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3 Basics of Geophysical Fluid Dynamics
3.7.8 Impacts of the Nonlinear Terms
The nonlinear terms are important in the dynamics of many processes. For instance,
these terms are the reason for the existence of turbulence which makes mixing a soup
with a spoon much more efficien than just waiting until the soup has mixed itself.
The reader can also blame these terms for the unreliability of weather forecasts for
longer than 5 days ahead.
3.8 Fundamental Conservation Principles
3.8.1 A List of Principles
There are several conservation principles that need to be considered when studying
flui motions. These are:
1. Conservation of momentum (Newton’s laws of motion)
2. Conservation of mass
3. Conservation of interal energy (heat)
4. Conservation of salt.
In addition to this comes the so-called equation of state that links the fiel variables such as temperature and salinity to the density of the fluid All these equations
are coupled with each other, which makes the equations describing flui motions a
coupled system of partial differential equations.
3.8.2 Conservation of Momentum
Conservation of momentum is an expression of changes in fl w speed and/or direction as a result of forces. The frictional stress imposed by winds along the sea surface
acts as a boundary source term in the momentum equations. Friction at the sea f ow
acts as a sink term in these equations. Forces of relevance to fluid are explored in
the next sections.
3.8.3 Conservation of Volume – The Continuity Equation
Water is largely incompressible, so that the mass of a given water volume cannot
change much under compression. Conservation of mass can therefore be expressed
in terms of conservation of volume. To understand this important concept, consider
a virtual volume element (Fig. 3.5). For simplicity, we orientate this element in such
a way that its face normals are parallel to the directions of the Cartesian coordinate
system. The side-lengths of this box are δx, δy and δz, and the volume is δV =
δx · δy · δz.
3 Basics of Geophysical Fluid Dynamics
3.7.8 Impacts of the Nonlinear Terms
The nonlinear terms are important in the dynamics of many processes. For instance,
these terms are the reason for the existence of turbulence which makes mixing a soup
with a spoon much more efficien than just waiting until the soup has mixed itself.
The reader can also blame these terms for the unreliability of weather forecasts for
longer than 5 days ahead.
3.8 Fundamental Conservation Principles
3.8.1 A List of Principles
There are several conservation principles that need to be considered when studying
flui motions. These are:
1. Conservation of momentum (Newton’s laws of motion)
2. Conservation of mass
3. Conservation of interal energy (heat)
4. Conservation of salt.
In addition to this comes the so-called equation of state that links the fiel variables such as temperature and salinity to the density of the fluid All these equations
are coupled with each other, which makes the equations describing flui motions a
coupled system of partial differential equations.
3.8.2 Conservation of Momentum
Conservation of momentum is an expression of changes in fl w speed and/or direction as a result of forces. The frictional stress imposed by winds along the sea surface
acts as a boundary source term in the momentum equations. Friction at the sea f ow
acts as a sink term in these equations. Forces of relevance to fluid are explored in
the next sections.
3.8.3 Conservation of Volume – The Continuity Equation
Water is largely incompressible, so that the mass of a given water volume cannot
change much under compression. Conservation of mass can therefore be expressed
in terms of conservation of volume. To understand this important concept, consider
a virtual volume element (Fig. 3.5). For simplicity, we orientate this element in such
a way that its face normals are parallel to the directions of the Cartesian coordinate
system. The side-lengths of this box are δx, δy and δz, and the volume is δV =
δx · δy · δz.