Applications of High Order Methods to Vortex Instability Calculations

González, Leo M.; Theofilis, Vassilios; Meseguer-Garrido, Fernando

doi:10.1007/978-3-642-15337-2_38

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“…González-Gutiérrez et al [37] utilizaron una metodología espectral de alto orden adaptada para estudiar la inestabilidad de flujos con vórtices. Validaron sus resultados con el caso de un Bqv aislado de densidad constante con Re = 1200 y q = 0.8, planteando el problema desde el punto de vista de un análisis BiGlobal EVP.…”

Section: Flujos De Vórticesunclassified

Análisis de estabilidad de flujos viscosos e incompresibles de densidad estratificada mediante métodos numéricos de alto y bajo orden

González¹

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The present work deals with several types of fluid instabilities such as the Rayleigh-Taylor instability (RTI), Kelvin-Helmholtz instability (KHI), and Centrifugal instability (CTI) for incompressible, viscous and stratified density flows. Firstly, the computation of the spectrum of eigenvalues and eigenfunctions of linear problems derived from the RTI, KHI and CTI is performed by numerically solving the corresponding eigenvalue problem (EVP). Both the RTI and KHI are studied in one-dimensional (1D) and two-dimensional (2D) geometries, whereas the CTI is only analysed in 2D geometry. These canonic cases are extended to different versions where viscosity, surface tension and an stratified density distributions are added to the problem and the changes in the spectrum and the modal structure of the dominant modes is studied. The importance of extending the results to the two-dimensional case is twofold. First, it opens the possibility of generalizing the computation to more complex geometries that could contain fixed or floating bodies and second, allows the computation of flow instabilities of base flows which are particular solutions of the steady Navier-Stokes solutions. Secondly, for the RTI, it was found useful to study stability by using the initial value problem approach (IVP), as consequence we ensure the inclusion of certain continuum modes, otherwise neglected. This methodology includes a branch cut in the complex plane, consequently, in addition to discrete modes (surface RTI modes), a set of continuum modes (internal RTI modes) also appears. As a result, the usual information given by the normal mode analysis is now completed. Furthermore, a new role is found for surface tension, transforming surface RTI modes into internal RTI modes belonging to a continuous spectrum at a critical wavenumber. As a consequence, the cut-off wavenumber disappears: i.e. the growth rate of the RTI surface mode does not decay to zero at the cut-off wavenumber, as previous researchers used to believe. Finally, we found that the Rayleigh-Taylor instability exhibits essentially different time asymptotic behavior above and below the critical wavenumber.This thesis collects results from two publications (JCR), as well some original work. Artículos, ponencias y comunicacionesLa calidad de esta tesis doctoral está avalada por la publicación de parte de su contenido en dos artículos de revistas de reconocido prestigio incluidas en el catálogo JCR, una comunicación en un congreso internacional y dos ponencias. ArtículosA. de Andrea González and L. M. González-Gutiérrez. Effects of a semi-infinite stratification on the Rayleigh-Taylor instability in an interface with surface tension. AIP Advances, 7(9): 095319, 2017. L. M. González-Gutiérrez and A. de Andrea González. Numerical computation of the Rayleigh-Taylor instability for a viscous fluid with regularized interface properties. Phys. Rev. E , 100:013101, 2019. ComunicacionesA. de Andrea González. Effects of a semi-infinite stratification on Rayleigh-Taylor instability in an interfa...

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Section: Flujos De Vórticesunclassified

Análisis de estabilidad de flujos viscosos e incompresibles de densidad estratificada mediante métodos numéricos de alto y bajo orden

González¹

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Applications of High Order Methods to Vortex Instability Calculations

Cited by 1 publication

References 14 publications

Análisis de estabilidad de flujos viscosos e incompresibles de densidad estratificada mediante métodos numéricos de alto y bajo orden

Análisis de estabilidad de flujos viscosos e incompresibles de densidad estratificada mediante métodos numéricos de alto y bajo orden

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