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Equations of Motion; Surface Gravity Waves

  • Joseph Pedlosky
Chapter

Abstract

For a rotating stratified fluid, the general equations of motion can be written as:
  1. 1.
    Momentum equation:
    $$ \rho \left[ {\frac{{d\vec u}}{{dt}} + 2\Omega \times \vec u} \right] = - \nabla p + \mu {\nabla ^2}\vec u + k\nabla (\nabla \cdot \vec u)\;(if\;\mu \;cons\tan t,\;k\;is\sec ondvisosity) $$
    (3.1)
     
  2. 2.
    Mass conservation:
    $$ \frac{{\partial \rho }}{{\partial t}} + \nabla \cdot (\rho \vec u) = 0\;;and $$
    (3.2)
     
  3. 3.
    Thermodynamic energy equation:
    $$ \frac{{ds}}{{dt}} = H $$
    where s is specific entropy and H is the nonreversible heat addition. This can be rewritten, assuming that s is a thermodynamic function of p and ρ,
    $$ {c_p}\frac{{dT}}{{dt}} - \frac{{\alpha T}}{{\rho t}}\frac{{dp}}{{dt}} = \Phi + \frac{k}{\rho }{\nabla ^2}T + Q + k{(\nabla \cdot \vec u)^2} \equiv H $$
    (3.3)
     
where s is specific entropy and H is the nonreversible heat addition.

Keywords

Wave Packet Group Velocity Phase Speed Velocity Potential Surface Gravity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, London, pp 615 (especially Chapter 1)Google Scholar
  2. Kundu PK (1990) Fluid mechanics. Academic Press, San Diego, pp 638 (especially Chapter 5)Google Scholar
  3. Lamb H (1945) Hydrodynamics, 6th edition. Dover Publications, New York, pp 738Google Scholar
  4. Stoker JJ (1957) Water waves. Interscience, New York, pp 567Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Joseph Pedlosky
    • 1
  1. 1.Department of Physical OceanographyWoods Hole Oceanographic InstitutionWoods HoleUSA

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