| 1. |
- Augier, Pierre, et al.
(författare)
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Spectral analysis of the transition to turbulence from a dipole in stratified fluid
- 2012
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Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 713, s. 86-108
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the spectral properties of the turbulence generated during the nonlinear evolution of a Lamb-Chaplygin dipole in a stratified fluid for a high Reynolds number Re = 28 000 and a wide range of horizontal Froude number F-h epsilon [0.0225 0.135] and buoyancy Reynolds number R = ReFh2 epsilon [14 510]. The numerical simulations use a weak hyperviscosity and are therefore almost direct numerical simulations (DNS). After the nonlinear development of the zigzag instability, both shear and gravitational instabilities develop and lead to a transition to small scales. A spectral analysis shows that this transition is dominated by two kinds of transfer: first, the shear instability induces a direct non-local transfer toward horizontal wavelengths of the order of the buoyancy scale L-b = U/N, where U is the characteristic horizontal velocity of the dipole and N the Brunt-Vaisala frequency; second, the destabilization of the Kelvin-Helmholtz billows and the gravitational instability lead to small-scale weakly stratified turbulence. The horizontal spectrum of kinetic energy exhibits epsilon(2/3)(K)k(h)(-5/3) power law (where k(h) is the horizontal wavenumber and epsilon(K) is the dissipation rate of kinetic energy) from k(b) = 2 pi/L-b to the dissipative scales, with an energy deficit between the integral scale and k(b) and an excess around k(b). The vertical spectrum of kinetic energy can be expressed as E(k(z)) = C(N)N(2)k(z)(-3) + C epsilon(2/3)(K)k(z)(-5/3) where C-N and C are two constants of order unity and k(z) is the vertical wavenumber. It is therefore very steep near the buoyancy scale with an N(2)k(z)(-3) shape and approaches the epsilon(2/3)(K)k(z)(-5/3) spectrum for k(z) > k(o), k(o) being the Ozmidov wavenumber, which is the cross-over between the two scaling laws. A decomposition of the vertical spectra depending on the horizontal wavenumber value shows that the N(2)k(z)(-3) spectrum is associated with large horizontal scales vertical bar k(h)vertical bar < k(b) and the epsilon(2/3)(K)k(z)(-5/3) spectrum with the scales vertical bar k(h)vertical bar > k(b).
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| 2. |
- Chevalier, Mattias, 1973-
(författare)
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Feedback and adjoint based control of boundary layer flows
- 2004
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Linear and nonlinear optimal control have been investigated in transitional channel and boundary layer .ows. The flow phenomena that we study are governed by the incompressible Navier–Stokes equations and the main aim with the control is to prevent transition from laminar to turbulent flows. A linear model-based feedback control approach, that minimizes an objective function which measures the perturbation energy, can be formulated where the Orr– Sommerfeld/Squire equations model the flow dynamics. A limitation with the formulation is that it requires complete state information. However, the control problem can be combined with a state estimator to relax this requirement. The estimator requires only wall measurements to reconstruct the flow in an optimal manner.Physically relevant stochastic models are suggested for the estimation problem which turns out to be crucial for fast convergence. Based on these models the estimator is shown to work for both in.nitesimal as well as finite amplitude perturbations in direct numerical simulations of a channel flow at Recl = 3000.A stochastic model for external disturbances is also constructed based on statistical data from a turbulent channel flow at ReT = 100. The model is successfully applied to estimate a turbulent channel flow at the same Reynolds number.The combined control and estimation problem, also known as a compensator, is applied to spatially developing boundary layers. The compensator is shown to successfully reduce the perturbation energy for Tollmien–Schlichting waves and optimal perturbations in the Blasius boundary layer. In a Falkner– Skan–Cooke boundary layer the perturbation energy of traveling and stationary cross-flow disturbances are also reduced.A nonlinear control approach using the Navier–Stokes equations and the associated adjoint equations are derived and implemented in the context of direct numerical simulations of spatially-developing three-dimensional boundary layer .ows and the gradient computation is veri.ed with .nite-di.erences. The nonlinear optimal control is shown to be more e.cient in reducing the disturbance energy than feedback control when nonlinear interactions are becoming signi.cant in the boundary layer. For weaker disturbances the two methods are almost indistinguishable.
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| 3. |
- Chomaz, Jean Marc, et al.
(författare)
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Spectral analysis of the transition to turbulence from a dipole in stratified fluid
- 2013
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Ingår i: ETC 2013 - 14th European Turbulence Conference. - : Zakon Group LLC.
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Konferensbidrag (refereegranskat)abstract
- We investigate through numerical simulations the spectral properties of the turbulence generated during the nonlinear evolution of a Lamb-Chaplygin dipole in a stratified fluid for a high Reynolds number Re = 28000 and a wide range of horizontal Froude number Fh ∈ [0.0225 0.135] and buoyancy Reynolds number R = ReFh2 ∈ [14 510]. A spectral analysis shows that this transition is dominated by two kinds of transfers: first, the shear instability induces a direct non-local transfer toward horizontal wavelengths of the order of the buoyancy scale Lb = U/N, where U is the characteristic horizontal velocity of the dipole and N the Brunt-Väisälä frequency; second, the destabilization of the Kelvin-Helmholtz billows and the gravitational instability lead to small-scale weakly stratified turbulence. We show that the anisotropic spectra at the maximum of dissipation share many characteristics with those obtained from numerical simulations of forced stratified turbulence and from measurements in the atmosphere and in the ocean. The article presenting this study [2] is the subject of a Focus on Fluids article [10].
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