# Book: Geophysical Flows (Omta)

• 1: General concept: Newton's 2nd law
A fluid is any substance that is able to flow which can be a gas, a liquid, or in some cases even a solid. In reality, fluids consist of molecules, particles that interact with each other. However, fluid mechanics deals with very large collections of such particles and it would be impossible to describe all the interactions between them. Therefore, the individual particles and their interactions are not taken into account: fluids are considered as a continuum.
You may remember that "air tends to flow from high pressure to low pressure". To understand why this happens, it is key to realize that gases (but also liquids) exert a force on their surroundings because of the thermal motion of the molecules. This force is in all directions, as the thermal motion is in all directions.
• 3: The Coriolis Force
The Coriolis force is a central element of the dynamics of ocean and atmosphere flows. A rigorous derivation using vector calculus is given in many textbooks on classical mechanics, but such derivations are often not the most effective way to obtain a conceptual understanding. Therefore, we will provide a more intuitive qualitative explanation here.
• 4: Turbulent Diffusion
Transport rates in both the ocean and the atmosphere are enhanced by many orders of magnitude through stirring by eddies of various sizes that are collectively named 'turbulence'. The study of turbulence forms a very large and complicated topic that we are not going to cover in-depth here. Instead, we will try to provide an idea of turbulence as a phenomenon and of the role it plays in the ocean and the atmosphere.
• 5: Geostrophic Balance
Geostrophic balance is arguably the most central concept in physical oceanography and dynamical meteorology. Although higher-order processes are responsible for all the interesting dynamics, it is important to realize that almost all large-scale flows in the atmosphere and ocean are in geostrophic balance to leading order. The only place where geostrophic balance never holds is at the Equator where there is no Coriolis force.
• 6: Wind Stress
The force exerted by the wind on the ocean surface gives rise to a vertical velocity gradient in the upper boundary layer of the ocean, as depicted below. Essentially, the wind adds momentum to the ocean surface which is then transported downward through diffusion associated with the vertical momentum gradient.
• 7: Basis of Wind-Driven Circulation - Ekman spiral and transports
Arctic explorer Fridtjof Nansen noticed something strange: icebergs tend to drift at an angle to the right of the prevailing wind direction. To explain this remarkable observation, Ekman (1905) formulated a theory that is still a cornerstone of physical oceanography. The central assumption is that near the ocean surface, the largest deviations from geostrophic balance occur as a result of the wind stress which leads to momentum diffusion in the vertical direction.
• 8: Ocean Currents - Subtropical (and subpolar) Gyres
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Thumbnail: NASA/Goddard Space Flight Center Scientific Visualization Studio. Image used with permission (Public Domain; NASA)