Related papers: Instability criterion for oblique modes in stratif…
A Taylor-Couette setup with radial heating is considered where a Boussinesq fluid is sheared in the annular region between two concentric, independently rotating cylinders maintained at different temperatures. Linear stability analysis is…
Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium…
In this paper, we investigate the Rayleigh-Taylor instability problem for two compressible, immiscible, inviscid flows rotating with an constant angular velocity, and evolving with a free interface in the presence of a uniform gravitational…
We investigate the effect of surface tension on the linear Rayleigh--Taylor (RT) instability in stratified incompressible viscous fluids with or without (interface) surface tension. The existence of linear RT instability solutions with…
The excitation conditions of the magnetorotational instability are studied for axially unbounded Taylor-Couette flows of various gap widths between the cylinders. The cylinders are considered as made from both perfect-conducting or…
The Tayler instability of an azimuthal magnetic field with one or two ``rings'' along the radius is studied for an axially unbounded Taylor-Couette flow. The rotation law of the conducting fluid is a quasi-Keplerian one. Without rotation…
Primary instability of the lid-driven flow in a cube is studied by a comprehensive linear stability approach. Two cases, in which the lid moves parallel to the cube sidewall or parallel to the diagonal plane, are considered. The SIMPLE…
Rotating waves (RW) bifurcating from the axisymmetric basic magnetized spherical Couette (MSC) flow are computed by means of Newton-Krylov continuation techniques for periodic orbits. In addition, their stability is analysed in the…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that…
Applying a sufficiently rapid start-stop to the outer cylinder of the Couette-Taylor system, structures approximately aligned with the axis were recorded in the classic work of Coles (1965). These short-lived rolls are oriented…
The linear stability of MHD Taylor-Couette flow of infinite vertical extension is considered for liquid sodium with its small magnetic Prandtl number Pm of order of 10^-5 and an uniform axial magnetic field. The sign of the constant a in…
The linear stability of inviscid, incompressible, two-dimensional, plane parallel, shear flow was considered over a century ago by Rayleigh, Kelvin, and others. A principal result on the subject is Rayleigh's celebrated inflection point…
This paper reports the stability conditions for intense zonal flows (ZFs) and the growth rate $\gamma_{\rm TI}$ of the corresponding "tertiary" instability (TI) within the generalized Hasegawa--Mima plasma model. The analytic calculation…
The linear stability of MHD Taylor-Couette flows in axially unbounded cylinders is considered, for magnetic Prandtl number unity. Magnetic fields varying from purely axial to purely azimuthal are imposed, with a general helical field…
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…
The buoyancy-induced parallel flow in a vertical cylindrical porous layer is analysed. A radial thermal gradient caused by a uniformly distributed heat source is assumed to induce the buoyant flow. The layer boundaries are modelled as…
In this paper, we obtain the optimal instability threshold of the Couette flow for Navier-Stokes equations with small viscosity $\nu>0$, when the perturbations are in the critical spaces $H^1_xL_y^2$. More precisely, we introduce a new…
The magnetohydrodynamic stability of axially unbounded cylindrical flows is considered which contain a toroidal magnetic background field with the same radial profile as the linear azimuthal velocity. Chandrasekhar (1956) has shown for…
The magnetorotational instability (MRI) of differential rotation under the simultaneous presence of axial and azimuthal components of the (current-free) magnetic field is considered. For rotation with uniform specific angular momentum the…
A more restrictively general stability criterion of two-dimensional inviscid parallel flow is obtained analytically. First, a sufficient criterion for stability is found as either $-\mu_1<\frac{U''}{U-U_s}<0$ or $0<\frac{U''}{U-U_s}$ in the…