# Ambiguity in mean-flow-based linear analysis

@article{Karban2020AmbiguityIM, title={Ambiguity in mean-flow-based linear analysis}, author={U. Karban and B. Bugeat and Eduardo Martini and Aaron Towne and Andr{\'e} V. G. Cavalieri and Lutz Lesshafft and Akshat Agarwal and Peter Jordan and Tim Colonius}, journal={Journal of Fluid Mechanics}, year={2020}, volume={900} }

Abstract Linearisation of the Navier–Stokes equations about the mean of a turbulent flow forms the foundation of popular models for energy amplification and coherent structures, including resolvent analysis. While the Navier–Stokes equations can be equivalently written using many different sets of dependent variables, we show that the properties of the linear operator obtained via linearisation about the mean depend on the variables in which the equations are written prior to linearisation, and…

## 15 Citations

### Efficient global resolvent analysis via the one-way Navier–Stokes equations

- PhysicsJournal of Fluid Mechanics
- 2022

Resolvent analysis is a powerful tool for modelling and analysing transitional and turbulent flows and, in particular, for approximating coherent flow structures. Despite recent algorithmic advances,…

### A basis for flow modelling

- EngineeringJournal of Fluid Mechanics
- 2020

Abstract Reduced-order models are often sought to efficiently represent key dynamical phenomena present among the broad range of temporal and spatial scales associated with unsteady and turbulent…

### Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets

- PhysicsJournal of Fluid Mechanics
- 2021

Abstract Response modes computed via linear resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in…

### A time-domain linear method for jet noise prediction and control trend analysis

- PhysicsAerospace Science and Technology
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### Self-similar mechanisms in wall turbulence studied using resolvent analysis

- Environmental ScienceJournal of Fluid Mechanics
- 2022

Abstract Self-similarity of wall-attached coherent structures in a turbulent channel at $Re_\tau =543$ is explored by means of resolvent analysis. In this modelling framework, coherent structures are…

### Mean resolvent operator of statistically steady flows

- Chemistry
- 2022

This paper introduces a new operator relevant to input-output analysis and control of ﬂows in a statistically steady regime far from the steady base ﬂow: the mean resolvent R 0 . It is deﬁned as the…

### An empirical model of noise sources in subsonic jets, formulated in a linear resolvent framework

- Physics28th AIAA/CEAS Aeroacoustics 2022 Conference
- 2022

Modelling the noise emitted by turbulent jets is made diﬃcult by their acoustic ineﬃciency: only a tiny fraction of the near-ﬁeld turbulent kinetic energy is propagated to the far ﬁeld as acoustic…

### Multi-scale study of the transitional shock-wave boundary layer interaction in hypersonic flow

- Physics, EngineeringTheoretical and Computational Fluid Dynamics
- 2021

A high-fidelity simulation of the massively separated shock/transitional boundary layer interaction caused by a 15-degrees axisymmetrical compression ramp is performed at a free stream Mach number of…

### Global linear stability analysis of a flame anchored to a cylinder

- Engineering, PhysicsJournal of Fluid Mechanics
- 2022

Abstract This study investigates the linear stability of a laminar premixed flame, anchored on a square cylinder and confined inside a channel. Many modern linear analysis concepts have been…

### Shift of the Flow Stability Limit in the Presence of Random Rotational Velocity Fluctuations

- Physics, EngineeringTechnical Physics
- 2022

Nonlinear stability of isothermal 3D flows of a viscous incompressible nonstratified fluid in the rotating spherical layer in the presence of noise is studied numerically. The transition between a…

## References

SHOWING 1-10 OF 50 REFERENCES

### Colour of turbulence

- Computer ScienceJournal of Fluid Mechanics
- 2017

This paper addresses the problem of how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier–Stokes equations and develops models for coloured-in-time forcing using a maximum entropy formulation together with a regularization that serves as a proxy for rank minimization.

### Eddy viscosity for resolvent-based jet noise models

- Physics25th AIAA/CEAS Aeroacoustics Conference
- 2019

Response modes computed via linear resolvent analysis have shown promising results for qualitatively modeling both the hydrodynamic and acoustic fields in jets when compared to data-deduced modes…

### Stability of slowly diverging jet flow

- PhysicsJournal of Fluid Mechanics
- 1976

Coherent axisymmetric structures in a turbulent jet are modelled as linear instability modes of the mean velocity profile, regarded as the profile of a, fictitious laminar inviscid flow. The usual…

### The colour of forcing statistics in resolvent analyses of turbulent channel flows

- Environmental Science, PhysicsJournal of Fluid Mechanics
- 2020

Abstract In resolvent analyses of turbulent channel flows it has been common practice to neglect or model the nonlinear forcing term that forms the input of the resolvent. However, the spatiotemporal…

### Resolvent-based modeling of coherent wave packets in a turbulent jet

- Physics, Environmental SciencePhysical Review Fluids
- 2019

Coherent turbulent wavepacket structures in a jet at Reynolds number 460 000 and Mach number 0.4 are extracted from experimental measurements, and are modelled as linear fluctuations around the mean…

### A critical-layer framework for turbulent pipe flow

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 2010

A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale…

### A critical layer model for turbulent pipe flow

- Physics, Environmental Science
- 2018

A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale…

### On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 2019

The ability of linear stochastic response analysis to estimate coherent motions is investigated in turbulent channel flow at the friction Reynolds number $\text{Re}_{\unicode[STIX]{x1D70F}}=1007$ .…

### Wavepacket models for supersonic jet noise

- PhysicsJournal of Fluid Mechanics
- 2014

Abstract Gudmundsson and Colonius (J. Fluid Mech., vol. 689, 2011, pp. 97–128) have recently shown that the average evolution of low-frequency, low-azimuthal modal large-scale structures in the near…

### Conditions for validity of mean flow stability analysis

- PhysicsJournal of Fluid Mechanics
- 2016

This article provides theoretical conditions for the use and meaning of a stability analysis around a mean flow. As such, it may be considered as an extension of the works by McKeon & Sharma (J.…