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We analyze the linear stability of a stalled accretion shock in a perfect gas with a parametrized cooling function L ~ rho^{beta-alpha} P^alpha. The instability is dominated by the l=1 mode if the shock radius exceeds 2-3 times the accretor…
It is increasingly common for models of shallow-layer overland flows to include equations for the evolution of the underlying bed (morphodynamics) and the motion of an associated sedimentary phase. We investigate the linear stability…
In [F. Jiang, S. Jiang, On instability and stability of three-dimensional gravity driven viscous flows in a bounded domain, Adv. Math., 264 (2014) 831--863], Jiang et.al. investigated the instability of Rayleigh--Taylor steady-state of a…
This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by…
We study analytically the development of gravitational instability in an expanding shell having finite thickness. We consider three models for the radial density profile of the shell: (i) an analytic uniform-density model, (ii) a…
Numerical simulations of geological CO2 storage in deep saline aquifers have demonstrated that vertical equilibrium (VE) models offer a robust and computationally efficient framework for reservoir optimization and upscaling. These studies…
When representing convective instability mechanisms with the streamwise BiGlobal stability approach, results suffer from a sensitivity to the streamwise domain truncation length and boundary conditions. The methodology proposed in this…
The standard method to generate dynamical models with a finite extent is to apply a truncation in binding energy to the distribution function. This approach has the disadvantages that one cannot choose the density to start with, that the…
Localized patterns in singularly perturbed reaction-diffusion equations typically consist of slow parts -- in which the associated solution follows an orbit on a slow manifold in a reduced spatial dynamical system -- alternated by fast…
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…
A persistent spatial organization of eddies is identified in the lowest portion of the stably-stratified planetary boundary layer. The analysis uses flow realizations from published large-eddy simulations (Sullivan et al., J Atmos Sci…
Buoyancy-driven turbulent convection leads to a fully compressible flow with a strong top-down asymmetry of first- and second-order statistics when the adiabatic equilibrium profiles of temperature, density and pressure decay very strongly…
These fluid dynamics video sequences show two Rayleigh-Taylor instability experiments. The first video sequence shows an experiment where two layers of uniform density are arranged such that the density of the upper layer is greater than…
We consider turbulence driven by a large-scale horizontal shear in Kolmogorov flow (i.e. with sinusoidal body forcing) and a background linear stable stratification with buoyancy frequency $N_B^2$ imposed in the third, vertical direction in…
We study the linear stability of inviscid steady parallel flow of an ideal gas in a channel of finite width. Compressible isothermal two-dimensional monochromatic perturbations are considered. The eigenvalue problem governing density and…
We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even…
We study a system of non-identical bistable particles that is driven by a dynamical constraint and coupled through a non-local mean-field. Assuming piecewise affine constitutive laws we prove the existence of traveling wave solutions and…
According to field observations, the atmospheric boundary layer is usually unstably stratified before a dust and sandstorm, the particle-laden turbulent gravity current with an extremely high Reynolds number. In this paper, an inviscid…
We explore various models for the pattern forming instability in a laser-driven cloud of cold two-level atoms with a plane feedback mirror. Focus is on the combined treatment of nonlinear propagation in a diffractively thick medium and the…
We show that the rotating Rayleigh-Benard convection, where a rotating fluid is heated from below, exhibits non-Hermitian topological states. Recently, Favier and Knobloch (JFM 2020) hypothesized that the robust wall modes in rapidly…