In atmospheric studies the motion of the earth's atmosphere can sometimes be modeled with the equation

\[\frac{D \vec{V}}{D t}+2 \vec{\Omega} \times \vec{V}=-\frac{1}{ho} abla p\]

where \(\vec{V}\) is the large-scale velocity of the atmosphere across the Earth's surface, \(abla p\) is the climatic pressure gradient, and \(\vec{\Omega}\) is the Earth's angular velocity. What is the meaning of the term \(\vec{\Omega} \times \vec{V}\) ? Use the pressure difference, \(\Delta p\), and typical length scale, \(L\) (which could, for example, be the magnitude of, and distance between, an atmospheric high and low, respectively), to nondimensionalize this equation. Obtain the dimensionless groups that characterize this flow.