Chapter 5
3D Level Modelling
Abstract This chapter introduces the reader to fully three-dimensional hydrodynamic level models. Exercises address isolated oceanic eddies, eddy formation in
a strait, density-driven exchange flows through a strait, coastal upwelling in three
dimensions, the thermohaline deep circulation in the ocean, and, as a highlight,
equatorially trapped Kelvin waves accompanying El-Ni˜ no events.
5.1 The Basic Equations
5.1.1 The Basics
This section outlines the full three-dimensional equations governing the dynamics
of an incompressible fluid with a free surface. This comprises the momentum equations, the continuity equation, and a density-conservation equation, plus boundary
conditions.
5.1.2 Conservation of Momentum
As in the vertical-ocean slice model, dynamic pressure is separated into two
parts:
P = p + q
(5.1)
where (lower-case) p refers to the hydrostatic pressure field with reference to an
undisturbed (horizontal) sea level, and q includes pressure effects imposed by a
tilted sea surface and by nonhydrostatic pressure contributions. Again, the first pressure part p is diagnosed from the hydrostatic balance:
∂ p
∂z
= − (ρ − ρ o ) g
(5.2)
J. K¨ ampf, Advanced Ocean Modelling, DOI 10.1007/978-3-642-10610-1 5,
C
Springer-Verlag Berlin Heidelberg 2010
125
3D Level Modelling
Abstract This chapter introduces the reader to fully three-dimensional hydrodynamic level models. Exercises address isolated oceanic eddies, eddy formation in
a strait, density-driven exchange flows through a strait, coastal upwelling in three
dimensions, the thermohaline deep circulation in the ocean, and, as a highlight,
equatorially trapped Kelvin waves accompanying El-Ni˜ no events.
5.1 The Basic Equations
5.1.1 The Basics
This section outlines the full three-dimensional equations governing the dynamics
of an incompressible fluid with a free surface. This comprises the momentum equations, the continuity equation, and a density-conservation equation, plus boundary
conditions.
5.1.2 Conservation of Momentum
As in the vertical-ocean slice model, dynamic pressure is separated into two
parts:
P = p + q
(5.1)
where (lower-case) p refers to the hydrostatic pressure field with reference to an
undisturbed (horizontal) sea level, and q includes pressure effects imposed by a
tilted sea surface and by nonhydrostatic pressure contributions. Again, the first pressure part p is diagnosed from the hydrostatic balance:
∂ p
∂z
= − (ρ − ρ o ) g
(5.2)
J. K¨ ampf, Advanced Ocean Modelling, DOI 10.1007/978-3-642-10610-1 5,
C
Springer-Verlag Berlin Heidelberg 2010
125