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3 Basics of Geophysical Fluid Dynamics
3.7.2 Newton’s Laws of Motion
Equations (3.5) already state the firs two of Newton’s laws of motion (Newton,
1687). Newton’s f rst law of motion states that, in an absolute coordinate system
void of any rotation or translation, both speed and direction of motion of a body
remain unchanged in the absence of forces. If there is a force, on the other hand,
there will be a certain change in motion. This is known as Newton’s second law of
motion.
3.7.3 Apparent Forces
Apparent forces come into play in a rotating coordinate system such as our Earth.
One of these apparent forces is the Coriolis force that gives rise to circular weather
patterns in the atmosphere, eddies in the ocean, or Jupiter’s Red Spot.
3.7.4 Lagrangian Trajectories
Imagine that you sit on a flui parcel of a certain temperature moving with the f ow.
The path along which you move is called a Lagrangian trajectory, based on work by
Lagrange (1788). Without any heat exchange with the ambient fluid the temperature
of your flui parcel remains constant and this feature can be formulated as:
dT
dt
= 0
(3.6)
where “T” is temperature and the “d” symbol now refers to a change of temperature
along the pathway of motion.
3.7.5 Eulerian Frame of Reference and Advection
Instead of moving with the f ow, you could stand still at a f xed location and measure
changes in temperatures as the flui moves past. This perspective is called the Eulerian system, based on work by Euler (1736). In this case, you would notice a change
in temperature if a fl w exists that carries differences (gradients) in temperature
towards you. This process is called advection. In Cartesian coordinates, the effect
of temperature advection can be expressed as:
∂ T
∂t
= −u
∂ T
∂ x
− v
∂ T
∂ y
− w
∂ T
∂z
(3.7)
This advection equation constitutes a partial differential equation.
3 Basics of Geophysical Fluid Dynamics
3.7.2 Newton’s Laws of Motion
Equations (3.5) already state the firs two of Newton’s laws of motion (Newton,
1687). Newton’s f rst law of motion states that, in an absolute coordinate system
void of any rotation or translation, both speed and direction of motion of a body
remain unchanged in the absence of forces. If there is a force, on the other hand,
there will be a certain change in motion. This is known as Newton’s second law of
motion.
3.7.3 Apparent Forces
Apparent forces come into play in a rotating coordinate system such as our Earth.
One of these apparent forces is the Coriolis force that gives rise to circular weather
patterns in the atmosphere, eddies in the ocean, or Jupiter’s Red Spot.
3.7.4 Lagrangian Trajectories
Imagine that you sit on a flui parcel of a certain temperature moving with the f ow.
The path along which you move is called a Lagrangian trajectory, based on work by
Lagrange (1788). Without any heat exchange with the ambient fluid the temperature
of your flui parcel remains constant and this feature can be formulated as:
dT
dt
= 0
(3.6)
where “T” is temperature and the “d” symbol now refers to a change of temperature
along the pathway of motion.
3.7.5 Eulerian Frame of Reference and Advection
Instead of moving with the f ow, you could stand still at a f xed location and measure
changes in temperatures as the flui moves past. This perspective is called the Eulerian system, based on work by Euler (1736). In this case, you would notice a change
in temperature if a fl w exists that carries differences (gradients) in temperature
towards you. This process is called advection. In Cartesian coordinates, the effect
of temperature advection can be expressed as:
∂ T
∂t
= −u
∂ T
∂ x
− v
∂ T
∂ y
− w
∂ T
∂z
(3.7)
This advection equation constitutes a partial differential equation.