Method to determine cutoff frequencies for acoustic waves propagating in nonisothermal media

Abstract

A method to determine cutoff frequencies for linear acoustic waves propagating in nonisothermal media is introduced. The developed method is based on wave variable transformations that lead to Klein-Gordon equations, and the oscillation theorem is applied to obtain the turning point frequencies. Physical arguments are used to justify the choice of the largest turning point frequency as the cutoff frequency. The method is used to derive the cutoff frequencies in nonisothermal media modeled by exponential and power law temperature gradients, for which the cutoffs cannot be obtained based on known analytical solutions. An interesting result is that the acoustic cutoff frequencies calculated by the method are local quantities that vary in the media, and that their specific values at a given height determine the frequency that acoustic waves must have in order to be propagating at this height. To extend this physical interpretation of the acoustic cutoff frequency to nonisothermal media of arbitrary temperature gradients, a generalized version of the method applicable to these media is also presented.

Linear Alfvén waves in the solar atmosphere

“…The analytical solutions obtained by these authors showed that linear Alfvén waves form standing wave patterns in their isothermal model. The reason for the existence of these standing waves is wave reflection and the resulting constructive interference between the propagating and reflected Alfvén waves (see also Musielak et al 2006).…”

“…(18) and (19) in their standard form, i.e., without the first derivative term; the wave equations written in their standard forms are often referred to as Klein-Gordon equations (e.g., Rae & Roberts 1982;Musielak et al 1987Musielak et al , 2006. Because there is no term with the first derivative in the wave equation for V z , this equation is already written in its standard form.…”

“…where Ω crit is the so-called critical frequency (e.g., Musielak et al 1992Musielak et al , 2006 given by…”

“…(23) and (24) to be equal to the term 1/4y 2 from Euler's equation (see Musielak et al 2006). The results are…”

“…After obtaining the turning-point frequencies for both wave variables, we now follow Musielak et al (2006) and select the cutoff-frequency Ω cut,y from the condition…”