Related papers: On computing the instability index of a non-selfad…
We consider a problem of stability of a membrane of an infinite span and a finite chord length, submerged in a uniform flow of finite depth with free surface. In the shallow water approximation, Nemtsov (1985) has shown that an…
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…
Interior stagnation point flows of viscoelastic liquids arise in a wide variety of applications including extensional viscometry, polymer processing and microfluidics. Experimentally, these flows have long been known to exhibit…
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…
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…
A recently proposed connection between the threshold for the stability of the iterative solution of integral equations for the pair correlation functions of a classical fluid and the structural instability of the corresponding real fluid is…
This paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from…
In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use…
We consider the linearized instability of 2D irrotational solitary water waves. The maxima of energy and the travel speed of solitary waves are not obtained at the highest wave, which has a 120 degree angle at the crest. Under 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…
We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by…
In this technical report, we consider a nonlinear 4th-order degenerate parabolic partial differential equation that arises in modelling the dynamics of an incompressible thin liquid film on the outer surface of a rotating horizontal…
We study Kolmogorov flow on a three dimensional, periodic domain with aspect ratios fixed to unity. Using an energy method, we give a concise proof of the linear stability of the laminar flow profile. Since turbulent motion is observed for…
We analyse numerically the linear stability of a liquid metal flow in a rectangular duct with perfectly electrically conducting walls subject to a uniform transverse magnetic field. A non-standard three dimensional vector stream…
We show possibility of the Plane Couette (PC) flow instability for Reynolds number Re>Reth=140. This new result of the linear hydrodynamic stability theory is obtained on the base of refusal from the traditionally used assumption on…
The no-slip boundary condition results in a velocity shear forming in fluid flow near a solid surface. This shear flow supports the turbulence characteristic of fluid flow near boundaries at Reynolds numbers above $\approx1000$ by making…
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 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 nonlinear instability of a smooth steady density profile solution of the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field, including a Rayleigh-Taylor…
Elastic turbulence has been found in computations of planar viscoelastic Taylor-Couette flow using the Oldroyd-B model, apparently generated by a linear instability (van Buel et al. Europhys. Lett., 124, 14001, 2018). We demonstrate that no…