Related papers: Linear stability analysis in inhomogeneous equilib…
The steady motion of a viscous incompressible fluid in a multiply-connected, planar, bounded domain (perforated with a large number of small holes) is modeled through the Navier-Stokes equations with non-homogeneous Dirichlet boundary data…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
Modal linear stability analysis has proven very successful in the analysis of coherent structures of turbulent flows. Formally, it describes the evolution of a disturbance in the limit of infinite time. In this work we apply modal linear…
This work employs for the first time invariant solutions of the Navier-Stokes equations to study the interaction between finite-size particles and near-wall coherent structures. We consider horizontal plane Couette flow and focus on…
Conditions for the stability under linear perturbations around the homogeneous cooling state are studied for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal ($\alpha$) and tangential…
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…
The stability of astrophysical jets in the linear regime is investigated by presenting the methodology to find the growth rates of the various instabilities. We perturb a cylindrical axisymmetric steady jet, linearize the relativistic ideal…
We study the Rayleigh-Taylor problem for two incompressible, immiscible, viscous magnetohydrodynamic (MHD) flows, with zero resistivity, surface tension (or without surface tenstion) and special initial magnetic field, evolving with a free…
We consider the Keller-Segel model for chemotaxis with a nonlinear diffusion coefficent and a singular sensitivity function. We show the existence of travelling waves for wave speeds above a critical value, and establish local…
We present a robust optimisation framework for computing invariant solutions of wall-bounded flows by recasting the Navier-Stokes equations as a variational problem as established in Ashtari and Schneider, JFM (2023). The approach minimises…
Spatial linear instability analysis is employed to investigate the instability of a viscoelastic liquid jet in a co-flowing gas stream. The theoretical model incorporates a non-uniform axial base profile represented by a hyperbolic tangent,…
Two-dimensional free-surface flow over localised topography is examined with the emphasis on the stability of hydraulic-fall solutions. A Gaussian topography profile is assumed with a positive or negative amplitude modelling a bump or a…
We study here the steady state attained in a granular gas of inelastic rough spheres that is subject to a spatially uniform random volume force. The stochastic force has the form of the so-called white noise and acts by adding impulse to…
We prove a sufficient condition for nonlinear stability of relative equilibria in the planar $N$-vortex problem. This result builds on our previous work on the Hamiltonian formulation of its relative dynamics as a Lie--Poisson system. The…
We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schr{\"o}dinger (NLS) equation. The method of studying the stability relies on freezing the radial…
The Boltzmann kinetic theory for a model of a confined quasi-two dimensional granular mixture derived previously [Garz\'o, Brito and Soto, Phys. Fluids \textbf{33}, 023310 (2021)] is considered further to analyze two different problems.…
Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…
We establish that solitary stationary waves in three dimensional viscous incompressible fluids are a generic phenomenon and that every such solution is a vanishing wave-speed limit along a one parameter family of traveling waves. The…
We present a unified variational mechanics framework for cavitating turbulent flows and structural motions via a stabilized finite element formulation. To model the finite mass transfer rate in cavitation phenomena, we employ the homogenous…
A formal derivation of linear hydrodynamics for a granular fluid is given. The linear response to small spatial perturbations of the homogeneous reference state is studied in detail using methods of non-equilibrium statistical mechanics. A…