A THEORY OF SMALL-AMPLITUDE LONG WAVES.
Technical rept. nos. 16 and 19,
JOHNS HOPKINS UNIV BALTIMORE MD
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A theory of small-amplitude, long, water waves is developed by expansion in terms of the two small parameters involved. The first approximation is required to be the familiar equations of infinitesimal, long waves. An investigation is made of the accuracy of the classical equations of finite-amplitude, hydrostatic disturbances. It appears that the simple hydrostatic approximation neglects terms which are just as important as those retained, although in certain cases the equations of hydrostatic disturbances may be useful to predict developments for limited periods of time. The first few sets of differential equations are integrated in a special case. The study leads to the derivation of the properties of a new kind of finiteamplitude, long wave. Author