Let's say temperature on a constant-p surface (say, 1000mb) decreases to the north, resulting in a southerly temperature gradient (gradients "point" from low to high). Both R and p are positive and greater than zero, so "k" (which is the "up" unit vector) crossed with a southerly vector yields an easterly vector. If we take the negative of this (from the - sign), we have a westerly vector. Now, pressure decreases with height, so, since dV/dP is a vector that point to the west, the wind becomes more westerly with height (wind vectors point more to the east as one goes "up" in the atmosphere). Well, this explains why there's a mean westerly current of air in the middle latitudes in the northern hemisphere!

Low-level flow is, generally, pretty weak. If we assume this, then we can see that where the temperature gradient is the strongest we should expect the strongest flow aloft (though, remember, we must consider that isentropic surfaces are sloped, so the upper-level jet tends to be displaced north of the low-level thermal gradient IN THE MEAN). In the case of the strongest temperature gradient, the magnitude of dV/dP is the greatest (since k x grad(t) is greatest there), which means that, in our example above, the winds become more westerly (stronger) with height. Above the tropopause, the temperature gradient reverses, which explains why winds decrease as you near the tropopause.

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