Related papers: Stabilities of Parallel Flow and Horizontal Convec…
In this paper, the stability of inviscid parallel flow between two parallel walls is studied. Firstly, it is obtained that the profile of the base flow for this classical problem is a uniform flow. Secondly, it is shown that the solution of…
The linear stability of buoyant parallel flow in a vertical porous layer with an annular cross-section is investigated. The vertical cylindrical boundaries are kept at different uniform temperatures and they are assumed to be impermeable.…
The horizontal convection within a rectangle tank is numerically simulated. The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf bifurcation of $Ra$ from steady solutions to periodic solutions, and the critical…
General stability criterions of two-dimensional inviscid parallel flow are obtained analytically for the first time. First, a criterion for stability is found as $\frac{U''}{U-U_s}>-\mu_1$ everywhere in the flow, where $U_s$ is the velocity…
The stability of buoyant flows occurring in the mixed convection regime for a viscous fluid in a horizontal plane-parallel channel with adiabatic walls is investigated. The basic flow features a parallel velocity field under stationary…
The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillation. There exists a simple…
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…
Vertical convection is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity (see e.g. Wang et al. 2021). We consider the linear stability of the steady two-dimensional flow…
Ortiz-P\'erez and D\'avalos investigated the stability of parallel convective flow. From the article it seems that this equations of flow obtained by the authors. Meanwhile, it is well studied theoretically and experimentally(exact solution…
Rayleigh showed that inviscid flow is unstable if the velocity profile has an inflection point in parallel flows. However, whether viscous flows is unstable or not is still not proved so far when there is an inflection point in the velocity…
The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid…
Convection of an internally heated fluid, confined between top and bottom plates of equal temperature, is studied by direct numerical simulation in two and three dimensions. The unstably stratified upper region drives convection that…
The stability problem in terms of two measures for semiflows in space conv(R^n) was investigated. On the basis of comparison principle the obtained result is used to study the stability criteria for a certain semiflow in space conv(R^n).…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
In this work, the linear stability of the viscous incompressible fluid flow between two parallel horizontal porous stationary plates with the assumption that there is a small constant suction at upper plate and a small constant injection at…
We study numerically and theoretically the gravity-driven flow of a viscous liquid film coating the inner side of a horizontal cylindrical tube and surrounding a shear-free dynamically inert gaseous core. The liquid-gas interface is prone…
This manuscript has been accepted for publication in Physical Review Fluids, see https://journals.aps.org/prfluids/accepted/53075Se8O0b1b109b1cc0061b280aaa122f0f92dc. The stability of a pulsatile quasi-two-dimensional duct flow was…
This work deals with stability of two-phase stratified air-water flows in horizontal circular pipes. For this purpose, we performed a linear stability analysis, which considers all possible three-dimensional infinitesimal disturbances and…
We study the stability of two-fluid flow through a plane channel at Reynolds numbers of a hundred to a thousand in the linear and nonlinear regimes. The two fluids have the same density but different viscosities. The fluids, when miscible,…
This study considers the linear stability of Poiseuille-Rayleigh-B\'enard flows, subjected to a transverse magnetic field to understand the instabilities that arise from the complex interaction between the effects of shear, thermal…