Related papers: On circular flows: linear stability and damping
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 study instability of unidirectional flows for the linearized 2D Navier-Stokes equations on the torus. Unidirectional flows are steady states whose vorticity is given by Fourier modes corresponding to a single vector $\mathbf p \in…
We consider a model of steady, incompressible non-Newtonian flow with neglected convective term under external forcing. Our structural assumptions allow for certain non-degenerate power-law or Carreau-type fluids. We provide the full-range…
Upon decreasing the Reynolds number, plane Couette flow first forms alternately turbulent and laminar oblique bands out of featureless turbulence below some upper threshold R_t. These bands exist down to a global stability threshold R_g…
We consider the compressible Oldroyd-B model derived in \cite{Barrett-Lu-Suli}, where the existence of global-in-time finite energy weak solutions was shown in two dimensional setting. In this paper, we first state a local well-posedness…
We study the nonlinear stability of the two-dimensional Navier-Stokes equations around the Couette shear flow in the channel domain $\mathbb{R}\times[-1,1]$ subject to Navier slip boundary conditions. We establish a quantitative stability…
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…
The current work analyses the onset characteristics of buoyancy and thermocapillary-driven instabilities in two-layer binary fluid systems near their upper critical solution temperature (UCST). The dynamics of the binary fluids are modelled…
In this note, we investigate the stability property of shear flows under the 2D stationary Navier-Stokes equations, and we obtain that the Couette flow $(y,0)$ is stable under the space of $\mathcal{D}^{1,q}(\mathbb{R}^2)$ for any…
We are concerned with rigidity properties of steady Euler flows in two-dimensional bounded annuli. We prove that in an annulus, a steady flow with no interior stagnation point and tangential boundary conditions is a circular flow, which…
We prove the nonlinear inviscid damping for a class of monotone shear flows in $T\times [0,1]$ for initial perturbation in Gevrey-$1/s$($s>2$) class with compact support. The main idea of the proof is to use the wave operator of a slightly…
We establish finite-time singularity formation for $C^{1,\alpha}$ solutions to the Boussinesq system that are compactly supported on $\mathbb{R}^2$ and infinitely smooth except in the radial direction at the origin. The solutions are smooth…
We reveal and investigate a new type of linear axisymmetric helical magnetorotational instability which is capable of destabilizing viscous and resistive rotational flows with radially increasing angular velocity, or positive shear. This…
We report the temporal and spatio-temporal stability analyses of anti-symmetric, free shear, viscoelastic flows obeying the Oldroyd-B constitutive equation in the limit of low to moderate Reynolds number and Weissenberg number. The…
We consider enstrophy dissipation in two-dimensional (2D) Navier-Stokes flows and focus on how this quantity behaves in thelimit of vanishing viscosity. After recalling a number of a priori estimates providing lower and upper bounds on this…
The nonlinear asymptotic stability of shear flows in the 2D Euler equations has traditionally been linked to inviscid damping in the periodic setting. Since Gevrey regularity is required to suppress the ``echo'' phenomenon, asymptotic…
The Lamb-Chaplygin dipole (Lamb1895,Lamb1906,Chaplygin1903) is one of the few closed-form relative equilibrium solutions of the 2D Euler equation characterized by a continuous vorticity distribution. We consider the problem of its linear…
The single droplet under shear is a foundational problem in fluid mechanics. In computational fluid dynamics, the two-dimensional (2D) formulation offers advantages in both computational efficiency and relevance, yet its theoretical…
In this paper, we consider a wave equation with strong damping and logarithmic nonlinearity. This paper aims to study the local and global existence, uniqueness and the uniform energy decay rate of a weak solution under some sufficient…
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…