I wish to provide a counterbalance argument.
it's just not wavy, it's a chaos of pressure-fronts, wind is doughnuts, and waves have equilibrium points and transmission media.
Scientific litterature doesn't use the word wave to describe squalls and pressure fronts, and clouds also illustrate the general behaviour of wind. Atmospheric stratification can generate 2D boundary wave clouds which form on stratospheric 2D pressure and temperature boundaries, and on oil-water boundaries: https://en.wikipedia.org/wiki/Wave_cloud
Wind follows laws of turbulence and chaotic flow displacement, whereas waves travel backwards and forwards on an equilibrium point. Waves are energy displacement with a radial wave front, whereas squalls are not radial. When we look at clouds, generally there's no wave distributions visible.
To view what a squall does, it's best to consider what smoke does. The smoke doesn't displace air using the elasticity of air, like a sound wave, it actively flows and generates a pressure front which displaces air sideways as much as forwards, it's quite a complex effect which is not totally like waves.