Chapter 7 - Some Mathematics:
The Equations of Motion
7.9 Important Concepts
- Gravity, buoyancy, and wind are the dominant forces acting on the ocean.
- Earth's rotation produces a pseudo force, the Coriolis force.
- Conservation laws applied to flow in the ocean lead to equations of motion;
conservation of salt, volume and other quantities can lead to deep insights
into oceanic flow.
- The transformation from equations of motion applied to fluid parcels to
equations applied at a fixed point in space greatly complicates the equations
of motion. The linear, first-order, ordinary differential equations describing
Newtonian dynamics of a mass accelerated by a force become nonlinear, partial
differential equations of fluid mechanics.
- Flow in the ocean can be assumed to be incompressible except when de-scribing
sound. Density can be assumed to be constant except when density is multiplied
by gravity g. The assumption is called the
- Conservation of mass leads to the continuity equation, which has an especially
simple form for an incompressible fluid.