Hydrodynamic Stability

Drazin, P. G.; Reid, W. H.

doi:10.1017/cbo9780511616938

Cited by 1,408 publications

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“…(a) Inflectional instability: The presence of inflection points in U 0 (y) (see figures 4a and c) would be an instability mechanism from the well-known Rayleigh's theorem given in the inviscid limit (Drazin & Reid 1981). Such inflection points in the velocity profile were also observed in the experiment of Kessler (1985a), and Pedley & Kessler (1992) indeed speculated that they might play a role in generating the blip instability.…”

Section: Physical Mechanisms Of the Instabilities: Budget Analysismentioning

confidence: 74%

“…From this viewpoint, it is interesting to note that the inflection points in U 0 (y) in the present study appear only at low flow rates where the varicose instability is significantly destabilised. We note that this mechanism essentially stems from the term iαD 2 U 0v in (2.21c) (Drazin & Reid 1981), and, in the absence of this term, the inflectional instability would not appear, as in plane Couette flow where the velocity is simply a linear function of the wall-normal coordinate.…”

Section: Physical Mechanisms Of the Instabilities: Budget Analysismentioning

confidence: 94%

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Stability of downflowing gyrotactic microorganism suspensions in a two-dimensional vertical channel

Hwang

Pedley²

2014

J. Fluid Mech.

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Hydrodynamic focusing of cells along the region of the most rapid flow is a robust feature in downflowing suspensions of swimming gyrotactic microorganisms. Experiments performed in a downward pipe flow have reported that the focussed beam-like structure of the cells is often unstable and results in the formation of regular-spaced axisymmetric blips, but the mechanism by which they are formed has not been well understood. To elucidate this mechanism, in this study, we perform a linear stability analysis of a downflowing suspension of randomly swimming gyrotactic cells in a two-dimensional vertical channel. On increasing the flow rate, the basic state exhibits a focussed beam-like structure. It is found that this focussed beam is unstable with the varicose mode, the spatial structure, wavelength, phase speed, and behaviour with the flow rate of which are remarkably similar to those of the blip instability in the pipe flow experiment. To understand the physical mechanism of the varicose mode, we perform an analysis which calculates the term-by-term contribution to the instability. It is shown that the leading physical mechanism in generating the varicose instability originates from the horizontal gradient in the cell-swimming-vector field formed by the non-uniform shear in the base flow. This mechanism is found to be supplemented by cooperation with the gyrotactic instability mechanism observed in uniform suspensions.

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Section: Physical Mechanisms Of the Instabilities: Budget Analysismentioning

confidence: 74%

Section: Physical Mechanisms Of the Instabilities: Budget Analysismentioning

confidence: 94%

Stability of downflowing gyrotactic microorganism suspensions in a two-dimensional vertical channel

Hwang

Pedley²

2014

J. Fluid Mech.

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“…Drazin & Reid (1981) equations (8.6)-(8.8) with nonlinearities reinstated ) the fully nonlinear equations for the total flow field U and temperature field Θ are ∂ U ∂τ + U · ∇U = −∇P + Ra P r Θŷ + P r∇ 2 U (4.1)…”

Section: Appendix Bmentioning

confidence: 99%

Exact coherent structures in stably stratified plane Couette flow

Olvera

Kerswell

2017

J. Fluid Mech.

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. The existence of exact coherent structures in stably-stratified plane Couette flow (gravity perpendicular to the plates) is investigated over Reynolds-Richardson number (ReRi b ) space for a fluid of unit Prandtl number (P r = 1) using a combination of numerical and asymptotic techniques. Two states are repeatedly discovered using edge-tracking -EQ7 and EQ7-1 in the nomenclature of Gibson & Brand (2014) -and found to connect with 2-dimensional convective roll solutions when tracked to negative Ri b (the RayleighBenard problem with shear). Both these states and Nagata's (1990) original exact solution feel the presence of stable stratification when Ri b = O(Re −2 ) or equivalently when the Rayleigh number Ra := −Ri b Re 2 P r = O(1). This is confirmed via a stratified extension of the Vortex-Wave-Interaction (VWI) theory of Hall & Sherwin (2010). If the stratification is increased further, EQ7 is found to progressively spanwise and crossstream localise until a second regime is entered at Ri b = O(Re −2/3 ). This corresponds to a stratified version of the Boundary Reduced Equation (BRE) regime of Deguchi, Hall & Walton (2013). Increasing the stratification further, appears to lead to a third, ultimate regime where Ri b = O(1) in which the flow fully localises in all three directions at the minimal Kolmogorov scale which then corresponds to the Osmidov scale. Implications for the laminar-turbulent boundary in the (Re-Ri b ) plane are briefly discussed.

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“…Two powerful existing techniques for finding eigenvalues and eigenfunctions numerically are the compound matrix (see e.g. Brown & Marletta [9]; Davies [18]; Drazin & Reid [21]; Gardner et al [24]; Greenberg & Marletta [30], [31], [32]; Ivansson [46]; Straughan & Walker [91]) and the Chebyshev tau method (see e.g. Dongarra et al.…”

Section: Introductionmentioning

confidence: 99%

Convection in Porous Media

2013

Convection Heat Transfer

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source• a link is made to the metadata record in Durham E-Theses• the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. AbstractThe subject of thermal convection in fluid and porous media is investigated, coupled with the development of efficient spectral finite element methods to improve on the more commonly used techniques for these types of problems.Convection induced by the selective absorption of radiation in a porous medium is DeclarationThe work in this thesis is based on research carried out at the Numerical Analysis

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Hydrodynamic Stability

Cited by 1,408 publications

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Stability of downflowing gyrotactic microorganism suspensions in a two-dimensional vertical channel

Stability of downflowing gyrotactic microorganism suspensions in a two-dimensional vertical channel

Exact coherent structures in stably stratified plane Couette flow

Convection in Porous Media

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