Inviscid instability of a stably stratified boundary layer

International audienceThe three-dimensional stability of an inflection-free boundary layer flow of length scale L and maximum velocity U0 in a stably stratified fluid of constant Brunt-Väisälä frequency N is examined in an inviscid Boussinesq framework. The plane of the boundary layer is assumed to be inclined with an angle θ with respect to the vertical direction of stratification. The stability analysis is performed using both numerical and theoretical methods for all the values of θ and Froude number F = U0 /(LN ). The boundary layer flow is found to be unstable whatever F as soon as θ ̸= 0. The growth rate of the most unstable mode is shown to increase with the inclination angle to reach its maximum for a vertical boundary layer θ = π/2. The unstable modes are 3D in nature. The mechanism of instability is shown to be associated with internal gravity wave emission. In the weakly stratified limit, both the oscillation frequency and the growth rate are found to scale with the Brunt-Väisälä frequency N. In the strongly stratified limit, frequency and growth rate become independent of the Froude number and proportional to the sine of the inclination angle (as long as F / sin θ ≪ 1)

Instabilités rayonnantes tri-dimensionnelles d'un jet plan stratifié

La stabilité tri-dimensionnelle d'un jet plan de Bickley est étudiée sous l'hypothèse de Boussinesq en faisant varier l'angle formé par le plan de cisaillement et la stratification. Nous analysons dans quelle mesure le mode de Kelvin-Helmholtz peut avoir une structure rayonnante et plus généralement comment des ondes internes (ou ondes de gravité) associées à des modes rayonnants instables, peuvent être générées spontanément

1D model of precursors to frictional stick-slip motion allowing for robust comparison with experiments

We study the dynamic behaviour of 1D spring-block models of friction when the external loading is applied from a side, and not on all blocks like in the classical Burridge-Knopoff-like models. Such a change in the loading yields specific difficulties, both from numerical and physical viewpoints. To address some of these difficulties and clarify the precise role of a series of model parameters, we start with the minimalistic model by Maegawa et al. (Tribol. Lett. 38, 313, 2010) which was proposed to reproduce their experiments about precursors to frictional sliding in the stick-slip regime. By successively adding (i) an internal viscosity, (ii) an interfacial stiffness and (iii) an initial tangential force distribution at the interface, we manage to (i) avoid the model's unphysical stress fluctuations, (ii) avoid its unphysical dependence on the spatial resolution and (iii) improve its agreement with the experimental results, respectively. Based on the behaviour of this improved 1D model, we develop an analytical prediction for the length of precursors as a function of the applied tangential load. We also discuss the relationship between the microscopic and macroscopic friction coefficients in the model.Comment: 13 pages, 14 figures, accepted in Tribology Letter

Instabilités radiatives des jets et couches limites atmosphériques

L atmosphère est le siège d écoulements complexes qui peuvent être sources d ondes internes de gravité. Nous nous intéressons en particulier ici aux instabilités radiatives et de cisaillement (ou de Kelvin-Helmholtz). Les études de stabilité d une couche cisaillée dans un fluide stratifié se sont souvent limitées aux cas où la direction du cisaillement de l écoulement moyen était la même que celle de la stratification ; Miles (1961) et Howard (1961) ont ainsi trouvé une condition nécessaire de stabilité basée sur le nombre de Richardson : Ri > 1/4. Dans cette thèse, nous montrons que cette condition n est plus nécessaire dès que le cisaillement et la stratification ne sont pas alignés : nous démontrons qu un jet de Bickley plan peut être déstabilisé pour tous les nombres de Richardson. Bien que le mode le plus instable reste 2D, nous montrons qu il existe une famille infinie de modes instables 3D possédant une structure rayonnante. Une analyse WKBJ est formulée et fournie les principales caractéristiques de ces modes. Nous étudions également une couche limite stratifiée et non visqueuse sur une paroi inclinée en présence d effets non-Boussinesq et compressible. Nous montrons que cet écoulement est instable dès la paroi n est pas horizontale pour tous les nombres de Froude et que le comportement d une perturbation 3D dans un fluide très stratifié est le même qu une perturbation 2D dans un fluide compressible. Des applications des résultats au courant-jet et à une couche limite atmosphérique sont proposées.Complex flows occur in the atmosphere and they can be source of internal gravity waves. We focus here on the sources associated with radiative and shear (or Kelvin-Helmholtz) instabilities. Stability studies of shear layers in a stably stratified fluid concern mainly cases where shear and stratification are aligned along the same direction. In these cases, Miles (1961) and Howard (1961) found a necessary condition for stability based on the Richardson number : Ri > 1/4. In this thesis, we show that this condition is not necessary when shear and stratification are not aligned : we demonstrate that a two-dimensional planar Bickley jet can be unstable for all Richardson numbers. Although the most unstable mode remains 2D, we show there exists an infinite family of 3D unstable modes exhibiting a radiative structure. A WKBJ theory is found to provide the main characteristics of these modes. We also study an inviscid and stratified boundary layer over an inclined wall with non- Boussinesq and compressible effects. We show that this flow is unstable as soon as the wall is not horizontal for all Froude numbers and that strongly stratified 3D perturbations behave exactly like compressible 2D perturbations. Applications of the results to the jet stream and the atmospheric boundary layer are proposed.AIX-MARSEILLE1-Inst.Médit.tech (130552107) / SudocSudocFranceF

Inviscid instability of a stably stratified compressible boundary layer on an inclined surface

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Shear Instability in a Stratified Fluid when Shear and Stratification are not aligned

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Aerodynamics of buoyant releases within a longitudinally ventilated tunnel

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