INTRODUCTORY
OCEANOGRAPHYINTRODUCTORY
OCEANOGRAPHY
|
|
The explanation given below comes from one of the best summary books about the theory and observations of the Gulf Stream ever written (The Gulf Stream , Cambridge University Press, 1965, written by Dr. Henry Stommel) -- unfortunately, the book is out of print.
In the text of the lesson from which you linked to this page, I discussed the three vorticities that are balanced on both sides of an ocean basin only when the current on the western side of the basin is intensified. These vorticities I called Wind Stress, Frictional and Coriolis Effect (CE). Mathematically, vorticity of an element of fluid is equal to twice its angular velocity, and the vorticity of a vertical column of water is taken as positive if CCW and negative if CW.
Wind Stress tendency and Frictional tendency are quite self-explanatory (CW (-) and CCW (+), respectively), but it is necessary to be more precise in defining and discussing the vorticity tendency due to the change in CE with latitude. The proper term for the vorticity induced by the CE is Planetary Vorticity.
Regardless of hemisphere, a column of water flowing northward without convergence or divergence has a negative-vorticity (CW) tendency, while those moving southward have a positive-vorticity (CCW) tendency. This follows because of the variation of the CE with latitude -- e.g., in the Northern Hemisphere, a northward flowing current will be subjected to an increasingly larger CE [inducing a CW (-) vorticity], while a southward flowing current will be subjected to an increasingly smaller CE [inducing a CCW (+) vorticity].
If the ocean circulation in a basin is perfectly symmetrical, the balance of the three vorticity tendencies can be modeled as shown in Table 1 below (the numbers shown in the table are arbitrary order-of-magnitude values for illustrative purposes only, and BC means Boundary Current). Note that the sum of the vorticity values on the western side of the basin do not balance those on the eastern side.
VORTICITY TENDENCIES IN A SYMMETRICAL CIRCULATION
Wind Stress Frictional Planetary Sum
If, on the other hand, the ocean circulation in a basin is non-symmetrical, the balance of the three vorticity tendencies can be modeled as shown in Table 2 below. By increasing the velocity of the current of the western BC, both the frictional and planetary vorticities on the western side would increase, while the eastern BC would not be changed significantly. Note that now the net sum of vorticity values on each side of the basin are zero and, therefore, balanced.
VORTICITY TENDENCIES IN AN ASYMMETRIC CIRCULATION
Wind Stress Frictional Planetary Sum
|
|
|
