ON THE PROPAGATION OF FREQUENCIES AND ENERGY IN CERTAIN TYPES OF OCEANIC AND ATMOSPHERIC WAVES

Abstract

In this paper the energy and frequency propagation in certain types of plane waves in the atmosphere and in the ocean are investigated, these wave trains being characterized by the property that frequency and wave number are slowly varying functions of the space coordinate and time. The assumption is made that wave crests are conserved, and on this basis a simple kinematic relationship between frequency and wave number is established. Wave trains for which the physical theory results in a frequency equation of such a character that phase velocity and wave length uniquely determine each other are then found to possess a characteristic group velocity, and it is shown that frequencies (and hence group velocities) are propagated with this characteristic group velocity. In the more general case the frequency equation resulting from the physical theory is found to contain a correction term which is an explicit function of the space coordinate and time. In that case observers travelling with the convent... Abstract In this paper the energy and frequency propagation in certain types of plane waves in the atmosphere and in the ocean are investigated, these wave trains being characterized by the property that frequency and wave number are slowly varying functions of the space coordinate and time. The assumption is made that wave crests are conserved, and on this basis a simple kinematic relationship between frequency and wave number is established. Wave trains for which the physical theory results in a frequency equation of such a character that phase velocity and wave length uniquely determine each other are then found to possess a characteristic group velocity, and it is shown that frequencies (and hence group velocities) are propagated with this characteristic group velocity. In the more general case the frequency equation resulting from the physical theory is found to contain a correction term which is an explicit function of the space coordinate and time. In that case observers travelling with the convent...