Finite vertical oscillation of fluid parcel in a heterogeneous, incompressible sea water—Part I

Abstract

The solutions of vertical oscillation of finite amplitude of a fluid parcel in a heterogeneous, incompressible sea water were obtained, solving rigorously the equation of motion, retaining small terms to the third order of the amplitude non-dimensionized by a vertical reference length. The motion is asymmetric with respect to its equilibrium position and the period of motion is longer than that of infinitesimal Väisälä oscillation. When the vertical velocity of the parcel exceeds certain critical value, oscillation of large amplitude sets in near the outskirts of the thermocline, its period being more than twice larger than that of Väisälä oscillation. The apprehension whether this type of the increased vertical motion might be influenced or denied by the horizontal motion in such a case as in internal waves is also discussed. From some observations which will be appeared in Part II, we found oscillations of large amplitude with the period which is in good agreement with the theoretical result.