We review our recent results of global onedimensional (1-D) MHD simulations for the acceleration of solar and stellar winds. We impose transverse photospheric motions corresponding to the granulations, which generate outgoing Alfvén waves. We treat the propagation and dissipation of the Alfvén waves and consequent heating from the photosphere by dynamical simulations in a self-consistent manner...

It is shown that the nonlinear mapping relation between a surface gravity wave spectrum and its SAR image spectrum, as derived by Hasselmann and Hasselmann [1], is not complete. The reason for this is that the velocity bunching effect is so nonlinear that effects of skewness and kurtosis are as important as the nonlinear terms already retained in the Hasselmann and Hasselmann approach. An analy...

Bicritical points at wave numbers k(b) larger than the critical wave numbers k(c) are found in parametric surface waves (Faraday waves) using both numerical simulations and nonlinear analysis. Because k(b)-k(c) is small, it is argued that subcritical bifurcations at k>k(b) can be easily observed in experiments. In the second part we present a generic argument predicting the existence of nonline...

geophysical fluids such as atmosphere and ocean often have stable density stratification; hence internal gravity waves are generated and propagated through them which are important in momentum and energy transfer in these media. these waves are also believed to generate layered structures in such media. recently there have been numerous theoretical, experimental and numerical studies on the way...

We have recently shown [1] that fully-localized threedimensional wave envelopes (so-called dromions) can exist and propagate on the surface of ice-covered waters. Here we show that the inertia of the ice can play an important role in the size, direction and speed of propagation of these structures. We use multiple-scale perturbation technique to derive governing equations for the weakly nonline...

A Boussinesq-type model is derived which is accurate to O(kh) 4 and which retains the full representation of the fluid kinematics in nonlinear surface boundary condition terms, by not assuming weak nonlinearity. The model is derived for a horizontal bottom , and is based explicitly on a fourth-order polynomial representation of the vertical dependence of the velocity potential. In order to achi...

Nonlocal generalizations of Burgers’ equation were derived in earlier work by Hunter [Contemp. Math. 1989], and more recently by Benzoni-Gavage and Rosini [Comput. Math. Appl. 2009], as weakly nonlinear amplitude equations for hyperbolic boundary value problems admitting linear surface waves. The local-in-time well-posedness of such equations in Sobolev spaces was proved by Benzoni-Gavage [Diff...

Among hyperbolic Initial Boundary Value Problems (IBVP), those coming from a variational principle ‘generically’ admit linear surface waves, as was shown by Serre [J. Funct. Anal. 2006]. At the weakly nonlinear level, the behavior of surface waves is expected to be governed by an amplitude equation that can be derived by means of a formal asymptotic expansion. Amplitude equations for weakly non...

Bispectral and trispectral analyses are used to detect secondary and tertiary wave components resulting from nonlinear interactions among largeamplitude ocean surface gravity waves in 8and 13-m water depths. Bispectra of bottom-pressure measurements indicate forced secondary waves at frequencies 2fp about twice the primary power spectral peak frequency fp. However, the interpretation of the bis...

It is now well known that the focussing nonlinear Schrödinger equation allows plane waves to be modulationally unstable, and at the same time supports breather solutions which are often invoked as models for rogue waves. This suggests a direct connection between modulation instability and the existence of rogue waves. In this chapter we review this connection for a suite of long wave models, su...