The influence of surface tension upon trapped waves and hydraulic falls

We consider steady two-dimensional free-surface flows past submerged obstructions on the bottom of a channel. The flow is assumed to be irrotational, and the fluid inviscid and incompressible. Both the effects of gravity and surface tension are considered. Critical flow solutions with subcritical flow upstream and supercritical flow downstream are sought using fully nonlinear boundary integral equation techniques based on the Cauchy integral formula. When a second submerged obstruction is included further upstream in the flow configuration in the absence of surface tension, solutions which have a train of waves trapped between the two obstacles before the critical flow have already been found (Dias and Vanden-Broeck 2004). We extend this work by including the effects of surface tension. Trapped wave solutions are found upstream for small values of the Bond number, for some values of the Froude number. Other types of trapped waves are found for stronger tension when the second obstruction is placed downstream of the hydraulic fall generated by the first obstacle

Solitary waves on a ferrofluid jet

The propagation of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet subjected to a magnetic field is investigated. An azimuthal magnetic field is generated by an electric current flowing along a stationary metal rod which is mounted along the axis of the moving jet. A numerical method is used to compute fully-nonlinear travelling solitary waves and predictions of elevation waves and depression waves by Rannacher & Engel (2006) using a weakly-nonlinear theory are confirmed in the appropriate ranges of the magnetic Bond number. New nonlinear branches of solitary wave solutions are identified. As the Bond number is varied, the solitary wave profiles may approach a limiting configuration with a trapped toroidal-shaped bubble, or they may approach a static wave (i.e. one with zero phase speed). For a sufficiently large axial rod, the limiting profile may exhibit a cusp

Finite depth effects on solitary waves in a floating ice sheet

A theoretical and numerical study of two-dimensional nonlinear flexural-gravity waves propagating at the surface of an ideal fluid of finite depth, covered by a thin ice sheet, is presented. The ice-sheet model is based on the special Cosserat theory of hyperelastic shells satisfying Kirchhoff׳s hypothesis, which yields a conservative and nonlinear expression for the bending force. From a Hamiltonian reformulation of the governing equations, two weakly nonlinear wave models are derived: a 5th-order Korteweg–de Vries equation in the long-wave regime and a cubic nonlinear Schrödinger equation in the modulational regime. Solitary wave solutions of these models and their stability are analysed. In particular, there is a critical depth below which the nonlinear Schrödinger equation is of focusing type and thus admits stable soliton solutions. These weakly nonlinear results are validated by comparison with direct numerical simulations of the full governing equations. It is observed numerically that small- to large-amplitude solitary waves of depression are stable. Overturning waves of depression are also found for low wave speeds and sufficiently large depth. However, solitary waves of elevation seem to be unstable in all cases

Residues and Presents in Contemporary Shrinking Temporalities

Taking into consideration the inherent crisis in our experience and perception of time, we will have to ask ourselves what is the link between the way in which we engage with the “present” and with the “aesthetic” in our postmodern societies as we experience the opposing categories of the “resisting” and the “elusive”. Zygmunt Bauman believes that our “liquid culture” is marked by discontinuity and forgetting as our social realities become more and more fragmented. Frederic Jameson also mentions the ways in which “the displacement of old-fashioned industrial labor by the newer cybernetic kind” has changed continuity based possibilities of engaging with reality. A temporality of “passive reception” rather than “agency” characterizes our possibilities of making sense of reality. It is highly important to discuss about the language of an aesthetic, cultural and subjective “present” as a possibility of creating meaning from inside categories of experience that oppose our culture of the fugitive and disengagement

Numerical study of solitary wave attenuation in a fragmented ice sheet

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. A key new contribution is to modeling fragmented sea ice, which is accomplished by allowing the coefficient of flexural rigidity to vary spatially so that distributions of ice floes can be directly specified in the physical domain. Two-dimensional simulations are performed to examine the attenuation of solitary waves by scattering through an irregular array of ice floes. Two different measures based on the wave profile are used to quantify its attenuation over time for various floe configurations. Slow (near linear) or fast (exponential-like) decay is observed depending on such parameters as incident wave height, ice concentration and ice fragmentation

Numerical and experimental study on the steady cone-jet mode of electro-centrifugal spinning

This study focuses on a numerical investigation of an initial stable jet through the air-sealed electro-centrifugal spinning process, which is known as a viable method for the mass production of nanofibers. A liquid jet undergoing electric and centrifugal forces, as well as other forces, first travels in a stable trajectory and then goes through an unstable curled path to the collector. In numerical modeling, hydrodynamic equations have been solved using the perturbation method—and the boundary integral method has been implemented to efficiently solve the electric potential equation. Hydrodynamic equations have been coupled with the electric field using stress boundary conditions at the fluid-fluid interface. Perturbation equations were discretized by a second order finite difference method, and the Newton method was implemented to solve the discretized non-linear system. Also, the boundary element method was utilized to solve electrostatic equations. In the theoretical study, the fluid was described as a leaky dielectric with charges only on the surface of the jet traveling in dielectric air. The effect of the electric field induced around the nozzle tip on the jet instability and trajectory deviation was also experimentally studied through plate-plate geometry as well as point-plate geometry. It was numerically found that the centrifugal force prevails on electric force by increasing the rotational speed. Therefore, the alteration of the applied voltage does not significantly affect the jet thinning profile or the jet trajectory