Related papers: Time-Periodic Quasigeostrophic Motion under Dissip…
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
A comprehensive analysis of general relativistic spacetimes which admit a shear-free, irrotational and geodesic timelike congruence is presented. The equations governing the models for a general energy-momentum tensor are written down.…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
We show that the equation of quasigeostrophic (QG) potential vorticity conservation in geophysical fluid dynamics follows from Hamilton's principle for stationary variations of an action for geodesic motion in the f-plane case or its…
We give an interpretation of the global shallow water quasi-geostrophic equations on the sphere $\Sph^2$ as a geodesic equation on the central extension of the quantomorphism group on $\Sph^3$. The study includes deriving the model as a…
We consider a 2-layer quasi-geostrophic ocean model where the upper layer is forced by a steady Kolmogorov wind stress in a periodic channel domain, which allows to mathematically study the nonlinear development of the resulting flow. The…
We investigate an inequality constraining the energy and potential enstrophy flux in the two-layer quasi-geostrophic model. This flux inequality is unconditionally satisfied for the case of two-dimensional Navier-Stokes turbulence. However,…
The Blackstock-Crighton equations describe the motion of a viscous, heat-conducting, compressible fluid. They are used as models for acoustic wave propagation in a medium in which both nonlinear and dissipative effects are taken into…
In this paper, we study a nonlinear fluid-structure interaction problem between a viscoelastic beam and a compressible viscous fluid. The beam is immersed in the fluid which fills a two-dimensional rectangular domain with periodic boundary…
Rapidly rotating spherical kinematic dynamos are computed using the combination of a quasi geostrophic (QG) model for the velocity field and a classical spectral 3D code for the magnetic field. On one hand, the QG flow is computed in the…
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. We implement an elaborate scheme for building global quasiperiodic solutions…
We establish the existence of quasi-periodic traveling wave solutions for the $\beta$-plane equation on $\mathbb{T}^2$ with a large quasi-periodic traveling wave external force. These solutions exhibit large sizes, which depend on the…
We consider a class of ordinary differential equations describing one-dimensional quasiperiodically forced systems in the presence of large damping. We give a fully constructive proof of the existence of response solutions, that is…
Many records in environmental sciences exhibit asymmetric trajectories and there is a need for simple and tractable models which can reproduce such features. In this paper we explore an approach based on applying both a time change and a…
Enstrophy is an averaged measure of fluid vorticity. This quantity is particularly important in {\em rotating} geophysical flows. We investigate the dynamical evolution of enstrophy for large-scale quasi-geostrophic flows under random wind…
We present an experimental and theoretical study of the effect of spatio-temporal fluctuations in quasi-reversible systems displaying a spatial quintic supercritical bifurcation. The saturation mechanism is drastically changed by the…
The quasi-isotropic expansion for a simple two-fluid cosmological model, including radiation and string gas is constructed. The first non-trivial order expressions for the metric coefficients, energy densities and velocities are explicitly…
We present the results of a combined theoretical and experimental investigation into the vertical dynamics of floating discs subjected to an imposed time-periodic forcing. The axisymmetric and inviscid wavefield is governed by a linear…
We prove the first bifurcation result of time quasi-periodic traveling waves solutions for space periodic water waves with vorticity. In particular we prove existence of small amplitude time quasi-periodic solutions of the gravity-capillary…
The magnetised solar wind modulates the Galactic cosmic ray flux in the heliosphere up to rigidities as high as 40 GeV. In this work, we present a new and straightforward extension of the popular, but limited force-field model, thus…