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:
“Let us begin to understand the argument.
There is a solution to everything: Science.”
—Allen Tate (1899–1979)
“All the followers of science are fully persuaded that the processes of investigation, if only pushed far enough, will give one certain solution to each question to which they can be applied.... This great law is embodied in the conception of truth and reality. The opinion which is fated to be ultimately agreed to by all who investigate is what we mean by the truth, and the object represented in this opinion is the real.”
—Charles Sanders Peirce (1839–1914)
“That primitive head
So ambitiously vast,
Yet so rude in its art,
Is as easily read
For the woes of the past
As a clinical chart.”
—Robert Frost (1874–1963)