| EPSRC Reference: |
GR/S96616/02 |
| Title: |
Stability of inviscid flows through a given domain with permeable boundary |
| Principal Investigator: |
Vladimirov, Professor VA |
| Other Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
University of York |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 March 2006 |
Ends: |
29 February 2008 |
Value (£): |
83,780
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| EPSRC Research Topic Classifications: |
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The aim of the project is to study unusual phenomena in a flow of a fluid through a given domain when the fluid enters the domain through one part of the boundary (the inlet) and leaves it through another part (the outlet). A typical example is a flow in a pipe of finite length when the ends of the pipe represent inlet and outlet of the flow domain. Another example is given by meteorology. Conventional short-time weather forecast involves solving equations of fluid mechanics in a domain which is bounded by two meridians and two parallels. The boundary of this forecast domain is, of course, permeable for air and the problem of boundary conditions naturally arises. A mathematical model that can be numerically studied using computers appears only after such boundary conditions are specified. One more important example is the problem of calculation and design of ventilation systems based on blowing or exhaustion of air. A key requirement here is to ensure the absence of stagnation zones in a ventilated room. Surely, certain approaches to this problem have been developed in practical engineering, but the creation of a more fundamental theory will, no doubt, eventually lead to considerable improvement of such empirical methods. Finally, we should mention a similar problem of transport of an admixture (e.g. a pollutant) in the atmosphere and ocean when there are its sources and sinks. The importance of such problems is evident already from the above examples.-However, they are still insufficiently explored. In fact, in fluid mechanics overwhelming majority of papers deal with fluid flows which are either bounded by rigid impermeable walls or extend to infinity.In this project, mainly flows of an inviscid fluid are studied, and the effect of small viscosity is taken into account by the asymptotic theory of boundary layers, special attention being paid to boundary layers at the outlet. All the phenomena listed below, being known for viscous fluids, are completely unknown in inviscid fluid dynamics. First we consider the existence and uniqueness problem for steady and forced time-periodic flows. Also, we point out conditions for non-existence of these regimes caused by permanent acceleration of motion. When a steady or forced time-periodic flow exists, natural questions about its stability and instability, dependence on parameters and branching arise. We study the stability of steady and both forced and self-oscillatory periodic flows paying special attention to non-existence of stagnation zones (the case of proper ventilation). We investigate the general problem of monotonouos and oscillatory instability of a steady flow and corresponding transitions to steady and self-oscillatory secondary regimes. Parametric resonance and parametric stabilization/destabilization effects will be also studied. The possibility of creation of stagnation zones will be specially examined. General approaches will be realized for a number of flows in rectilinear and curved pipes and ducts with various distributions of velocity and vorticity at the inlet.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.york.ac.uk |