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    [[The]] energy method and corresponding Eigenvalue problem for Navier slip flow

    Author
    Prince, Nathaniel
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    177479_Prince_rpi_0185E_10933.pdf (1001.Kb)
    Other Contributors
    Herron, Isom H., 1946-; Hirsa, Amir H.; Siegmann, W. L.; Banks, Jeffrey;
    Date Issued
    2016-08
    Subject
    Mathematics
    Degree
    PhD;
    Terms of Use
    This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.;
    Metadata
    Show full item record
    URI
    https://hdl.handle.net/20.500.13015/1751
    Abstract
    We derive the energy equation for a perturbation of finite amplitude for Poiseuille flow between two infinite plates, with no-slip boundary conditions on the upper plate and Navier slip boundary conditions on the lower plate. To determine an energy Reynolds number that guarantees the decay of all perturbations, we use the calculus of variations to extremalize a functional associated with the energy of a perturbation. After showing that the Euler-Lagrange equations we obtain for this base flow - and, in fact, any parallel base flow with Navier slip boundary conditions - are the same as the one we would obtain with no-slip boundary conditions, we look for solutions in the form of normal modes and eventually wind up with a coupled system of two ordinary differential equations. The minimum eigenvalue of this system is precisely the energy Reynolds number that we wish to determine. Using Chebyshev interpolation, we employ MATLAB to find this eigenvalue. After briefly examining the energy equations for combined Couette- Poiseuille flow, we adapt the method for the case of Taylor-Couette flow and show once again that the Euler-Lagrange equations we obtain are the same as the one we would obtain with no-slip boundary conditions. Using Lagrange interpolation, we find the energy Reynolds number for Taylor-Couette flow.;
    Description
    August 2016; School of Science
    Department
    Dept. of Mathematical Sciences;
    Publisher
    Rensselaer Polytechnic Institute, Troy, NY
    Relationships
    Rensselaer Theses and Dissertations Online Collection;
    Access
    Restricted to current Rensselaer faculty, staff and students. Access inquiries may be directed to the Rensselaer Libraries.;
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    • RPI Theses Online (Complete)

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