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Free Content Similarity solutions of the thermocline equations

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We apply symmetry group methods to find the group of transformations of the dependent and independent variables that leave the thermocline equations unchanged, These transformations lead to an optimal subset of sixteen forms of similarity solution, Each form obeys an equation with one fewer dependent variable than the original thermocline equations. Previously obtained similarity solutions, which are based solely upon scaling symmetries, are special cases of just three of these forms. Two of the sixteen forms lead to linear, two-dimensional, advection-diffusion equations for the temperature, Bernoulli functional or potential vorticity. Simple exact solutions contain "internal boundary layers" that resemble the thermocline in subtropical gyres.

Document Type: Research Article


Publication date: May 1, 1991

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  • The Journal of Marine Research publishes peer-reviewed research articles covering a broad array of topics in physical, biological and chemical oceanography. Articles that deal with processes, as well as those that report significant observations, are welcome. In the area of biology, studies involving coupling between ecological and physical processes are preferred over those that report systematics. Authors benefit from thorough reviews of their manuscripts, where an attempt is made to maximize clarity. The time between submission and publication is kept to a minimum; there is no page charge.
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