Related papers: On the stability of laminar flows between plates
We consider the stability of a laminar flow $U\in C^4([-1,1])$ in the two-dimensional channel $\mathbb{R} \times[-1,1]$ in the large Reynolds number limit. Assuming that $U$ is strictly monotone but allowing $U^{\prime\prime}$ to vanish, we…
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…
In this paper, we investigate the nonlinear stability of the Couette flow for the two-dimensional compressible Navier--Stokes equations at high Reynolds numbers ($Re$) regime. It was proved that if the initial data $(\rho_{in},u_{in})$…
A numerical study of the problem of laminar infinite flow of viscous incompressible fluid around a rotating circular cylinder at Reynolds number $ 50 \le {\rm Re} \le 500 $ and dimensionless rotation rate $ 0 \le \alpha \le 7 $ has been…
Accurate prediction of the transition from laminar flow to turbulence remains an unresolved challenge despite its importance for understanding a variety of environmental, biological, and industrial phenomena. Well over a century of…
In this article we consider the linear stability of the two-dimensional flow induced by the linear stretching of a surface in the streamwise direction. The basic flow is a rare example of an exact analytical solution of the Navier-Stokes…
A flexible sheet in uniform parallel flow is studied in order to quantify its fluid dynamic drag and fluid-elastic stability characteristics. An experimental campaign is undertaken that involves a cantilevered sheet in air flow…
The dynamics and stability of a fluid-filled hollow cylindrical shell rolling on an inclined plane are analyzed. We study the motion in two dimensions by analyzing the interaction between the fluid and the cylindrical shell. An analytical…
Although the critical Reynolds number for linear instability of the laminar flow in a straight pipe is infinite, we show that it is finite for a divergent pipe, and approaches infinity as the inverse of the divergence angle. The velocity…
In plane Couette flow, the incompressible fluid between two plane parallel walls is driven by the motion of those walls. The laminar solution, in which the streamwise velocity varies linearly in the wall-normal direction, is known to be…
In this paper we show that steady states $u$ of the pressureless Euler equation which belong to $L^3_{loc}(\mathbb{R}^2,\mathbb{R}^2)$ are shear flows. This is achieved by combining results of degenerate Monge-Amp\`ere-type equations with…
In pipe, channel and boundary layer flows turbulence first occurs intermittently in space and time: at moderate Reynolds numbers domains of disordered turbulent motion are separated by quiescent laminar regions. Based on direct numerical…
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 show stability of pairs of Ricci flat metrics and parallel spinor fields with respect to the spinor flow, i.e. we show that the spinor flow with initial conditions near such pairs converges to a critical point with exponential speed.…
The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even…
Verifying nonlinear stability of a laminar fluid flow against all perturbations is a central challenge in fluid dynamics. Past results rely on monotonic decrease of a perturbation energy or a similar quadratic generalized energy. None show…
We study the steady states of the Euler equations on the periodic channel or annulus. We show that if these flows are laminar (layered by closed non-contractible streamlines which foliate the domain), then they must be either parallel or…
The identification of stream in the straight pipe as a flexible rod has allowed to present the criterion expression for determination of transition of the laminar flow regime to the turbulent as a loss of stability of the rectilinear static…
It is shown that linear instability of plane Couette flow can take place even at finite Reynolds numbers which meets with known experimental data. This new result of the linear theory of hydrodynamic stability is obtained only due by…
Annular Couette flow is the flow between two coaxial cylinders driven by the axial translation of the inner cylinder. It is investigated using direct numerical simulation in long domains, with an emphasis on the laminar-turbulent…