To simplify the problem of characterizing Global Atmospheric Dynamics mathematically, Planck's Natural Unit criteria is helpful. Its simple Integer Math, of counting Whole Numbers of things like Days, Years, Rossby Waves, Hurricanes, and so forth. Yes, there are borderline cases, like not-quite hurricanes, and Rossby Packets, but many detail uncertainties tend to cancel out and/or not critically determine correctness of a broad model. With prudent caution, we are free to model a wave packet as a particle, to enable computation, and employ other such abstractions, like effective Field Theories. Analogues allow us to use mathematical tools from wherever they are found. This heuristic practice in engineering is "case-based" reasoning from "similarity cases".
Taking the geophysical abstraction to an extreme, we can consider the Atmosphere as a single quasi-particle, and the Earth as an interacting quasi-particle. We can quantify these masses and their bulk relative motion to estimate their shared kinetic energy. At the other end of the ladder-of-abstraction we can locate data-points, like the readings of meteorological stations. If one starts from the huge raw data-sets, seeking to reach the top-most abstraction levels, its easy to get lost, and not see the "big picture". Science works from both ends, top-down and bottom-up.
Whether we can resolve the Climate Change Crisis with Wind Energy starts as a top-down question. The answer may be bottom-up, like whether humans can behaviorally reduce their carbon footprints to 5% of present levels (as estimated by Union of Concerned Scientists members in '90s). The risk is that the answer is "No", that folks either will not change so radically, or an authoritarian Green Fascism might prevail. Top-down GeoEngineering is another possibility, with its own risks of abuse. Perhaps its too Utopian to hope for a "magic bullet" intervention, but maybe there is such possibility.
We may just muddle through the Holocene Extinction like we are the Covid Pandemic, as an all-of-the-above scenario. In that case, planetary-scale wind energy application could still be critical. We have to learn all we can about the atmosphere, but that is not enough; we actually have to try to apply that knowledge, as the essence of the Green Math quest. Entertaining debate about Atmospheric QM Analogues and Ancient Wind Folklore is part of Green Math due-diligence, not a-priori sterile. Green Math aims beyond "shut-up and calculate".