Extension of the Eulerian–Lagrangian description to nonlinear perturbations in an arbitrary inviscid flow

Minotti, Angelot; Brazier, Jean-Philippe; Simon, Franck

doi:10.1016/j.jsv.2012.05.017

Journal of Sound and Vibration

2012

DOI: 10.1016/j.jsv.2012.05.017

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Extension of the Eulerian–Lagrangian description to nonlinear perturbations in an arbitrary inviscid flow

Angelot Minotti¹,

Jean-Philippe Brazier²,

Franck Simon³

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Cited by 2 publications

References 25 publications

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Discontinuities and nonlinear shear Alfvén waves by the mixed Eulerian-Lagrangian kinematic description

Liu

Zhu

2017

Physics of Plasmas

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In the frame of mixed Eulerian–Lagrangian description, a large-perturbation magnetohydrodynamic (MHD) equilibrium system is developed to describe the propagation of nonlinear Alfvén waves in an ideal magnetofluid. The system is only dependent on the reference flow variables and the displacement vector of the fluid particles. Some interesting results are obtained: nonlinear MHD wave speeds are obtained; fixing the equilibrium magnetic field, a large-negative gradient of displacement can generate directional discontinuities; a large-positive pressure perturbation or magnetic perturbation can bring about a high velocity nonlinear Alfvén wave while a large-negative pressure perturbation or magnetic perturbation can bring about a low velocity nonlinear Alfvén wave; a great-negative magnetic perturbation may give birth to counter-propagating Alfvén waves. Our results have a high relevance to such issues as discontinuities, counter-propagating nonlinear Alfvén waves, and ultra-speed Alfvén waves in interplanetary space.

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Discontinuities and nonlinear shear Alfvén waves by the mixed Eulerian-Lagrangian kinematic description

Liu

Zhu

2017

Physics of Plasmas

View full text Add to dashboard Cite

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90 Years of Galbrun’s Equation: An Unusual Formulation for Aeroacoustics and Hydroacoustics in Terms of the Lagrangian Displacement

Maeder

Gabard

Marburg

2020

J. Theor. Comp. Acout.

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The field of aeroacoustics has gained much attention since the well-known acoustic analogies were first published in the 1950s. In parallel, the continuous growth of computational resources has enabled researchers and engineers to investigate phenomena involving flow-induced noise or sound propagation effects related to arbitrary velocity fields. To describe the latter mentioned physical processes, Galbrun utilized a mixed Eulerian–Lagrangian framework to describe perturbations of the underlying fluid dynamics. While less known compared to the more common linearized Euler equations, Galbrun’s equation provides an original framework. Since its publication in 1931, a number of scholars have further developed the approach first proposed by Galbrun. This paper provides a review of the existing literature dedicated to the use of Galbrun’s equation by highlighting possible advantages of the underlying theory as well as difficulties when utilizing numerical methods for solving problems in time or frequency domain. Furthermore, this work intents to serve as a companion for researchers interested in the field of aeroacoustics and hydroacoustics associated with Galbrun’s equation.

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Extension of the Eulerian–Lagrangian description to nonlinear perturbations in an arbitrary inviscid flow

Cited by 2 publications

References 25 publications

Discontinuities and nonlinear shear Alfvén waves by the mixed Eulerian-Lagrangian kinematic description

Discontinuities and nonlinear shear Alfvén waves by the mixed Eulerian-Lagrangian kinematic description

90 Years of Galbrun’s Equation: An Unusual Formulation for Aeroacoustics and Hydroacoustics in Terms of the Lagrangian Displacement

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