Self-focusing dynamics of patches of ripples

The dynamics of focussing of extended patches of nonlinear capillary gravity waves within the primitive fluid dynamic equations is presented. It is found that, when the envelope has certain properties, the patch focusses initially in accordance to predictions from nonlinear Schrodinger equation, and focussing can concentrate energy to the vicinity of a point or a curve on the fluid surface. After initial focussing, other effects dominate and the patch breaks up into a complex set of localised structures lumps and breathers - plus dispersive radiation. We perform simulations both in the inviscid regime and for small viscosities. Lastly we discuss throughout the similarities and differences between the dynamics of ripple patches and self-focussing light beams. (C) 2016 The Authors. Published by Elsevier B.V

On asymmetric generalized solitary gravity-capillary waves in finite depth

Generalized solitary waves propagating at the surface of a fluid of finite depth are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. Both the effects of gravity and surface tension are included. It is shown that in addition to the classical symmetric waves, there are new asymmetric solutions. These new branches of solutions bifurcate from the branches of symmetric waves. The detailed bifurcation diagrams as well as typical wave profiles are presented

Stability and dynamics of two-dimensional fully nonlinear gravity-capillary solitary waves in deep water

The stability and dynamics of two-dimensional gravity capillary solitary waves in deep water within the fully nonlinear water-wave equations arc numerically studied. It is well known that there are two families of symmetric gravity capillary solitary waves depression waves and elevation waves bifurcating from infinitesimal periodic waves at the minimum of the phase speed. The stability of both branches was previously examined by Calvo &amp; Akylas (J. Fluid Mech., vol. 452, 2002, pp. 123-143) by means of a numerical spectral analysis. Their results show that the depression solitary waves with single-valued profiles are stable, while the elevation branch experiences a stability exchange at a turning point on the speed amplitude curve. In the present paper, we provide numerical evidence that the depression solitary waves with an overhanging structure arc also stable. On the other hand, Dias et of. (Eur. j. Mech. B, vol. 15, 1996, pp. 17-36) numerically traced the elevation branch and discovered that its speed amplitude bifurcation curve features a &#39;snake-like&#39; behaviour with many turning points, whereas Calvo &amp; Akylas (J. Fluid Mech., vol. 452, 2002, pp. 123-143) only considered the stability exchange near the first turning point. Our results reveal that the stability exchange occurs again near the second turning point. A branch of asymmetric solitary waves is also considered and found to be unstable, even when the wave profile consists of a depression wave and a stable elevation one. The excitation of stable gravity capillary solitary waves is carried out via direct numerical simulations. In particular, the stable elevation waves, which feature two troughs connected by a small dimple, can he excited by moving two fully localised, well-separated pressures on the free surface with the speed slightly below the phase speed minimum and removing the pressures simultaneously after a period of time.</p

Modelling nonlinear electrohydrodynamic surface waves over three-dimensional conducting fluids

The evolution of the free surface of a three-dimensional conducting fluid in the presence of gravity, surface tension and vertical electric field due to parallel electrodes, is considered. Based on the analysis of the Dirichlet-Neumann operators, a series of fully nonlinear models is derived systematically from the Euler equations in the Hamiltonian framework without assumptions on competing length scales can therefore be applied to systems of arbitrary fluid depth and to disturbances with arbitrary wavelength. For special cases, well-known weakly nonlinear models in shallow and deep fluids can be generalized via introducing extra electric terms. It is shown that the electric field has a great impact on the physical system and can change the qualitative nature of the free surface: (i) when the separation distance between two electrodes is small compared with typical wavelength, the Boussinesq, Benney-Luke (BL) and Kadomtsev-Petviashvili (KP) equations with modified coefficients are obtained, and electric forces can turn KP-I to KP-II and vice versa; (ii) as the parallel electrodes are of large separation distance but the thickness of the liquid is much smaller than typical wavelength, we generalize the BL and KP equations by adding pseudo-differential operators resulting from the electric field; (iii) for a quasi-monochromatic plane wave in deep fluid, we derive the cubic nonlinear Schrodinger (NLS) equation, but its type (focusing or defocusing) is strongly influenced by the value of the electric parameter. For sufficient surface tension, numerical studies reveal that lump-type solutions exist in the aforementioned three regimes. Particularly, even when the associated NLS equation is defocusing for a wave train, lumps can exist in fully nonlinear models

Study of Characteristics of Cloud Cavity Around Axisymmetric Projectile by Large Eddy Simulation

Cavitation generally occurs where the pressure is lower than the saturated vapor pressure. Based on large eddy simulation (LES) methodology, an approach is developed to simulate dynamic behaviors of cavitation, using k - mu transport equation for subgrid terms combined with volume of fluid (VOF) description of cavitation and the Kunz model for mass transfer. The computation model is applied in a 3D field with an axisymmetric projectile at cavitation number sigma = 0.58. Evolution of cavitation in simulation is consistent with the experiment. Clear understanding about cavitation can be obtained from the simulation in which many details and mechanisms are present. The phenomenon of boundary separation and re-entry jet are observed. Re-entry jet plays an important role in the bubble shedding.</p