Modal and nonmodal stability of a stably stratified boundary layer flow

Parente, E.; Robinet, Jean-Christophe; Palma, P. De; Cherubini, Stefania

doi:10.1103/physrevfluids.5.113901

Cited by 6 publications

(10 citation statements)

References 40 publications

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“…2020; Parente et al. 2020) employ Dirichlet boundary conditions in the far field when performing a local stability analysis on semi-infinite domains. While this type of boundary condition is an adequate one for computing the discrete modes of the spectrum, it is not accurate for the computation of their continuous counterparts.…”

Section: Figurementioning

confidence: 99%

“…In fact, the study by Parente et al. (2020) is the first to do so in regards to the latter theory. The present study extends their linear and local analysis in two meaningful ways, namely it (i) applies modal as well as non-modal theory, where the latter is done through an analysis of the pseudospectra (Trefethen & Embree 2005), to unstably stratified horizontal boundary layers and (ii) uses input–output analysis (Jovanović 2021) to study the optimal flow response with respect to imposed disturbances, which could in turn provide insights in terms of control strategies for the present flows.…”

Section: Introductionmentioning

confidence: 96%

“…Finally, both modal and non-modal (Schmid 2007) linear stability analyses of mixed convection boundary layers appeared recently when Parente et al. (2020) studied a stably stratified horizontal boundary layer. The modal analysis was performed under the scope of spatial stability and the non-modal analysis was evaluated using a direct-adjoint looping procedure.…”

Section: Introductionmentioning

confidence: 99%

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Stability and receptivity analyses of mixed convection in unstably stratified horizontal boundary layers

et al. 2023

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A linear stability analysis is employed to investigate thermal effects in shear flows. The cases analysed consist of unstably stratified horizontal boundary layers under a mixed convection regime, where forced and free convection mechanisms compete. Governing equations are given by the incompressible Navier–Stokes equations with the Oberbeck–Boussinesq approximation, where the base flow comes from their boundary layer approximation. Modal and non-modal analyses are used to investigate the behaviour of small-amplitude disturbances superposed to this base flow. An evaluation of the inertial, shearing and buoyancy mechanisms in the mixed convection boundary layer stability is performed through variations in the Reynolds, Prandtl and Richardson numbers. On the one hand, the spectra lead to the parametric conditions for the time-asymptotic onset of instability, which is still caused by Tollmien–Schlichting (TS) waves as in the traditional Blasius case. However, thermal effects have a destabilizing effect on them, more so for liquids than gases. On the other hand, the pseudospectra obtained from a resolvent analysis indicate the existence of transient growth at this same onset. However, contrary to the traditional Blasius case, thermal effects cause it to be dominated by the continuous frequency spectrum instead of the discrete TS modes. In order to elucidate this qualitative change, a componentwise input–output analysis is employed to quantify the receptivity to specific external disturbances. It shows that thermal effects directly impact the conversion of thermal to kinetic linear disturbance energy, causing a strong amplification of the flow response due to the non-normality of the linear operator. Results reveal that heating from below causes the forcing and response modes of the input–output analysis to have a free-stream spatial support due to non-modal excitation of the continuous spectrum. Such a behaviour suggests that the unstably stratified boundary layer is susceptible to free-stream thermal disturbances, which can potentially impact bypass transition.

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Section: Figurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Stability and receptivity analyses of mixed convection in unstably stratified horizontal boundary layers

et al. 2023

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“…Parente et al. (2020) considered the modal and non-modal linear stability of a stably stratified Blasius boundary layer flow. The influences of Richardson, Reynolds and Prandtl numbers on the temporal and spatial linear stability were discussed.…”

Section: Introductionmentioning

confidence: 99%

“…And the radiative instability was shown to exhibit a much larger growth rate than the viscous instability in a large Froude-number interval with large Reynolds numbers. Parente et al (2020) considered the modal and non-modal linear stability of a stably stratified Blasius boundary layer flow. The influences of Richardson, Reynolds and Prandtl numbers on the temporal and spatial linear stability were discussed.…”

Section: Introductionmentioning

confidence: 99%

Finite-amplitude instability of the buoyancy boundary layer in a thermally stratified medium

Xiao

Zhao

2022

J. Fluid Mech.

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The finite-amplitude instability of the buoyancy-driven boundary layer is considered on a vertical plate immersed in a thermally stratified ambient medium, where the wall and surrounding fluid have different temperature gradients. Although the linear stability in this configuration has been investigated, the finite-amplitude solution arising from the critical instability has been studied only for specific parameter values. We extend this by using the amplitude expansion method. The primary bifurcations to the two-dimensional least unstable mode for different temperature gradient ratios ( $0 \leqslant \lambda \leqslant 10$ ) and Prandtl numbers ( $10^{-1} \leqslant Pr \leqslant 10^{4}$ ) are investigated. Only supercritical bifurcations are found to occur when $0 \leqslant \lambda < 2$ and $Pr \leqslant 2800$ , while subcritical bifurcations are also found for larger values of temperature gradient ratio and Prandtl number. Analysis of the contribution of the nonlinear terms in the Landau coefficient reveals that the interaction of the modification of the mean flow and second harmonic for velocity with the fundamental mode for temperature plays an important role in subcritical bifurcation. Based on the Landau equation, the threshold amplitude of the nonlinear equilibrium solution is discussed as well. These encouraging results should be helpful for understanding such a buoyancy-driven flow system.

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