The exact depth of the atmospheric currents driving the polar hexagon on Neptune remains a subject of ongoing scientific investigation. Current hydrodynamic models suggest that these massive, stable wave patterns are not merely superficial phenomena. Instead, they are likely driven by deep-seated atmospheric circulation patterns that extend hundreds of kilometers below the visible cloud tops.
As these currents move deeper into the planet, they encounter significantly increasing pressure and temperature. At certain depths, the composition of the gas shifts, and the extreme pressure begins to influence the fluid dynamics of the atmosphere. This transition from a gaseous state to a more supercritical or liquid-like state eventually disrupts the organized wave patterns that form the hexagon shape. While we cannot pinpoint the exact kilometer of this transition without more precise data, scientists believe the dynamics are tied to the deep internal heat flow of the planet.
For more information on planetary science and recent findings regarding gas giant atmospheres, you can visit NASA at https://science.nasa.gov.