Time dependent hydraulic falls and trapped waves over submerged obstructions

We consider the classical problem of a free surface flowing past one or more disturbances in a channel. The fluid is assumed to be inviscid and incompressible, and the flow, irrotational. Both the effects of gravity and surface tension are considered. The stability of critical flow steady solutions, which have subcritical flow upstream of the disturbance and supercritical flow downstream, is investigated. We compute the initial steady solution using boundary integral equation techniques based on Cauchy integral formula and advance the solution forward in time using a mixed Euler-Lagrange method along with Adams-Bashforth-Moulton scheme. Both gravity and gravity-capillary critical flow solutions are found to be stable. The stability of solutions with a train of waves trapped between two disturbances is also investigated in the pure gravity and gravity-capillary cases

Hydraulic falls under a floating ice plate due to submerged obstructions

AbstractSteady two-dimensional nonlinear flexural–gravity hydraulic falls past a submerged obstruction on the bottom of a channel are considered. The fluid is assumed to be ideal and is covered above by a thin ice plate. Cosserat theory is used to model the sheet of ice as a thin elastic shell, and boundary integral equation techniques are then employed to find critical flow solutions. By utilising a second obstruction, solutions with a train of waves trapped between two obstructions are investigated.</jats:p

Deformation of an elastic cell in a uniform stream and in a circulatory flow

The deformation of a circular, inextensible elastic cell is examined when the cell is placed into two different background potential flows: a uniform stream and a circulatory flow induced by a point vortex located inside the cell. In a circulatory flow a cell may deform into a mode m shape with m-fold rotational symmetry. In a uniform stream, shapes with two-fold rotational symmetry tend to be selected. In a weak stream a cell deforms linearly into an ellipse with either its major or its minor axis aligned with the oncoming flow. This marks an interesting difference with a bubble with constant surface tension in a uniform stream, which can only deform into a mode 2 shape with its major axis perpendicular to the stream (Vanden-Broeck & Keller, 1980b). In general, as the strength of the uniform stream is increased from zero, solutions emerge continuously from the cell configurations in quiescent fluid found by Flaherty et al. (1972). A richly populated solution space is described with multiple solution branches which either terminate when a cell reaches a state with a point of self-contact or loop round to continuously connect cell states which exist under identical conditions in the absence of flow

Solitary interfacial hydroelastic waves

Solitary waves travelling along an elastic plate present between two fluids with different densities are computed in this paper. Different two-dimensional configurations are considered: the upper fluid can be of infinite extent, bounded by a rigid wall or under a second elastic plate. The dispersion relation is obtained for each case and numerical codes based on integro-differential formulations for the full nonlinear problem are derived

The non-local AFM water-wave method for cylindrical geometry

We develop an AFM (Ablowitz-Fokas-Musslimani) method applicable to studying water waves in a cylindrical geometry. As with the established AFM method for two-dimensional and three-dimensional water waves, the formulation involves only surface variables and is amenable to numerical computation. The method is developed for a general cylindrical surface, and we demonstrate its use for numerically computing fully nonlinear axisymmetric periodic and solitary waves on a ferrofluid column

Numerical Simulation of Solitary-Wave Scattering and Damping in Fragmented Sea Ice

A numerical model for direct phase-resolved simulation of nonlinear ocean waves propagating through fragmented sea ice is proposed. In view are applications to wave propagation and attenuation across the marginal ice zone. This model solves the full equations for nonlinear potential flow coupled with a nonlinear thin-plate formulation for the ice cover. Distributions of ice floes can be directly specified in the physical domain by allowing the coefficient of flexural rigidity to be spatially variable. Dissipation due to ice viscosity is also taken into account by including diffusive terms in the governing equations. Two-dimensional simulations are performed to examine the attenuation of solitary waves by scattering and damping through an irregular array of ice floes. Wave attenuation over time is quantified for various floe configurations

Numerical and experimental investigation on static electric charge model at stable cone-jet region

In a typical electro-spinning process, the steady stretching process of the jet beyond the Taylor cone has a significant effect on the dimensions of resulting nanofibers. Also, it sets up the conditions for the onset of the bending instability. The focus of this work is the modeling and simulation of the initial stable jet phase seen during the electro-spinning process. The perturbation method was applied to solve hydrodynamic equations, and the electrostatic equation was solved by a boundary integral method. These equations were coupled with the stress boundary conditions derived appropriate at the fluid-fluid interface. Perturbation equations were discretized by the second-order finite difference method, and the Newton method was implemented to solve the discretized nonlinear system. Also, the boundary element method was utilized to solve the electrostatic equation. In the theoretical study, the fluid is described as a leaky dielectric with charges only on the jet surface in dielectric air. In this study, electric charges were modeled as static. Comparison of numerical and experimental results shows that at low flow rates and high electric field, good agreement was achieved because of the superior importance of the charge transport by conduction rather than convection and charge concentration. In addition, the effect of unevenness of the electric field around the nozzle tip was experimentally studied through plate-plate geometry as well as point-plate geometry

Benjamin-Ono Kadomtsev-Petviashvili’s models in interfacial electro-hydrodynamics

Three-dimensional nonlinear potential free surface flows in the presence of vertical electric fields are considered. Both the effects of gravity and surface tension are included in the dynamic boundary condition. An asymptotic analysis (based on the assumptions of small depth and small free surface displacements) is presented. It is shown that the problem can be modelled by a Benjamin-Ono Kadomtsev-Petviashvili equation. Furthermore a fifth order Benjamin-Ono Kadomtsev-Petviashvili equation is derived to describe the flows in the particular case of values of the Bond number close to 1/3

Experimental and numerical study on isolated and non-isolated jet behavior through centrifuge spinning system

This work presents a comparison between an isolated and a non-isolated curved liquid jet emerging from a rotating nozzle through centrifuge spinning system. In the centrifugal spinning process, a polymer solution has been pushed by the centrifugal force through small nozzle of a rapidly rotating cylindrical drum. Thereby thin fibers are formed and collected on a collector in the form of a web. Centrifuge spinning suffered from a strong air resistance which leads to a more deflected jet as well as its rapidly solvent evaporation resulting in thicker nanofibers. In this work, centrifuge spinning has been equipped by a rotating collector, whereas the fabrication process was skillfully sealed from ambient airflow. A comparison was drawn between the trajectory of Newtonian liquid jets fabricated by centrifuge spinning and air-sealed centrifuge spinning. The captured images of the liquid jet trajectory using a high speed camera showed that non-isolated liquid jets were more curved than isolated liquid jets due to air resistance. A pre-presented non-linear analysis of the Navier-Stokes equations was carried out and the numerical solutions were compared with the experiments.There was fairly good agreement between the isolated jet trajectory and the model-predicted one, but there were differences between the non-isolated jet trajectory and the simulation results. The non-isolated jet curved more compared to the others due to air drag. Also, the diameter of polymeric nanofibers was predicted and compared with experiments. Some qualitative agreement was found