Initial stage of plate lifting from a water surface

This study deals with the flow induced by a rigid flat plate of finite length, initially touching a horizontal water surface, when it starts to move upwards with constant acceleration. In the present model, negative hydrodynamic pressures on the lower (wetted) surface of the plate are allowed, and thus, the water follows the plate due to the resulting suction force. The acceleration of the plate and the plate length are such that gravity, surface tension and viscous effects can be neglected during the early stages of the motion. Under these assumptions, the initial two-dimensional, potential flow caused by the plate lifting is obtained by using the small-time expansion of the velocity potential. This small-time solution is not valid close to the plate edges, as it predicts there singular flow velocities and unbounded displacements of the water-free surface. It is shown that close to the plate edges the flow is nonlinear and self-similar to leading order. This nonlinear flow is computed by the boundary-element method combined with a time-marching scheme. The numerical time-dependent solution approaches the self-similar local solution with time

On the astrophysical robustness of neutron star merger r-process

In this study we explore the nucleosynthesis in the dynamic ejecta of compact binary mergers. We are particularly interested in the question how sensitive the resulting abundance patterns are to the parameters of the merging system. Therefore, we systematically investigate combinations of neutron star masses in the range from 1.0 to 2.0 \Msun and, for completeness, we compare the results with those from two simulations of a neutron star black hole merger. The ejecta masses vary by a factor of five for the studied systems, but all amounts are (within the uncertainties of the merger rates) compatible with being a major source of cosmic r-process. The ejecta undergo a robust r-process nucleosynthesis which produces all the elements from the second to the third peak in close-to-solar ratios. Most strikingly, this r-process is extremely robust, all 23 investigated binary systems yield practically identical abundance patterns. This is mainly the result of the ejecta being extremely neutron rich (\ye $\approx0.04$) and the r-process path meandering along the neutron drip line so that the abundances are determined entirely by nuclear rather than by astrophysical properties. This robustness together with the ease with which both the second and third peak are reproduced make compact binary mergers the prime candidate for the source of the observed unique heavy r-process component.Comment: accepted for publication in MNRA

Water entry of a flat elastic plate at high horizontal speed

The two-dimensional problem of an elastic-plate impact onto an undisturbed surface of water of infinite depth is analysed. The plate is forced to move with a constant horizontal velocity component which is much larger than the vertical velocity component of penetration. The small angle of attack of the plate and its vertical velocity vary in time, and are determined as part of the solution, together with the elastic deflection of the plate and the hydrodynamic loads within the potential flow theory. The boundary conditions on the free surface and on the wetted part of the plate are linearized and imposed on the initial equilibrium position of the liquid surface. The wetted part of the plate depends on the plate motion and its elastic deflection. To determine the length of the wetted part we assume that the spray jet in front of the advancing plate is negligible. A smooth separation of the free-surface flow from the trailing edge is imposed. The wake behind the moving body is included in the model. The plate deflection is governed by Euler’s beam equation, subject to free–free boundary conditions. Four different regimes of plate motion are distinguished depending on the impact conditions: (a) the plate becomes fully wetted; (b) the leading edge of the plate touches the water surface and traps an air cavity; (c) the free surface at the forward contact point starts to separate from the plate; (d) the plate exits the water. We could not detect any impact conditions which lead to steady planing of the free plate after the impact. It is shown that a large part of the total energy in the fluid–plate interaction leaves the main bulk of the liquid with the spray jet. It is demonstrated that the flexibility of the plate may increase the hydrodynamic loads acting on it. The impact loads can cause large bending stresses, which may exceed the yield stress of the plate material. The elastic vibrations of the plate are shown to have a significant effect on the fluid flow in the wake

Interaction of flexural-gravity waves in ice cover with vertical walls

Diffraction of flexural-gravity waves in an ice cover by a bottom mounted structure with vertical walls is studied. The problem is solved by using the so-called vertical modes corresponding to the roots of the dispersion relation for flexural-gravity waves. These modes reduce the original three-dimensional problem to a set of two-dimensional diffraction problems with non-homogeneous boundary conditions on the rigid walls. Two unknown functions presenting in the boundary conditions for each mode are determined using the conditions at the contact line between the ice cover and the vertical walls. The clamped conditions at the contact line, where the ice cover is frozen to the wall, are considered in this study. The solution of the problem is obtained for a single vertical circular cylinder frozen in the ice cover. A general approach to the problem for vertical cylinders of any shapes is presented. The diffraction problems with vertical walls extended to infinity are discussed

Formation of corner waves in the wake of a partially submerged bluff body

We study theoretically and numerically the downstream flow near the corner of a bluff body partially submerged at a deadrise depth Δh into a uniform stream of velocity U, in the presence of gravity, g. When the Froude number, Fr=U/√gΔh, is large, a three-dimensional steady plunging wave, which is referred to as a corner wave, forms near the corner, developing downstream in a similar way to a two-dimensional plunging wave evolving in time. We have performed an asymptotic analysis of the flow near this corner to describe the wave's initial evolution and to clarify the physical mechanism that leads to its formation. Using the two-dimensions-plus-time approximation, the problem reduces to one similar to dam-break flow with a wet bed in front of the dam. The analysis shows that, at leading order, the problem admits a self-similar formulation when the size of the wave is small compared with the height difference Δh. The essential feature of the self-similar solution is the formation of a mushroom-shaped jet from which two smaller lateral jets stem. However, numerical simulations show that this self-similar solution is questionable from the physical point of view, as the two lateral jets plunge onto the free surface, leading to a self-intersecting flow. The physical mechanism leading to the formation of the mushroom-shaped structure is discussed

The ice response to an oscillating load moving along a frozen channel

Unsteady response of an ice cover to an oscillating load moving along a frozen rectangular channel is studied for large times. The channel is filled with ideal incompressible fluid. The ice cover is modelled by a thin elastic plate. The flow caused by the deflection of the ice cover is potential. The problem is formulated within the linear theory of hydroelasticity. External load is modelled by a smooth localized pressure distribution. The load has periodic magnitude and moves along the channel with constant speed. Joint system of equations for the ice plate and the flow potential is closed by initial and boundary conditions: the ice plate is frozen to the walls of the channel, the flow velocity potential satisfies the impermeability condition at the rigid walls of the channel and linearized kinematic and dynamic conditions at the ice-liquid interface; at the initial time the load is stationary, the fluid in the channel is at rest and the stationary ice deflection is determined from the plate equation for the initial magnitude of the load. The problem is solved with the help of the Fourier transform along the channel. The ice deflection profile across the channel is sought in the form of the series of the eigenmodes of the ice cover oscillations in a channel. The solution of the problem is obtained in quadratures and consists of three parts: (1) symmetric with respect to the load deflection corresponding to the stationary load; (2) deflection corresponding to steady waves propagating at the load speed; (3) deflection corresponding to waves propagating from the load and caused by the oscillations of the load. The number of the last waves, depending on the parameters, can not exceed four for each eigenmode. In this article the results of the analytical and numerical analysis of the considered problem is presented

Asymptotic behaviour of dam break flow for small times

Two dimensional impulsive flow of a fluid is studied within the potential flow theory. Initially the fluid is at rest and is held on one side of a vertical plate. The plate is withdrawn suddenly and gravity driven flow of the fluid starts. Attention is paid to the singular behaviour of the velocity field at the bottom point, where the vertical free surface meets the rigid bottom. The linear problem is solved by the Fourier series method. An inner region solution is found using Mellin transform at the bottom point. The jet formation is observed at the bottom point. Also the discontinuity at the upper corner point is dealt with Lagrangian variables. For the second order outer problem, domain decomposition method is used. Comparison of the shapes of the free surfaces near the upper corner point with leading and second order solutions shows that the second order outer solution outer makes a larger difference in the vertical free surface than in the horizontal portion, compared with leading order solution.The complete picture of the shapes of the free surfaces using Lagrangian description for the upper part and Eulerian description for the bottom part at the second order is obtained