Reconciliation of Governing Conservation Laws of the Propagation of Waves in a Varying Medium
Zhaohua Wu
FSU
5 March, 2pm
Abstract:
Waves are propagating disturbances that redistribute energy across space. Previous studies have shown that the conserved quantity for waves propagating on an inhomogeneously moving mean flow is wave action, rather than wave energy, raising questions about the validity of the energy conservation law-one of the foundational principles of physics. In this study, we demonstrate that wave action is proportional to the wave energy flux of forward-propagating waves in a varying medium. When the energy of reflected waves is accounted for, the total wave energy within the entire isolated system remains conserved. However, for forward-propagating waves alone, the conservation of wave energy is expressed through the conservation of wave action. This finding is not specific to any particular wave system but applies universally to all wave systems, including hydrodynamic and electromagnetic waves. The broader implications of this reconciliation for atmospheric and climate dynamics will also be explored.