Related papers: Spatiotemporal linear stability of viscoelastic su…
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
It is well-known that at the high Reynolds number, the linearized Navier-Stokes equations around the inviscid stable shear profile admit growing mode solutions due to the destabilizing effect of the viscosity. This phenomenon, called…
The stability of a horizontal interface between two viscous fluids, one of which is conducting and the other is dielectric, acted upon by a vertical time-periodic electric field is considered. The two fluids are bounded by electrodes…
The stability of a three-dimensional, incompressible, viscous flow through a finite-length duct is studied. A divergence-free basis technique is used to formulate the weak form of the problem. A SUPG (streamingline upwind Petrov-Galerkin)…
We propose a novel multiple-scale spatial marching method for flows with slow streamwise variation. The key idea is to couple the boundary region equations, which govern large-scale flow evolution, with local exact coherent structures that…
We propose a novel stability criterion for incompressible shear flows by combining input-output analysis and the small-gain theorem. The criterion yields an explicit threshold on the magnitude of velocity perturbations about a given base…
In this paper, we obtain the optimal instability threshold of the Couette flow for Navier-Stokes equations with small viscosity $\nu>0$, when the perturbations are in the critical spaces $H^1_xL_y^2$. More precisely, we introduce a new…
In wall-bounded flows, the laminar regime remain linearly stable up to large values of the Reynolds number while competing with nonlinear turbulent solutions issued from finite amplitude perturbations. The transition to turbulence of plane…
In this paper, we prove the stability threshold of $\alpha\leq \frac13$ for 2D Boussinesq equations around the Couette flow in $\mathbb{T}\times \mathbb{R}$ with Richardson number $\gamma^2>\frac14$ and different viscosity $\nu$ and thermal…
The linear dynamics and instability mechanisms of double-layered weakly viscoelastic fluid flowing over an inclined plane are analyzed in the presence of insoluble surfactant at both the free surface and interface. The constitutive equation…
A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We present here a new stochastic modelling in the constitution of fluid flow reduced-order models. This framework introduces a spatially inhomogeneous random field to represent the unresolved small-scale velocity component. Such a…
The main objective of this article is to derive a mathematical theory associated with the nonlinear stability and dynamic transitions of the basic shear flows associated with baroclinic instability, which plays a fundamental role in the…
This article presents a modelling of the formation of spanwise vorticity in the turbulent streaks of the oblique bands and spots of transitional plane Couette flow. A functional model is designed to mimic the coherent flow in the streaks.…
Using a reduced model focusing on the in-plane dependence of plane Couette flow, it is shown that the turbulent-to-laminar relaxation process can be understood as a nucleation problem similar to that occurring at a thermodynamic first-order…
Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. That suggests that…
The linear and non-linear dynamics of centrifugal instability in Taylor-Couette flow are investigated when fluids are stably stratified and highly diffusive. One-dimensional local linear stability analysis (LSA) on cylindrical Couette flow…
Axisymmetric viscoelastic pipe flow of Oldroyd-B fluids has been recently found to be linearly unstable by Garg et al. Phys. Rev. Lett., 121.024502 (2018). From a nonlinear point of view, this means that the flow can transition to…
We study the Couette Taylor instabilities for an incompressible viscous fluid between two coaxial cylinders of nearly equal radii, allowing counter-rotation with the ratio of rotation rate $\mu \in [-1,1]$. Working in a rotating frame and…