Hydrodynamic Stability in viscous, compressible flow
Hydrodynamic Stability in viscous, compressible flow
批准号:
0070765
负责人:
Kevin Zumbrun
金额:
$10.71万
依托单位:
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
2000
资助国家:
美国
项目状态:
已结题
起止时间:
2000-07-15 至 2003-06-30
中文摘要
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英文摘要
ABSTRACTThe principal investigator proposes several projects concerning multi-dimensional stability of flows in compressible, viscous, and reacting media. These include both shear flows of classical hydrodynamic stability and compressive flows of shock wave and combustion theory, the former exhibiting local symmetry parallel to and the latter normal to the flow. The unifying mathematical theme in these problems is the appearance of multiple length scales corresponding to small-scale transport and large-scale convective effects, with associated ``stiffness'' in the linearized perturbation problem. This leads to interesting, nonstandard issues in spectral and semigroup theory. At the same time, the inclusion of small-scale transport effects is highly desirable from the point of view of physical applications, which often occur at scales where these effects might be expected to be significant.The stability of regular flow patterns is an old and central topic in fluid, gas, and plasma dynamics, deciding which (stable) patterns will typicallybe observed, and which (unstable) are only mathematical and not physicallyobservable solutions. The transition from stability to instabilityis of particular importance, since it usually signals the arisal ofalternative, more complicated flow patterns close to the original(now unstable) one- this is a way to understand complicated flowsby the study of simpler and better-understood ones. Despite a largeand well-known body of theory on this subject, dating back to the late 1800's, there are still many aspects that are poorly understood, particularlyfor compressive, viscous, or reacting flows. Here, we propose to studyseveral of these issues arising in compressible gas and plasma dynamics,and in combustion, applications in which such usually-neglected effectsare of considerable practical importance. Our goal is, by includingthese mathematically problematic terms, to move existing theory fromthe qualitative to the quantitative regime, obtaining new informationof use to practitioners at the same time that we advance the mathematicaltheory.
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Multi-Dimensional and Vorticity Effects in Inclined Shallow Water Flow
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批准号:2206105
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项目类别:Standard Grant
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资助金额:$23.57万
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财政年份:2022
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负责人:Kevin Zumbrun
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依托单位:
Frontiers in Modulation, Dynamics, and Pattern Formation for Hyperbolic, Kinetic, and Convection-Reaction-Diffusion Systems
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批准号:2154387
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项目类别:Standard Grant
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资助金额:$23.57万
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财政年份:2022
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负责人:Kevin Zumbrun
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依托单位:
New Tools in the Study of Wave Propagation: Dynamical Systems for Kinetic Equations, Inviscid Limits for Modulated Periodic Waves, and Rigorous Numerical Stability Analysis
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批准号:1700279
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项目类别:Continuing Grant
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资助金额:$20.8万
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财政年份:2017
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负责人:Kevin Zumbrun
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依托单位:
New problems in continuum mechanics: asymptotic eigenvalue distributions, rigorous numerical stability analysis and weakly nonlinear asymptotics in periodic thin film flow
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批准号:1400555
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项目类别:Continuing Grant
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资助金额:$24.0万
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财政年份:2014
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负责人:Kevin Zumbrun
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依托单位:
Stability and dynamics of shock, detonation, and boundary layers
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批准号:0801745
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项目类别:Continuing Grant
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资助金额:$78.85万
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财政年份:2008
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负责人:Kevin Zumbrun
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依托单位:
Laser-Matter Interactions and Highly Nonlinear Geometrical Optics; Dynamics of Reacting Flows
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批准号:0505780
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项目类别:Standard Grant
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资助金额:$0.0万
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财政年份:2005
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负责人:Kevin Zumbrun
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依托单位:
Stability of compressible flow in real media
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批准号:0300487
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项目类别:Continuing Grant
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资助金额:$54.31万
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财政年份:2003
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负责人:Kevin Zumbrun
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依托单位:
I. Stability of Waves in Viscous Conservation Laws. II. Phase Transitions and Minimal Surfaces
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批准号:9706842
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项目类别:Continuing Grant
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资助金额:$8.06万
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财政年份:1997
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负责人:Kevin Zumbrun
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依托单位:
Mathematical Sciences: Problems in Conservation Laws
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批准号:9404384
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项目类别:Standard Grant
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资助金额:$4.0万
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财政年份:1994
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负责人:Kevin Zumbrun
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依托单位:
Mathematical Sciences: Postdoctoral Research Fellowship
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批准号:9107990
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项目类别:Fellowship Award
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资助金额:$7.5万
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财政年份:1991
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负责人:Kevin Zumbrun
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依托单位:
U.S.-Brazil Science & Technology Initiative: Stability of Undercompressive Viscous Shocks With Application to Oil Recovery
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批准号:9104216
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项目类别:Standard Grant
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资助金额:$0.0万
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财政年份:1991
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负责人:Kevin Zumbrun
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依托单位:
国内基金
海外基金
随机激励下多稳态系统的临界过渡识别及Basin Stability分析
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批准号:11872305
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项目类别:面上项目
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资助金额:65.0万元
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批准年份:2018
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负责人:徐伟
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依托单位: