Related papers: Linear and nonlinear instabilities in highly shear…
We perform direct numerical simulations of planar jets of non-Newtonian fluids at low Reynolds number, in typical laminar conditions for a Newtonian fluid. We select three different non-Newtonian fluid models characterized by shear-thinning…
We consider the flow of a generalized Newtonian fluid through a thin porous medium of thickness $\epsilon$, perforated by periodically distributed solid cylinders of size $\epsilon$. We assume that the fluid is described by the 3D…
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…
We study the instability of a dusty simple shear flow where the dust particles are distributed non-uniformly. A simple shear flow is modally stable to infinitesimal perturbations. Also, a band of particles remains unaffected in the absence…
Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single…
Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of…
Simple analytical criteria are derived to determine whether axisymmetric base flows in annuli and pipes are stable or unstable. Both axisymmetric and non-axisymmetric inviscid disturbances are considered. Our sufficient condition for…
We examine the linear stability of fluid interfaces subjected to a shear flow. Our main object is to generalize previous work to arbitrary Atwood number, and to allow for surface tension and weak compressibility. The motivation derives from…
In this paper, we analyze the dynamics of two layers of immiscible, inviscid, incompressible, and irrotational fluids through a full nonlinear system. Our goal is to establish a virial theorem and prove the polynomial growth of slope and…
We show that viscoelastic plane Poiseuille flow becomes linearly unstable in the absence of inertia, in the limit of high elasticities, for ultra-dilute polymer solutions. While inertialess elastic instabilities have been predicted for…
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
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…
It is well known that inertia-free shearing flows of a viscoelastic fluid with curved streamlines, such as the torsional flow between a rotating cone and plate, or the flow in a Taylor-Couette geometry, can become unstable to a…
We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a…
The study of shear layer instability in compressible flows is key to understanding phenomena from aerodynamics to astrophysical jets. Blumen's seminal paper [``Shear layer instability of an inviscid compressible fluid," J. Fluid Mech. {\bf…
Viscoelastic fluids exhibit elastic instabilities in simple shear flow and flow through curved streamlines. Surprisingly, we found in a porous medium such fluids show strikingly different hydrodynamic instabilities depicted by very large…
The velocity and friction properties of laminar pipe flow of a viscoelastic solution are bounded by the corresponding values for two Newtonian fluids, namely, the solvent and a fluid with a viscosity identical to the total viscosity of the…
Shear flows have an important impact on the dynamics in an assortment of different astrophysical objects including accreditation discs and stellar interiors. Investigating shear flow instabilities in a polytropic atmosphere provides a…
We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop a new method to find the sharp stability conditions. We study the flow with Sinus profile in details…
The unsteady Poiseuille flow of Carreau-Yasuda fluid in a pipe, caused by a variable pressure gradient, is studied theoretically. In a particular case, the steady flow is considered separately. It is proved that at some values of the…