centreline of the jet is small or O(1), but the asymptotic method may become invalid when the torsion is asymptotically large. This paper examines the torsion for a slender steady curved jet which emerges from an orifice on the outer surface of a rapidly rotating container. The torsion may become asymptotically large, close to the orifice when the Rossby number Rb " 1, which corresponds to especially high rotation rates. This paper examines this asymptotic limit in different scenarios and shows that the torsion may become asymptotically large inside a small inner region close to the orifice where the jet is not slender. Outer region equations which describe the slender jet are determined and the torsion is found not to be asymptotically large in the outer region; these equations can always be used to describe the jet even when the torsion is asymptotically large close to the orifice. It is in this outer region where travelling waves propagate down the jet and cause it to rupture in the unsteady formulation, and so the method developed by Wallwork et al. (2002, The trajectory and stability of a spiralling liquid jet. Part 1. Inviscid theory. J. Fluid Mech., 459, 43-65) and Decent et al. (2002, Free jets spun from a prilling tower. J. Eng. Math., 42, 265-282) can be used to accurately study the jet dynamics even when the torsion is asymptotically large at the orifice

A theory for the impact of a wave breaking onto a permeable barrier with jet generation

We model a water wave impact onto a porous breakwater. The breakwater surface is modelled as a thin barrier composed of solid matter pierced by channels through which water can flow freely. The water in the wave is modelled as a finite-length volume of inviscid, incompressible fluid in quasi-one-dimensional flow during its impact and flow through a typical hole in the barrier. The fluid volume moves at normal incidence to the barrier. After the initial impact the wave water starts to slow down as it passes through holes in the barrier. Each hole is the source of a free jet along whose length the fluid velocity and width vary in such a way as to conserve volume and momentum at zero pressure. We find there are two types of flow, depending on the porosity, ß , of the barrier. If ß : 0 = ß < 0.5774 then the barrier is a strong impediment to the flow, in that the fluid velocity tends to zero as time tends to infinity. But if ß : 0.5774 = ß = 1 then the barrier only temporarily holds up the flow, and the decelerating wave water passes through in a finite time. We report results for the velocity and impact pressure due to the incident wave water, and for the evolving shape of the jet, with examples from both types of impact. We account for the impulse on the barrier and the conserved kinetic energy of the flow. Consideration of small ß gives insight into the sudden changes in flow and the high pressures that occur when a wave impacts a nearly impermeable seawall

Gravity-capillary water waves generated by multiple pressure distributions

Abstract Steady two-dimensional free-surface flows subjected to multiple localised pressure distributions are considered. The fluid is bounded below by a rigid bottom, and above by a free-surface, and is assumed to be inviscid and incompressible. The flow is assumed irrotational, and the effects of both gravity and surface tension are taken into account. Forced solitary wave solutions are found numerically, using boundary integral equation techniques, based on Cauchy integral formula. The integrodifferential equations are solved iteratively by Newton&apos;s method. The behaviour of the forced waves is determined by the Froude number, the Bond number, and the coefficients of the pressure forcings. Multiple families of solutions are found to exist for particular values of the Froude number; perturbations from a uniform stream, and perturbations from pure solitary waves. Elevation waves are only obtained in the case of a negatively forced pressure distribution

Trapped waves on interfacial hydraulic falls over bottom obstacles

Hydraulic falls on the interface of a two-layer density stratified fluid flow in the presence of bottom topography are considered. We extend the previous work [Philos. Trans. R. Soc. London A 360, 2137 (2002)] to two successive bottom obstructions of arbitrary shape. The forced Korteweg-de Vries and modified Korteweg-de Vries equations are derived in different asymptotic limits to understand the existence and classification of fall solutions. The full Euler equations are numerically solved by a boundary integral equation method. New solutions characterized by a train of trapped waves are found for interfacial flows past two obstacles. The wavelength of the trapped waves agrees well with the prediction of the linear dispersion relation. In addition, the effects of the relative location, aspect ratio, and convexity-concavity property of the obstacles on interface profiles are investigated