Can the Wave Equation Accurately Describe Wind and Particle Movement?

[yetar]

I believe the PDE Utt-v^2*(Uxx+Uyy+Uzz) can be used to desribe air pressure, and how this pressure changes during time (with a given pressure in t=0)
My question is, does this equation also takes into account effects of movement of particles? Such as wind? Can it describe wind?
Or do we need some other equation to descibe wind?
What equation can be used to describe wind?

Thanks in advance.

 

[Clausius2]

I believe the PDE Utt-v^2*(Uxx+Uyy+Uzz) can be used to desribe air pressure, and how this pressure changes during time (with a given pressure in t=0)
My question is, does this equation also takes into account effects of movement of particles? Such as wind? Can it describe wind?
Or do we need some other equation to descibe wind?
What equation can be used to describe wind?

Thanks in advance.

This equation is often used to calculate pressure and density wave propagations in some fluid, when one assumes small departures from the mean value and incompressibility (Linear Acoustics). The wave equation only takes into account convective transport of momentum and unsteadiness of the flow field, so there is no dissipative effect.

The equations for describing the motion of wind over a complex geometry and taking into account Earth rotation effects, buoyancy, and dissipation are the Navier-Stokes equations. Usually the motion of wind is turbulent, so we use an special averaged version of the N-S equations (RANS) or we solve directly the N-S equations using numerical simulations (DNS).