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1. Gravitational wave memory and the wave equation

   https://doi.org/10.1088/1361-6382/ac7203  

   Garfinkle, David (June 2022, Classical and Quantum Gravity)

   Abstract Gravitational wave memory and its electromagnetic analog are shown to be straightforward consequences of the wave equation. From Maxwell’s equations one can derive a wave equation for the electric field, while from the Bianchi identity one can derive a wave equation for the Riemann tensor in linearized gravity. Memory in both cases is derived from the structure of the source of those wave equations. 

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2. Wave prediction using wave rider position measurements and NARX network in wave energy conversion

   https://doi.org/10.1016/j.apor.2018.10.016  

   Desouky, Mohammed A.A.; Abdelkhalik, Ossama (January 2019, Applied Ocean Research)
3. Accelerating Atmospheric Gravity Wave Simulations Using Machine Learning: Kelvin‐Helmholtz Instability and Mountain Wave Sources Driving Gravity Wave Breaking and Secondary Gravity Wave Generation

   https://doi.org/10.1029/2023GL104668  

   Dong, Wenjun; Fritts, David C; Liu, Alan Z; Lund, Thomas S; Liu, Han‐Li; Snively, Jonathan (August 2023, Geophysical Research Letters)

   NA (Ed.)

   Abstract Gravity waves (GWs) and their associated multi‐scale dynamics are known to play fundamental roles in energy and momentum transport and deposition processes throughout the atmosphere. We describe an initial machine learning model—the Compressible Atmosphere Model Network (CAM‐Net). CAM‐Net is trained on high‐resolution simulations by the state‐of‐the‐art model Complex Geometry Compressible Atmosphere Model (CGCAM). Two initial applications to a Kelvin‐Helmholtz instability source and mountain wave generation, propagation, breaking, and Secondary GW (SGW) generation in two wind environments are described here. Results show that CAM‐Net can capture the key 2‐D dynamics modeled by CGCAM with high precision. Spectral characteristics of primary and SGWs estimated by CAM‐Net agree well with those from CGCAM. Our results show that CAM‐Net can achieve a several order‐of‐magnitude acceleration relative to CGCAM without sacrificing accuracy and suggests a potential for machine learning to enable efficient and accurate descriptions of primary and secondary GWs in global atmospheric models. 

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4. Wave- and potential-driven instabilities in orbital pilot-wave dynamics

   https://doi.org/10.1017/jfm.2025.10341  

   Liu, Nicholas; Durey, Matthew; Bush, John WM (July 2025, Journal of Fluid Mechanics)

   We present the results of a theoretical investigation of orbital stability in pilot-wave hydrodynamics, wherein a droplet bounces and self-propels across the surface of a vertically vibrating liquid bath. A critical notion in pilot-wave hydrodynamics is that the bath plays the role of the system memory, recording the history of the droplet in its wave field. Quantised orbital motion may arise when the droplet is confined by either an axisymmetric potential or the Coriolis force induced by system rotation. We here elucidate the dependence of the stability of circular orbits on both the form of the confining force and the system memory. We first provide physical insight by distinguishing between potential- and wave-driven instabilities. We demonstrate that the former are a generic feature of classical orbital dynamics at constant speed, while the latter are peculiar to pilot-wave systems. The wave-driven instabilities are marked by radial perturbations that either grow monotonically or oscillate at an integer multiple of the orbital frequency, in which case they are said to be resonant. Conversely, for potential-driven wobbling, the instability frequency may be resonant or non-resonant according to the form of the applied potential. Asymptotic analysis rationalises the different stability characteristics for linear-spring and Coriolis forces, the two cases that have been explored experimentally. Our results are generalised to consider other potentials of interest in pilot-wave hydrodynamics, and elucidate the distinct roles of wave- and potential-driven instabilities. Our study highlights the limitations of prior heuristic arguments for predicting the onset of orbital instability. 

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5. Wave energy conversion under constrained wave-by-wave impedance matching with amplitude and phase-match limits

   https://doi.org/10.1016/j.apor.2019.101858  

   Korde, Umesh A. (September 2019, Applied Ocean Research)