Are these kind of structures buckling critical? I mean classic, Euler buckling of the whole column. If not, what physical factor determines the maximum height

Are these kind of structures buckling critical? I mean classic, Euler buckling of the whole column. If not, what physical factor determines the maximum height? Foundations? Motion from elastic vibrations, driven by vortex shedding? I can think of a bunch of potential things, but I just can't find a good reference. I ask, as I'm only familiar with stressed-skin aerospace structures, which are often locally buckling critical, or even in some cases (webs of wing beams, for example) actually allowed to buckle in what's called "diagonal tension".