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Adjoint Equations in Stability Analysis
Paolo Luchini,Alessandro Bottaro +1 more
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TLDR
Adjoint-based sensitivity analysis finds both analytical and numerical applications much beyond those originally imagined as mentioned in this paper, and can be used to identify optimal perturbations, pinpoint the most receptive path to break down, select the most destabilizing base-flow defect in a nominally stable configuration, and map the structural sensitivity of an oscillator.Abstract:
The objective of this article is to review some developments in the use of adjoint equations in hydrodynamic stability theory. Adjoint-based sensitivity analysis finds both analytical and numerical applications much beyond those originally imagined. It can be used to identify optimal perturbations, pinpoint the most receptive path to break down, select the most destabilizing base-flow defect in a nominally stable configuration, and map the structural sensitivity of an oscillator. We focus on two flow cases more closely: the noise-amplifying instability of a boundary layer and the global mode occurring in the wake of a cylinder. For both cases, the clever interpretation and use of direct and adjoint modes provide key insight into the process of the transition to turbulence.read more
Citations
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Journal ArticleDOI
Modal Analysis of Fluid Flows: An Overview
Kunihiko Taira,Steven L. Brunton,Scott T. M. Dawson,Clarence W. Rowley,Tim Colonius,Beverley McKeon,Oliver T. Schmidt,Stanislav Gordeyev,Vassilios Theofilis,Lawrence Ukeiley +9 more
TL;DR: The intent of this document is to provide an introduction to modal analysis that is accessible to the larger fluid dynamics community and presents a brief overview of several of the well-established techniques.
The nonlinear development of Gortler vortices in growing boundary layers
TL;DR: The growth of Gortler vortices in boundary layers on concave walls is investigated in this paper, and it is shown that the concept of a unique neutral curve so familiar in hydrodynamic-stability theory is not tenable in the gortler problem except for asymptotically small wavelengths.
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Sensitivity and Nonlinearity of Thermoacoustic Oscillations
Matthew P. Juniper,R. I. Sujith +1 more
TL;DR: In this article, a review explains why linear and nonlinear thermoacoustic behavior is so sensitive to parameters such as operating point, fuel composition, and injector geometry, and proposes tools to exploit this sensitivity in the future: adjoint-based sensitivity analysis to optimize passive control designs and complex systems theory to warn of impending thermo-acoustic oscillations and to identify the most sensitive elements of a thermo acoustic system.
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Effective adjoint approaches for computational fluid dynamics
TL;DR: The Jacobian-free method using source code transformation algorithmic differentiation to compute the partial derivatives is the best option because it computes exact derivatives with the lowest CPU time and the lowest memory requirements, and it also scales well up to 10 million cells and over one thousand CPU cores.
Journal ArticleDOI
Nonlinear Nonmodal Stability Theory
TL;DR: In this paper, a nonlinear extension of nonmodal analysis is proposed to find the disturbance to the flow state of a given amplitude that experiences the largest energy growth at a certain time later, which can reveal the disturbance of least amplitude for transition to another state such as turbulence.
References
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Journal ArticleDOI
Vortex Dynamics in the Cylinder Wake
TL;DR: A review of wake vortex dynamics can be found in this article, with a focus on the three-dimensional aspects of nominally two-dimensional wake flows, as well as the discovery of several new phenomena in wakes.
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Aerodynamic design via control theory
TL;DR: The purpose of the last three sections is to demonstrate by representative examples that control theory can be used to formulate computationally feasible procedures for aerodynamic design, Provided, therefore, that one can afford the cost of a moderate number of flow solutions.
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Hydrodynamic Stability Without Eigenvalues
TL;DR: A reconciliation of findings with the traditional analysis is presented based on the "pseudospectra" of the linearized problem, which imply that small perturbations to the smooth flow may be amplified by factors on the order of 105 by a linear mechanism even though all the eigenmodes decay monotonically.
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Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects
TL;DR: In this paper, two general algorithms for solving constrained minimization problems are presented and discussed in the context of analysis and assimilation of meteorological observations, in particular in terms of their computational cost.
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Three‐dimensional optimal perturbations in viscous shear flow
TL;DR: In this paper, a complete set of perturbations, ordered by energy growth, is found using variational methods. But the optimal perturbation is not of modal form, and those which grow the most resemble streamwise vortices, which divert the mean flow energy into streaks of streamwise velocity and enable the energy of the perturbance to grow by as much as three orders of magnitude.