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Non-modal stability in sliding Couette flow
Liu R(刘荣); Liu QS(刘秋生); Liu, R,Chinese Acad Sci, Inst Mech, Natl Micrograv Lab, Key Lab Micrograv, Beijing 100190, Peoples R China.
Source PublicationJOURNAL OF FLUID MECHANICS
2012-11-10
Volume710Pages:505-544
ISSN0022-1120
AbstractThe problem of an incompressible flow between two coaxial cylinders with radii a and b subjected to a sliding motion of the inner cylinder in the axial direction is considered. The energy stability and the non-modal stability have been investigated for both axisymmetric and non-axisymmetric disturbances. For the non-modal stability, we focus on two problems: response to external excitations and response to initial conditions. The former is studied by examining the epsilon-pseudospectrum, and the latter by examining the energy growth function G(t). Unlike the results of the modal analysis in which the stability of sliding Couette flow is determined by axisymmetric disturbances, the energy analysis shows that a non-axisymmetric disturbance has a critical energy Reynolds number for all radius ratios eta = a/b. The results for non-modal stability show that rather large transient growth occurs over a wide range of azimuthal wavenumber n and streamwise wavenumber alpha, even though the Reynolds number is far below its critical value. For the problem of response to external excitations, the response is sensitive to low-frequency external excitations. For all values of the radius ratio, the maximum response is achieved by non-axisymmetric and streamwise-independent disturbances when the frequency of external forcing omega = 0. For the problem of response to initial conditions, the optimal disturbance is in the form of helical streaks at low Reynolds numbers. With the increase of R e, the optimal disturbance becomes very close to straight streaks. For each eta, the maximum energy growth of streamwise-independent disturbances is of the order of Re-2, and the optimal time is of the order of R e. This relation is qualitatively similar to that for plane Couette flow, plane Poiseuille flow and pipe Poiseuille flow. Direct numerical simulations are applied to investigate the transition of the streamwise vortex (SV) scenario at Re = 1000 and 1500 for various eta. The initial disturbances are the optimal streamwise vortices predicted by the non-modal analysis. We studied the streak breakdown phase of the SV scenarios by examining the instability of streaks. Moreover, we have investigated the sustainment of the energy of disturbances in the SV scenario.
KeywordChannel Flow Transition To Turbulence Thread-annular Flow Self-sustaining Process Shear Flows Hydrodynamic Stability Global Stability Poiseuille Flow Reynolds-number Channel Flows Spiral Flow Transition
Subject Area流动的稳定性 ; 湍流
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Indexed BySCI ; EI
Language英语
WOS IDWOS:000310466900020
Funding OrganizationThis work was supported by National Natural Science Foundation of China (Grants No. 11102211, No. 50890182, and No. 11072249) and the Knowledge Innovation Program of Chinese Academy of Sciences (KGCX-SW-409).
DepartmentNML流动稳定性与复杂流动
Classification一类
Citation statistics
Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/46596
Collection国家微重力实验室
Corresponding AuthorLiu, R,Chinese Acad Sci, Inst Mech, Natl Micrograv Lab, Key Lab Micrograv, Beijing 100190, Peoples R China.
Recommended Citation
GB/T 7714
Liu R,Liu QS,Liu, R,Chinese Acad Sci, Inst Mech, Natl Micrograv Lab, Key Lab Micrograv, Beijing 100190, Peoples R China.. Non-modal stability in sliding Couette flow[J]. JOURNAL OF FLUID MECHANICS,2012,710:505-544.
APA Liu R,Liu QS,&Liu, R,Chinese Acad Sci, Inst Mech, Natl Micrograv Lab, Key Lab Micrograv, Beijing 100190, Peoples R China..(2012).Non-modal stability in sliding Couette flow.JOURNAL OF FLUID MECHANICS,710,505-544.
MLA Liu R,et al."Non-modal stability in sliding Couette flow".JOURNAL OF FLUID MECHANICS 710(2012):505-544.
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