## A Mathematical Theory Of The Vertical Distribution Of Temperature And Salinity In Water Under The Action Of Radiation, Conduction, Evaporation, And Mixing Due To The Resulting Convection

##### Date

1929

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A well recognized and important result of oceanic circulation is its effect upon the "normal" distribution of temperature. The term "normal" is used in this paper to denote that distribution of temperature, salinity, or any other physical or chemical property of water which would prevail in the absence of a general drift or flow of the water as a whole, either vertical or horizontal. Investigations of regions like that off the coast of California where conditions are usually far from normal (McEwen, 1912, 1914, 1915) raise the questions: How can the normal distribution of temperature be determined from observations made on the actual one, disturbed by both horizontal and vertical drift? What is the rate of drift? At what rate does solar radiation penetrate the surface? At what rate is heat lost from the surface? Such considerations led to a general investigation of the relation of temperature to the ever-present factors, radiation, evaporation, and the resulting alternating or mixing motion of small water masses, and the effect of a given drift, horizontal or vertical, upon the normal distribution of any property of the water. In this paper are presented the derivation of a basic theory, and certain numerical applications selected to illustrate this theory. Investigations of fresh-water lakes and reservoirs have proved invaluable in attempting to deal with the more complicated phenomena of the ocean, which formed the incentive for developing this theory.

##### Keywords

Mathematical Theory, Temperature, Salinity In Water, Convention