Related papers: Towards eliminating the nonlinear Kelvin wake
The wake of a circular cylinder performing rotary oscillations is studied using hydrodynamic tunnel experiments at $Re=100$. Two-dimensional particle image velocimetry on the mid-plane perpendicular to the axis of cylinder is used to…
The non--static generalized Langevin equation and its corresponding Fokker--Planck equation for the position of a viscous fluid particle were solved in closed form for a time dependent external force. Its solution for a constant external…
We consider the nonlinear Schr{\"o}dinger equation (NLSE) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{\kappa+1} (\psi^\star \psi)^{\kappa+1}$ in the presence of the external forcing terms of the form $r e^{-i(kx +…
The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface…
We simulate the Gross-Pitaevskii equation to model the development of turbulence in a quantum fluid confined by a cuboid box potential, and forced by shaking along one axis. We observe the development of isotropic turbulence from…
The nonlinear development of finite amplitude disturbances in mixed convection flow in a heated vertical annulus is studied by direct numerical simulation. The unsteady Navier Stokes equations are solved numerically by a spectral method for…
This paper is devoted to the stabilization of the water-wave equations with surface tension through of an external pressure acting on a small part of the free surface. It is proved that the energy decays to zero exponentially in time,…
The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…
The forced Korteweg-de Vries (fKdV) equation describes incompressible inviscid free surface flows over some arbitrary topography. We investigate solitary and hydraulic fall solutions to the fKdV equation. Numerical results show that the…
Ostrovsky's equation with time- and space- dependent forcing is studied. This equation is model for long waves in a rotating fluid with a non-constant depth (topography). A classification of Lie point symmetries and low-order conservation…
We argue that the physics of interacting Kelvin Waves (KWs) is highly non-trivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit…
The effect of an external pressure disturbance, being displaced with a constant speed along the free surface of a viscous thin film, is studied theoretically in the lubrication approximation in one- and two-dimensional geometries. In the…
We study the Muskat problem for one fluid in arbitrary dimension, bounded below by a flat bed and above by a free boundary given as a graph. In addition to a fixed uniform gravitational field, the fluid is acted upon by a generic force…
In this paper, we investigate the spectral stability of periodic traveling waves in the two dimensional gravity-capillary water wave problem. We derive a stability criterion based on an index function, whose sign determines the spectral…
Linear wave theory captures the essential physics of free-surface flows at a fraction of the computational cost of nonlinear and viscous methods, making it attractive for design, real-time control, and surrogate modeling applications.…
The KP-I equation arises as a weakly nonlinear model equation for gravity-capillary waves with Bond number $\beta>1/3$, also called strong surface tension. This equation has recently been shown to have a family of nondegenerate, symmetric…
All complex fluid motions, such as transition and turbulence, obeying the Navier-Stokes equations are non-linear phenomena. Some aspects of the non-linear terms of these equations are not well understood and are, in fact, misunderstood. The…
We prove that traveling waves in viscous compressible liquids are a generic phenomenon. The setting for our result is a horizontally infinite, finite depth layer of compressible, barotropic, viscous fluid, modeled by the free boundary…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids, and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the…