Nonlinear Oscillations of a Particle in a Long Wave in a Rotating, Viscous Fluid

Abstract

Analysis is made of the effects of a long wave of finite amplitude on the oscillation of a particle in a rotating, viscous fluid. It is shown that the zeroth-order solution of the Lagrangian equations of motion consists of the pressure wave and inertial frequencies, whereas the first-order solution gives three frequencies, namely the sum and difference of the pressure-wave and inertial frequencies, and a frequency of twice the pressure-wave frequency. The effects of the frictional force are to damp out the inertial oscillation but leave the other physically significant oscillations intact. Furthermore, it eliminates the solution which contributes to the amplification of the amplitude of particle trajectories in an inviscid fluid. A comparison of the frequencies predicted by the theory with those obtained from the flights of constant-pressure balloons is made.