Chapter 7, Problem 3P

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

$\frac{D\stackrel{\to }{V}}{Dt}+2\stackrel{\to }{\Omega }\times \stackrel{\to }{V}=-\frac{1}{\rho }\nabla p$

where $\stackrel{\to }{V}$ is the large-scale velocity of the atmosphere across the Earth’s surface, ∇p is the climatic pressure gradient, and $\stackrel{\to }{\Omega }$ is the Earth’s angular velocity. What is the meaning of the term $\stackrel{\to }{\Omega }$ × V? Use the pressure difference, Δp, 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.