IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-04068-9_19.html
   My bibliography  Save this book chapter

The Role of Potential Flow in the Theory of the Navier-Stokes Equations

In: Advances in Mathematical Fluid Mechanics

Author

Listed:
  • Daniel D. Joseph

    (University of Minnesota and University of California)

Abstract

Solutions of the Navier-Stokes equations for flows of incompressible fluids satisfying no-slip boundary conditions are discussed in the frame of the Helmholtz decomposition. The focus is on the steady flow of a body in an unbounded fluid. The decomposition of the velocity into rotational and irrotational parts can be uniquely determined as the velocity generated by the vorticity in the Biot-Savart law plus a harmonic velocity in which the body and boundary conditions are identified. It is shown that contribution of the rotational velocity to the drag is larger than the total which includes a negative contribution from the irrotational velocity, The dissipation due to the potential flow cannot be neglected in any exact theory as it is in the conventional boundary layer theory and elsewhere.

Suggested Citation

  • Daniel D. Joseph, 2010. "The Role of Potential Flow in the Theory of the Navier-Stokes Equations," Springer Books, in: Rolf Rannacher & Adélia Sequeira (ed.), Advances in Mathematical Fluid Mechanics, pages 311-317, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-04068-9_19
    DOI: 10.1007/978-3-642-04068-9_19
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-642-04068-9_19. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.