Are waves with negative spatial damping unstable?

Date

2020

Authors

Struchtrup, Henning
Nadler, Ben

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

Conventional plane harmonic waves decay in direction of propagation, but unconventional harmonic waves grow in the direction of propagation. While a single unconventional wave cannot be a solution to a physically meaningful boundary value problem, these waves may have an essential contribution to the overall solution of a problem as long as this is a superposition of unconventional and conventional waves. A fourth order diffusion equation with proper thermodynamic structure, and the Burnett equations of rarefied gas dynamics exhibit conventional and unconventional waves. Steady state oscillating boundary value problems are considered to discuss the interplay of conventional and unconventional waves. Results show that as long as the second law of thermodynamics is valid, unconventional waves may contribute to the overall solution, which, however is dominated by conventional waves, and behaves as these.

Description

Keywords

waves, stability, entropy, 2nd law of thermodynamics

Citation

Struchtrup, H. & Nadler, B. (2020, Septemeber). Are waves with negative spatial damping unstable? Wave Motion, 92. https://doi.org/10.1016/j.wavemoti.2020.102612