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Update l33.md
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johnryantaylor authored Jan 20, 2024
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Expand Up @@ -25,7 +25,7 @@ Average wind speed for the months of June - August at a height of 10m. Color sho

{numref}`fig:lowlevel-wind` shows the average wind speed and direction at a height of 10m above the ground (or the sea). Note that the wind speed is relatively weak at this height over land due to the extra drag induced by vegetation and topography. The wind patterns that we see in {numref}`fig:lowlevel-wind` drive the ocean circulation. In particular, both hemispheres have westerly jets (wind coming from the west and going to the east) at mid-latitudes and trade winds in the opposite direction (blowing to the west) at low latitudes. Here, we will refer to the regions between the maxima of the trade winds and the westerly jets as the _subtropics_. Note that the trade winds are much more pronounced than in {numref}`fig:climatological_wind` since the trade winds are confined to low levels in the atmosphere. Also note that in the Northern Hemisphere summer, the westerly jet in the Northern Hemisphere is weaker than it would be in winter.

When the wind blows over the ocean, it exerts a stress on the ocean surface, and this stress drives currents. We can model this stress and study its effects by adding an additional force to our equations of motion. Specifically, the new force will be the derivative of a viscous stress, and the viscous stress is proportional to the vertical derivative of the horizontal velocity where the constant of propotionality is the _viscosity_ \footnote{In reality the stress from the wind is transmitted to the ocean through complicated processes including breaking waves. However, it is common to model this using a viscous stress as we do here, and the mechanism by which the stress is transmitted from the atmosphere to the ocean isn't critical to the ocean's response.}. These are the same ideas that we used in the cryosphere lectures.
When the wind blows over the ocean, it exerts a stress on the ocean surface, and this stress drives currents in the upper ocean. These currents are strongly modified by the Coriolis acceleration, and this has important impacts on the distribution of nutrients and primary production in the upper ocean. We can model the wind stress and study its effects by adding an additional force to our equations of motion. Specifically, the new force will be the derivative of a viscous stress, and the viscous stress is proportional to the vertical derivative of the horizontal velocity where the constant of propotionality is the _viscosity_ \footnote{In reality the stress from the wind is transmitted to the ocean through complicated processes including breaking waves. However, it is common to model this using a viscous stress as we do here, and the mechanism by which the stress is transmitted from the atmosphere to the ocean isn't critical to the ocean's response.}. These are the same ideas that we used in the cryosphere lectures.

Specifically, the equations that we will consider are

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