Related papers: Modulational instability in wind-forced waves
Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single…
Experimental and theoretical studies on wind-wave generation have focused primarily on the air-water interface, where viscous effects are small. Here we characterize the influence of the liquid viscosity on the growth of mechanically…
In this paper, we study the structure and stability of line driven winds using numerical hydrodynamic simulations. We calculate the radiation force from an explicit non-local solution of the radiation transfer equation, rather than a…
The unsteady flow physics of wind-turbine wakes under dynamic forcing conditions are critical to the modeling and control of wind farms for optimal power density. Unsteady forcing in the streamwise direction may be generated by unsteady…
Three eigenvalue bounds are derived for the instability of ideal compressible stratified magnetohydrodynamic shear flows in which the base velocity, density, and magnetic field vary in two directions. The first bound can be obtained by…
Motivated by wind blowing over water, we use asymptotic methods to study the evolution of short wavelength interfacial waves driven by the combined action of these flows. We solve the Rayleigh equation for the stability of the shear flow,…
We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…
Nonlinear instability and refraction by ocean currents are both important mechanisms that go beyond the Rayleigh approximation and may be responsible for the formation of freak waves. In this paper, we quantitatively study nonlinear effects…
We study analytically and numerically the stability of the standing waves for a nonlinear Schr\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the…
The modulation instability is a focusing mechanism responsible for the formation of strong wave localizations not only on the water surface, but also in a variety of nonlinear dispersive media. Such dynamics is initiated from the injection…
We investigate shear driven wave generation at the interface between two immiscible fluids, using an exponential velocity profile with a sharp density interface representing stable stratification. At low Froude and high Bond numbers,…
Motivated by the central phenomenon of energy cascades in wave turbulence theory, we construct non-equilibrium statistical steady states (NESS), or invariant measures, for a simplified model derived from the nonlinear Schr\"odinger (NLS)…
Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…
The unsteady power generation of a wind turbine translating in the streamwise direction is relevant to floating offshore wind turbines, kite-mounted airborne wind turbines, and other non-traditional wind-energy systems. To study this…
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
We study strong instability (by blow-up) of the standing waves for the nonlinear Schr\"odinger equation with $\delta$-interaction on a star graph $\Gamma$. The key ingredient is a novel variational technique applied to the standing wave…
We present an investigation of the modulational instability of partially coherent signals in electrical transmission lines. Starting from the modified Ginzburg-Landau equations and the Wigner-Moyal representation, we derive a nonlinear…
We study the strong instability of standing waves for a system of nonlinear Schr\"odinger equations with quadratic interaction under the mass resonance condition in dimension $d=5$.
In the framework of Gurevich and Pitaevskii approach [1] we construct modulated by Whitham [2] solution of nonlinear Shrodinger (NS) equation partially saturating the modulational instability. This solution describes new scenario of…
Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schr{\"o}dinger equation in a…