Spatial versus temporal instabilities in a parametrically forced stratified mixing layer

Gelfgat, Alexander; Kit, E.

doi:10.1017/s0022112005008608

Cited by 24 publications

(44 citation statements)

References 63 publications

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“…Re>0.51, which is much smaller than usually considered cases and significantly smaller than the linear stability limit (Gelfgat & Kit, 2006). The graph shows that non-modal growth is possible also for α >1, at which the mixing layer flow is stable for any Reynolds number and also for the inviscid case.…”

Section: Appendix B -Eigenproblem and Complex Conjugated Eigenvaluesmentioning

confidence: 78%

“…The linear stability results are taken from Gelfgat & Kit (2006) and are rescaled according to the present formulation. Apparently, the ReE(α,0) values are smaller than critical Reynolds numbers of the linear stability analysis.…”

Section: Appendix B -Eigenproblem and Complex Conjugated Eigenvaluesmentioning

confidence: 99%

“…This flow is unstable within the inviscid model, and becomes linearly unstable at rather low Reynolds number if the viscous flow model is implied. The flow remains linearly stable for the streamwise wavenumber larger than unity (Drazin, 2001;Gelfgat & Kit, 2006). However, the instability development at early times still can be subject to a non-modal growth, so that the issue should be studied for the mixing layer flow as well.…”

Section: Introductionmentioning

confidence: 99%

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Non-modal disturbances growth in a viscous mixing layer flow

Vitoshkin¹,

Gelfgat²

2014

Fluid Dyn. Res.

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Non-modal transient growth of disturbances in an isothermal viscous mixing layer flow is studied for the Reynolds numbers varying from 100 up to 5000 at different streamwise and spanwise wavenumbers. It is found that the largest non-modal growth takes place at the wavenumbers for which the mixing layer flow is stable. In linearly unstable configurations the non-modal growth can only slightly exceed the exponential growth at short times. Contrarily to the fastest exponential growth, which is two-dimensional, the most profound non-modal growth is attained by oblique three-dimensional oblique waves propagating at an angle with respect to the base flow. By comparing results of several mathematical approaches, it is concluded that within the considered mixing layer model with the tanh base velocity profile, the non-modal optimal disturbances growth results from the discrete part of the spectrum only. Finally, full three-dimensional DNS with the optimally perturbed base flow confirms the presence of the structures determined by the transient growth analysis. The time evolution of optimal perturbations is presented and exhibit growth and decay of flow structures that sometimes become similar to those observed at late stages of time evolution of the KelvinHelmholtz billows. It is shown that non-modal optimal disturbances yield a strong mixing without a transition to turbulence.2

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Section: Appendix B -Eigenproblem and Complex Conjugated Eigenvaluesmentioning

confidence: 78%

Section: Appendix B -Eigenproblem and Complex Conjugated Eigenvaluesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-modal disturbances growth in a viscous mixing layer flow

Vitoshkin¹,

Gelfgat²

2014

Fluid Dyn. Res.

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“…The optimal vectors of the perturbations are represented as Fourier modes in the streamwise and spanwise directions (∝ e i(kx+mz) ). In the cross-stream direction the perturbations are discretized and resolved by central finite-difference schemes in the same way as in Gelfgat & Kit (2006). For the three profiles the 3D maximal growths are indeed larger by an order of magnitude than the corresponding 2D ones, and are attained at later stages.…”

Section: Numerical Comparison Between 2d and 3d Growthmentioning

confidence: 99%

On the role of vortex stretching in energy optimal growth of three-dimensional perturbations on plane parallel shear flows

et al. 2012

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The three-dimensional linearized optimal energy growth mechanism, in plane parallel shear flows, is re-examined in terms of the role of vortex stretching and the interplay between the spanwise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille and mixing-layer shear profiles is robust and resembles localized plane waves in regions where the background shear is large. The waves are tilted with the shear when the spanwise vorticity and the planar divergence fields are in (out of) phase when the background shear is positive (negative). A minimal model is derived to explain how this configuration enables simultaneous growth of the two fields, and how this mutual amplification affects the optimal energy growth. This perspective provides an understanding of the three-dimensional growth solely from the two-dimensional dynamics on the shear plane.

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“…The spatial formulation arises naturally in the so-called signalling problem (see e.g. Gelfgat & Kit 2006), when spatial instability can be viewed as the result of an upstream periodic source of excitation.…”

Section: Interpretation In Terms Of Spatial Spectrummentioning

confidence: 99%

On the response of large-amplitude internal waves to upstream disturbances

Camassa

Viotti

2012

J. Fluid Mech.

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Large-amplitude internal solitary waves generate shear flows that intensify from the wings of the waves to their maxima. Upstream perturbations of the hydrostatic equilibrium in the form of wave packets along the path of wave propagation are expected to trigger shear instability and ultimately generate Kelvin–Helmholtz roll-ups. In contrast, as shown here with accurate simulations of incompressible stratified Euler equations, large internal waves can act as suppressors of perturbations. The precise understanding of the mechanisms leading to different outcomes, including whether instability is excited, is the focus of this work. Under the action of shear flows, small-amplitude wave packets undergo stretching and filamentation, which lead to significant absorption of perturbation energy into the background shear. It is found that this typical behaviour is present in the self-induced shear by internal waves, regardless of whether the shear is stable or unstable, and can leave a quieter state in the wave’s wake for a wide range of perturbation parameters. In the unstable case, even once perturbations are selected to excite the instability, our results show that this absorption can act to reduce growth in the strong-shear region, effectively making roll-up development observable only downstream of the wave crest. Our approach is both analytical and numerical; a model valid for relatively thin pycnoclines and suitable for local spectral analysis is devised and used. Energy diagnostics on the simulations are implemented to validate the numerics and illustrate the energy exchanges between background wave flow and its shear. A link between the absorption mechanism and the clustering of local eigenvalues along the wave is proposed. This promotes an energetic coupling among neutral modes stronger than what may be expected to occur in slowly varying flows, and gives rise to multi-modal transient dynamics of the kind often referred to as non-normality effects. For those cases in which the wave-induced shear meets the conditions for local instability, it is found that the growth of disturbances is selective with respect to the sign of the mode excited upstream. Elements of this phenomenon are interpreted by asymptotic analysis for spatial growth in time-independent slowly varying media.

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Spatial versus temporal instabilities in a parametrically forced stratified mixing layer

Cited by 24 publications

References 63 publications

Non-modal disturbances growth in a viscous mixing layer flow

Non-modal disturbances growth in a viscous mixing layer flow

On the role of vortex stretching in energy optimal growth of three-dimensional perturbations on plane parallel shear flows

On the response of large-amplitude internal waves to upstream disturbances

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