Solution To The Linearized Primitive Equations
The analytic solution to the linearized primitive equations involves a sinusoidal oscillation in time and longitude, modulated by coefficients related to height and latitude.
where s and are the zonal wavenumber and angular frequency, respectively. The solution represents atmospheric waves and tides.
When the coefficients are separated into their height and latitude components, the height dependence takes the form of propagating or evanescent waves (depending on conditions), while the latitude dependence is given by the Hough functions.
This analytic solution is only possible when the primitive equations are linearized and simplified. Unfortunately many of these simplifications (i.e. no dissipation, isothermal atmosphere) do not correspond to conditions in the actual atmosphere. As a result, a numerical solution which takes these factors into account is often calculated using general circulation models and climate models.
Read more about this topic: Primitive Equations
Famous quotes containing the words solution to, solution and/or primitive:
“Coming out, all the way out, is offered more and more as the political solution to our oppression. The argument goes that, if people could see just how many of us there are, some in very important places, the negative stereotype would vanish overnight. ...It is far more realistic to suppose that, if the tenth of the population that is gay became visible tomorrow, the panic of the majority of people would inspire repressive legislation of a sort that would shock even the pessimists among us.”
—Jane Rule (b. 1931)
“There’s one solution that ends all life’s problems.”
—Chinese proverb.
“Perhaps our own woods and fields,—in the best wooded towns, where we need not quarrel about the huckleberries,—with the primitive swamps scattered here and there in their midst, but not prevailing over them, are the perfection of parks and groves, gardens, arbors, paths, vistas, and landscapes. They are the natural consequence of what art and refinement we as a people have.... Or, I would rather say, such were our groves twenty years ago.”
—Henry David Thoreau (1817–1862)