18
3 Basics of Geophysical Fluid Dynamics
3.2.2 Contours and Contour Interval
If a scalar varies spatially, this implies that it exhibits certain direction-dependent
gradients. Gradients in the spatial distribution of a scalar therefore constitutes a
vector field To avoid confusion, consider the following example: A mountain can
be characterised in terms of elevation of the ground above sea level. A map of this
mountain can be produced by connecting points of the same elevation. These lines
are called contours and the interval chosen between adjacent contour lines is called
contour interval (Fig. 3.1). If one walks along elevation contours, there will be no
change in elevation and it is impossible to climb or descent the mountain. In order to
do so, contours have to be crossed at a certain angle. The steepest ascent or descent
will be the one perpendicular to contour lines. The associated gradient, called bottom inclination or bottom slope, depends on direction and it is therefore a vector.
The mountain is steepest where the spacing between contour lines is the closest.
Fig. 3.1 Contours of elevation (m) above sea level of a mountain. The contour interval chosen is
500 m. Where are the steepest parts of the mountain? Can you climb the mountain by following a
contour line?
3.3 Location and Velocity
3.3.1 Location and Distance
For horizontal distances of up to 100 km, or so, the spherical shape of the Earth’s
surface can be ignored and a plane rectangular coordinate system can be used.
Fig. 3.2 shows such a so-called Cartesian coordinate system. The z-axis points
upward and the coordinate surface at z = 0 m define the (undisturbed) sea surface.
With reference to the point-of-origin, define by the coordinates x = 0, y = 0, and
z = 0, any location can now by specified
For convenience, specifi locations are written in the form of (x 1 , y 1 , z 1 ). The
location (10 m, 23 m, −10 m) is an example, where z = −10 m refers to a positive
depth of 10 m below the undisturbed sea surface. The distance of a certain location
from the point-of-origin is given by:
3 Basics of Geophysical Fluid Dynamics
3.2.2 Contours and Contour Interval
If a scalar varies spatially, this implies that it exhibits certain direction-dependent
gradients. Gradients in the spatial distribution of a scalar therefore constitutes a
vector field To avoid confusion, consider the following example: A mountain can
be characterised in terms of elevation of the ground above sea level. A map of this
mountain can be produced by connecting points of the same elevation. These lines
are called contours and the interval chosen between adjacent contour lines is called
contour interval (Fig. 3.1). If one walks along elevation contours, there will be no
change in elevation and it is impossible to climb or descent the mountain. In order to
do so, contours have to be crossed at a certain angle. The steepest ascent or descent
will be the one perpendicular to contour lines. The associated gradient, called bottom inclination or bottom slope, depends on direction and it is therefore a vector.
The mountain is steepest where the spacing between contour lines is the closest.
Fig. 3.1 Contours of elevation (m) above sea level of a mountain. The contour interval chosen is
500 m. Where are the steepest parts of the mountain? Can you climb the mountain by following a
contour line?
3.3 Location and Velocity
3.3.1 Location and Distance
For horizontal distances of up to 100 km, or so, the spherical shape of the Earth’s
surface can be ignored and a plane rectangular coordinate system can be used.
Fig. 3.2 shows such a so-called Cartesian coordinate system. The z-axis points
upward and the coordinate surface at z = 0 m define the (undisturbed) sea surface.
With reference to the point-of-origin, define by the coordinates x = 0, y = 0, and
z = 0, any location can now by specified
For convenience, specifi locations are written in the form of (x 1 , y 1 , z 1 ). The
location (10 m, 23 m, −10 m) is an example, where z = −10 m refers to a positive
depth of 10 m below the undisturbed sea surface. The distance of a certain location
from the point-of-origin is given by: