Related papers: Localised eigenmodes in a moving frame of referenc…

Motion in the atmosphere or mantle convection are two among phenomena of natural convection induced by internal heat sources. They bifurcate from the conduction state as a result of its loss of stability. In spite of their importance, due…

The propagation of internal gravity waves in stratified media, such as those found in ocean basins and lakes, leads to the development of geometrical patterns called "attractors". These structures accumulate much of the wave energy and make…

Viscous streaming refers to the rectified, steady flows that emerge when a liquid oscillates around an immersed microfeature, typically a solid body or a bubble. The ability of such features to locally concentrate stresses produces strong…

We consider a planar waveguide with combined Dirichlet and Neumann conditions imposed in a "twisted" way. We study the discrete spectrum and describe it dependence on the configuration of the boundary conditions. In particular, we show that…

This paper demonstrates the efficient extraction of unstable recurrent flows from two-dimensional turbulence by using nonlinear triads to diagnose recurrence in direct numerical simulations. Nearly recurrent episodes are identified from…

A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…

We present the applications of wavelet analysis methods in constrained variational framework to calculation of dynamical aperture. We construct represention via exact nonlinear high-localized periodic eigenmodes expansions, which allows to…

It is well-known that stable and unstable manifolds strongly influence fluid motion in unsteady flows. These emanate from hyperbolic trajectories, with the structures moving nonautonomously in time. The local directions of emanation at each…

We numerically investigate the flow structure of periodic steady water waves of fixed relative mass flux propagating on rotational flows with piece-wise constant vorticity. We show that for wave solutions along the global bifurcation…

We consider the influence of transverse confinement on the instability properties of velocity and density distributions reminiscent of those pertaining to exchange flows in stratified inclined ducts, such as the recent experiment of Lefauve…

A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…

This study performs global stability/receptivity analyses of hypersonic sweep flows around a blunt body with an infinite span. For the first time, we obtain the characteristics of the leading attachment-line mode to the variation of sweep…

We investigate the stability of stratified fluid layers undergoing homogeneous and periodic tidal deformation. We first introduce a local model which allows to study velocity and buoyancy fluctuations in a Lagrangian domain periodically…

We consider several different bidirectional Whitham equations that have recently appeared in the literature. Each of these models combine the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow…

We present a general formulation for stability analyses of radiative shocks with multiple cooling processes, longitudinal and transverse perturbations, and unequal electron and ion temperatures. Using the accretion shocks of magnetic…

A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…

Local bifurcation analysis plays a central role in understanding qualitative transitions in networked nonlinear dynamical systems, including dynamic neural network and opinion dynamics models. In this article we establish explicit bounds of…

We present a perturbation-based framework that captures buoyancy effects on modal instabilities in stratified boundary-layer flows within the fully compressible, non-Oberbeck-Boussinesq formulation. Treating the Richardson number as a small…

In order to understand the nonlinear stability of many types of time-periodic travelling waves on unbounded domains, one must overcome two main difficulties: the presence of embedded neutral eigenvalues and the time-dependence of the…

In this letter, we investigate how field redefinition influences the spectrum of linearized perturbations in relativistic fluid dynamics. We show that the hydrodynamic modes do not get affected under local field redefinition, whereas the…