Related papers: Nonlinear Evolution of a Baroclinic Wave and Imbal…
Flutter stability is a dominant design constraint of modern gas and steam turbines. To further increase the feasible design space, flutter-tolerant designs are currently explored, which may undergo Limit Cycle Oscillations (LCOs) of…
By using direct numerical simulations of up to a record resolution of 512x512x32768 grid points we discover the existence of a new metastable out-of-equilibrium state in rotating turbulence. We scan the phase space by varying both the…
We study the nonlinear evolution of the magnetic buoyancy instability in rotating and non-rotating gas layers using numerical solutions of non-ideal, isothermal MHD equations. The unstable magnetic field is either imposed through the…
In this paper, we develop a model to describe the generalized wave-particle instability in a quasi-neutral plasma. We analyze the quasi-linear diffusion equation for particles by expressing an arbitrary unstable and resonant wave mode as a…
This article explores the stability of stratified Couette flow in the viscous $3d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal…
In nonlinear systems, small perturbations are conventionally attributed to negligible nonlinearity, justifying linear approximations. Here, we uncover a notable exception to this paradigm in an electrokinetic (EK) flow. Using a novel dual…
Large-scale instabilities occurring in the presence of small-scale turbulent fluctuations are frequently observed in geophysical or astrophysical contexts but are difficult to reproduce in the laboratory. Using extensive numerical…
Sea ice attenuates waves propagating from the open ocean. Here we model the evolution of energetic unidirectional random waves in the marginal ice zone with a nonlinear Schr\"{o}dinger equation, with a frequency dependent dissipative term…
Caustics are natural phenomena in which nature concentrates the energy of waves. Although, they are known mostly in optics, caustics are intrinsic to all wave phenomena. For example, studies show that fluctuations in the profile of an ocean…
Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a…
Consider the dynamics of a gas bubble in an inviscid, compressible liquid with surface tension. Kinematic and dynamic boundary conditions couple the bubble surface deformation dynamics with the dynamics of waves in the fluid. This system…
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov stability of the front against fully…
In the presence of wave dissipation, phase-space structures emerge in nonlinear Vlasov dynamics. Their dynamics can lead to a nonlinear continuous shifting of the wave frequency (chirping). This report summarizes my personal contribution to…
In analogy with similar effects in adiabatic compressible fluid dynamics, the effects of buoyancy gradients on incompressible stratified flows are said to be `thermal'. The thermal rotating shallow water (TRSW) model equations contain three…
We consider a multilayer generalization of Ripa's inhomogeneous-density single-layer primitive-equation model. In addition to vary arbitrarily in horizontal position and time, the horizontal velocity and buoyancy fields are allowed to vary…
We report on a novel investigation of the nonlinear regime of the electron cyclotron drift instability, using a grid-based Vlasov simulation. It is shown that the instability occurs as a series of cyclotron resonances with the electron beam…
The search for solutions to the theory of weakly non-linear internal gravity wave turbulence is an active research topic. It is notably stimulated by the fact that this regime could drive fine-scale ocean dynamics for which the…
Submesoscale currents in the ocean's mixed layer (ML), consisting of fronts, eddies, and filaments, are characterized by order one Rossby (Ro) and Richardson (Ri) numbers. These currents play a crucial role in mediating vertical exchange…
We study the response of a simple quasi-geostrophic barotropic model of the atmosphere to various classes of perturbations affecting its forcing and its dissipation using the formalism of the Ruelle response theory. We investigate the…
We investigate the dynamics close to a homogeneous stationary state of Vlasov equation in one dimension, in presence of a small dissipation modeled by a Fokker-Planck operator. When the stationary state is stable, we show the stochastic…