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Three‐dimensional optimal perturbations in viscous shear flow
Transition to turbulence in plane channel flow occurs even for conditions under which modes of the linearized dynamical system associated with the flow are stable. In this paper an attempt is made toExpand
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Generalized Stability Theory. Part II: Nonautonomous Operators
Abstract An extension of classical stability theory to address the stability of perturbations to time-dependent systems is described. Nonnormality is found to play a central role in determining theExpand
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A Simple Approximate Result for the Maximum Growth Rate of Baroclinic Instabilities
Abstract The Charney problem for baroclinic instability involves the quasi-geostrophic instability of a zonal flow on a β plane where the zonal flow is characterized by a constant vertical shear. TheExpand
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Stochastic forcing of the linearized Navier–Stokes equations
Transient amplification of a particular set of favorably configured forcing functions in the stochastically driven Navier–Stokes equations linearized about a mean shear flow is shown to produce highExpand
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Tropical Cyclone Formation
Abstract The physics of tropical cyclone formation is not well understood, and more is known about the mature hurricane than the formative mechanisms that produce it. It is believed part of theExpand
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Optimal perturbations and streak spacing in wall‐bounded turbulent shear flow
The mean streak spacing of approximately 100 wall units that is observed in wall‐bounded turbulent shear flow is shown to be consistent with near‐wall streamwise vortices optimally configured to gainExpand
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Optimal excitation of perturbations in viscous shear flow
Evidence, both theoretical and experimental, is accumulating to support a mechanism for transition to turbulence in shear flow based on the 3‐D secondary instability of finite 2‐D departures fromExpand
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The initial growth of disturbances in a baroclinic flow
Abstract The growth of perturbations in a baroclinic flow is examined as an initial value problem. Although the long time asymptotic behavior is dominated by discrete exponentially growing normalExpand
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Optimal excitation of three‐dimensional perturbations in viscous constant shear flow
The three‐dimensional perturbations to viscous constant shear flow that increase maximally in energy over a chosen time interval are obtained by optimizing over the complete set of analyticExpand
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