Linear Acoustic Waves in a Nonisothermal Atmosphere. I. Simple Nonisothermal Layer Solution and Acoustic Cutoff Frequency

Abstract

We investigate the behavior of acoustic waves in a nonisothermal atmosphere based on the analytical solution of the wave equation. Specifically, we consider acoustic waves propagating upwardly in a simple nonisothermal layer where temperature either increases or decreases monotonically with height. We present the solutions for both velocity fluctuation and pressure fluctuation. In these solutions, either velocity or pressure is spatially oscillatory in one part of the layer and nonoscillatory in the other part, with the two parts being smoothly connected to one another. Since the two parts transmit the same amount of wave energy in each frequency, it is unreasonable to identify the oscillating solution with the propagating solution and the nonoscillating solution with the nonpropagating solution. The acoustic cutoff frequency is defined as the frequency that separates the solution that is spatially oscillatory for both velocity and pressure and the solution that is not oscillatory for either velocity or pressure. The cutoff frequency is found to be the same as the Lamb frequency at the bottom in the temperature-decreasing layer but higher than this in the temperature-increasing layer. Based on the transmission efficiency introduced to quantify the wave propagation, we suggest that the acoustic cutoff frequency should be understood as the center of the frequency band where the transition from low acoustic transmission to high transmission takes place, rather than as the frequency sharply separating the propagating solution and the nonpropagating solution.