This review discusses a recently developed optimization technique for analyzing the
nonlinear stability of a flow state. It is based on a nonlinear extension of nonmodal analysis …

The formation and amplification of streamwise velocity perturbations induced by cross-
stream disturbances is ubiquitous in shear flows. This disturbance growth mechanism, so …

We study Sobolev regularity disturbances to the periodic, plane Couette flow in the 3D
incompressible Navier-Stokes equations at high Reynolds number Re. Our goal is to …

We extend linear input/output (resolvent) analysis to take into account nonlinear triadic
interactions by considering a finite number of harmonics in the frequency domain using the …

In this paper, we study the transition threshold problem for the 2-D Navier–Stokes equations
around the Couette flow (y, 0) at high Reynolds number Re in a finite channel. We develop a …

In this paper, we study the transition threshold of the 3D Couette flow in Sobolev space at
high Reynolds number Re. It was proved that if the initial velocity v 0 satisfies for some c 0> …

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This article introduces and reviews recent work using a simple optimization technique for
analysing the nonlinear stability of a state in a dynamical system. The technique can be …

We propose a general strategy for determining the minimal finite amplitude disturbance that
triggers transition to turbulence in shear flows. This involves constructing a variational …

We study the modal and non-modal linear instability of inertia-dominated channel flow of
viscoelastic fluids modelled by the Oldroyd-B and FENE-P closures. The effects of polymer …