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The instability of ideal non-divergent zonal flows on the sphere is determined numerically by the instability criterion of Arnol'd (1966) for the sectional curvature. Zonal flows are unstable for all perturbations besides for a small set…
Wilton ripples are a type of periodic traveling wave solution of the full water wave problem incorporating the effects of surface tension. They are characterized by a resonance phenomenon that alters the order at which the resonant harmonic…
In some linearly unstable flows, secondary instability is found to have a much larger wavelength than that of the primary unstable modes, so that it cannot be recovered with a classical Floquet analysis. In this work, we apply a new…
The temporal instability of stably stratified flow was investigated by analyzing the Taylor-Goldstein equation theoretically. According to this analysis, the stable stratification $N^2\geq0$ has a destabilization mechanism, and the flow…
A modal stability analysis shows that plane Poiseuille flow of an Oldroyd-B fluid becomes unstable to a `center mode' with phase speed close to the maximum base-flow velocity, $U_{max}$. The governing dimensionless groups are the Reynolds…
The late-time growth of single-mode immiscible Rayleigh-Taylor instability is investigated over a comprehensive range of the Reynolds numbers ($1\leq Re \leq 10000$) and Atwood numbers $(0.05 \leq A \leq 0.7)$ using an improved lattice…
Contrasting with free shear flows presenting velocity profiles with inflection points which cascade to turbulence in a relatively mild way, wall bounded flows are deprived of (inertial) instability modes at low Reynolds numbers and become…
We consider a full set of harmonics for the Stokes wave in deep water in the absence of viscosity, and examine the role that higher harmonics play in modifying the classical Benjamin-Feir instability. Using a representation of the wave…
The aim of this paper is to give a result concerning the stability properties of the solutions of magnetohydrodynamics equations at small but finite Reynolds numbers. These solutions are found using the alpha-effect: this method gives us…
The notion of instability of a turbulent flow is introduced in the case of a von K\'arm\'an flow thanks to the monitoring of the spatio-temporal spectrum of the velocity fluctuations, combined with projection onto suitable Beltrami modes.…
We investigate the triangular instability of a Batchelor vortex subjected to a stationary triangular strain field generated by three satellite vortices, in the presence of weak axial flow. The analysis combines theoretical predictions with…
We discuss the irreversibility, nonlocality, and fluctuations, as well as the Lyapunov and hydrodynamic instabilities characterizing atomistic, smooth-particle, and finite-difference solutions of the two-dimensional Rayleigh-B\'enard…
This paper discusses the effect of rotation on the boundary layer in high Reynolds number flow over a ridge using a numerical method based on stabilised finite elements that captures steady solutions up to Reynolds number of order $10^6$.…
We show that grains streaming through a fluid are generically unstable if their velocity, projected along some direction, matches the phase velocity of a fluid wave (linear oscillation). This can occur whenever grains stream faster than any…
This work addresses the question of the stability of stratified, spatially periodic shear flows at low P\'eclet number but high Reynolds number. This little-studied limit is motivated by astrophysical systems, where the Prandtl number is…
We present three results on stability of rolls in Boussinesq convection in a plane horizontal layer with rigid boundaries that is rotating about an inclined axis with the angular velocity $\Omega=(\Omega_1,\Omega_2,\Omega_3)$. i. We call…
It is exactly proved that the classical Rayleigh Theorem on inflectional velocity instability is wrong which states that the necessary condition for instability of inviscid flow is the existence of an inflection point on the velocity…
Flows forced by a precessional motion can exhibit instabilities of crucial importance, whether they concern the fuel of a flying object or the liquid core of a telluric planet. So far, stability analyses of these flows have focused on the…
Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…
The stability of shear flows of electrically conducting fluids, with respect to finite amplitude three-dimensional localized disturbances is considered. The time evolution of the fluid impulse integral, characterizing such disturbances, for…