Related papers: Transient Growth in Shear Flows: Linearity vs Nonl…
Linear transient growth analysis is commonly used to suggest the structure of disturbances which are particularly efficient in triggering transition to turbulence in shear flows. We demonstrate that the addition of nonlinearity to the…
We propose a general strategy for determining the minimal finite amplitude isturbance to trigger transition to turbulence in shear flows. This involves constructing a variational problem that searches over all disturbances of fixed initial…
In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude…
Depending on the type of flow, the transition to turbulence can take one of two forms: either turbulence arises from a sequence of instabilities or from the spatial proliferation of transiently chaotic domains, a process analogous to…
Pipe flow and many other shear flows show a transition to turbulence at flow rates for which the laminar profile is stable against infinitesimal perturbations. In this brief review the recent progress in the understanding of this transition…
Non-normal transient growth of disturbances is considered as an essential prerequisite for subcritical transition in shear flows, i.e. transition to turbulence despite linear stability of the laminar flow. In this work we present numerical…
The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the 'bypass' path…
The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. "Optimal" perturbations are distinguished as extrema of certain functionals, and different functionals give…
The volatile transition from quiescent laminar to strongly fluctuating turbulent dynamics in shear flows remains only poorly understood despite its practical importance and more than a century of intense research. The theoretical…
The commonly accepted description of transition to turbulence in shear flows requires the presence of an external source of disturbances that get amplified by an essentially linear mechanism up to the point where breakdown to turbulence…
In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model…
In this note, we propose a new idea by analyzing the basic disturbance equations, and give starting equations for understanding the instability phenomena of laminar flows and transition to turbulence. It is considered that there is an…
The purpose of this contribution is to summarize and discuss recent advances regarding the onset of turbulence in shear flows. The absence of a clear cut instability mechanism, the spatio-temporal intermittent character and extremely long…
We investigate the energy transfer from the mean profile to velocity fluctuations in channel flow by calculating nonlinear optimal disturbances,i.e. the initial condition of a given finite energy that achieves the highest possible energy…
Transition to turbulence dramatically alters the properties of fluid flows. In most canonical shear flows, the laminar flow is linearly stable and a finite-amplitude perturbation is necessary to trigger transition. Controlling transition to…
One-dimensional models are presented for transitional shear flows. The models have two variables corresponding to turbulence intensity and mean shear. These variables evolve according to simple equations based on known properties of…
Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities…
This paper is concerned with the transition of the laminar flow in a duct of square cross-section. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers, rendering this flow a suitable candidate…
This work investigates efficient routes to turbulence in quasi-two-dimensional shear flows. Two-dimensional disturbances require high Reynolds numbers to incite transition from a steady base flow, as transient growth is modest. With the…
The theory of transient growth describes how linear mechanisms can cause temporary amplification of disturbances even when the linearized system is asymptotically stable as defined by its eigenvalues. This growth is traditionally quantified…