On a solenoidal Fourier–Chebyshev spectral method for stability analysis of the Hagen–Poiseuille flow

Meseguer, Alvaro; Mellibovsky, Fernando

doi:10.1016/j.apnum.2006.09.002

Cited by 27 publications

(18 citation statements)

References 22 publications

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“…4 are typical fields of the three modes. These results are consistant with the previous results of Meseguer and Mellibovsky [23] .…”

Section: Presentsupporting

confidence: 94%

“…These eigenvalues are quite consistent with the previous study which has used a different method [23] . Figure 2 shows the convergence of the first 200 eigenvalues sorted by their real part as the grid number M increases from 128 to 512.…”

Section: Linear Stability Of Laminar Base Flowsupporting

confidence: 92%

“…Meseguer and Mellibovsky [23] n = 0 To give more details, we study the spectrum distribution of eigenvalues (see Fig. 3) and their associated eigenvectors (see Fig.…”

Section: Presentmentioning

confidence: 99%

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Optimal transient growth in turbulent pipe flow

Yang

Huang

et al. 2015

Appl. Math. Mech.-Engl. Ed.

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The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the governing equations onto the subspace spanned by the radial vorticity and radial velocity. The method is validated by comparing with the previous studies. Two peaks of the maximum transient growth amplification curve are found at different Reynolds numbers ranging from 20 000 to 250 000. The optimal flow structures are obtained and compared with the experiments and DNS results. The location of the outer peak is at the azimuthal wave number n = 1, while the location of the inner peak is varying with the Reynolds number. It is observed that the velocity streaks in the buffer layer with a spacing of 100δv are the most amplified flow structures. Finally, we consider the optimal transient growth time and its dependence on the azimuthal wave length. It shows a self-similar behavior for perturbations of different scales in the optimal transient growth process.

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“…4 are typical fields of the three modes. These results are consistant with the previous results of Meseguer and Mellibovsky [23] .…”

Section: Presentsupporting

confidence: 94%

Section: Linear Stability Of Laminar Base Flowsupporting

confidence: 92%

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Optimal transient growth in turbulent pipe flow

Yang

Huang

et al. 2015

Appl. Math. Mech.-Engl. Ed.

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“…1(d) and 1(f) and identical structural features can be observed. Edge state simulations were carried out in a short periodic pipe of L ¼ D using the shoot and refine method described in [17,18] and an accurate pipe flow code based on the solenoidal Petrov-Galerkin formulation presented in [27]. The spectral resolution was set to 33 Â 77 Â 27 axial Â azimuthal Â radial grid points.…”

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confidence: 99%

Edge State in Pipe Flow Experiments

et al. 2012

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Recent numerical studies suggest that in pipe and related shear flows, the region of phase space separating laminar from turbulent motion is organized by a chaotic attractor, called an edge state, which mediates the transition process. We here confirm the existence of the edge state in laboratory experiments. We observe that it governs the dynamics during the decay of turbulence underlining its potential relevance for turbulence control. In addition we unveil two unstable traveling wave solutions underlying the experimental flow fields. This observation corroborates earlier suggestions that unstable solutions organize turbulence and its stability border. DOI: 10.1103/PhysRevLett.108.214502 PACS numbers: 47.27.Cn, 47.27.NÀ, 47.52.+j In most situations of practical interest fluid flows are turbulent. Often transition to turbulence occurs despite the linear stability of the laminar state [1,2] such as in flows through pipes, ducts or even in astrophysical Keplerian flows. In some other cases turbulence occurs well below the critical point given by linear instability analysis, such as in flows through channels. Moreover, it has been shown for these shear flows that the turbulent state has unstable characteristics [3][4][5][6][7] and that localized turbulent patches eventually decay back to laminar. That at higher Reynolds numbers turbulence is still the rule rather than the exception is due to its invasive nature which causes laminar gaps to be quickly consumed by adjacent turbulent domains [8,9]. The observation that localized turbulent domains are intrinsically unstable [3,4,10,11] offers prospects to control and relaminarize flows [12]. Such potential methods are of great practical interest because the drag in turbulent flows is significantly larger and this causes higher energy consumption and limits transport rates.From a dynamical point of view the stability boundary separating laminar from turbulent motion plays a key role in how flows transit to and from turbulence. This laminarturbulent boundary is highly convoluted and most likely possesses a fractal structure as shown in simulations [13]. Some signatures of this have also been observed in experiments [14]. Hence its complexity puts a complete description for transition in shear flows beyond reach in the foreseeable future. However, using a tracking method first proposed and applied to plane Poiseuille flow [15,16], it has been possible to compute phase-space trajectories on the laminar-turbulent boundary of pipe flow [17,18]. Surprisingly, the dynamics at this boundary, or edge, are organized by a single state: This so-called ''edge state'' [13] is a chaotic attractor within the edge, whereas in the full phase-space it is a repeller with a single unstable direction pointing towards turbulence on one side and towards laminar flow on the other.According to dynamical systems theory the disordered dynamics of turbulence as well as of its edge are organized around unstable solutions of the Navier-Stokes equations [19]. For pipe flow mainly traveling wave s...

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“…Also, most codes with high order of accuracy are, to the authors knowledge, written for serial computers, e.g. [15,21,26,30,34], although parallel, high order codes exist (see [17,39]). …”

Section: Introductionmentioning

confidence: 99%