Saturn's hexagon

Saturns' hexagon shape (Fig.1) is very similar to a shape of circular vortex disturbed by six sinusoidal stable waves along the vortex border.

Fig. 1. Saturn's hexagon (from https://www.sciencenews.org/article/saturn%E2%80%99s-six-sided-cloud-pattern-gets-close-look)

We should note, that disturbance of the vortex is not only on the border of the vortex, but could be clearly identified inside and outside blue vortex (look in Fig.1). So the amplitude A of the waves depends on the radial position of the disturbance: A = f(r). In position of the blue vortex border (Fig.1) amplitude of these waves A is approximately equal to 0.03R, where R is radius of the blue vortex: A(R) = 0.03R.

Figure 2 shows these 6 waves aligned along the vortex's border in polar coordinates (r/R, φ). Blue line is border of disturbed vortex (initial phase is φ₀ = 120º), black line border of non-disturbed circular vortex. Figure 3 shows the same in Cartesian coordinates. Figure 4 shows only disturbed vortex and Figure 1 shows an original picture of Saturn's hexagon.

Fig. 2. Position r/R of borders of circular (non-disturbed) and disturbed vortexes in polar coordinates

Fig. 3. Shapes of circular (non-disturbed) and disturbed vortexes in Cartesian coordinates

Fig. 4. Shape of disturbed vortex only for comparison to Fig.4


Now question: What is origin of these waves?

Suggestions:

1) Such waves may exist on border of two different fluid (different density and/or viscosity). Fluid can be the same, but temperature gradient can be reason of different density and/or viscosity. Different color points to different properties in Fig.4.

2) Stable streams from the center (Saturn's pole) to the border of the vortex and back. Something similar as Rayleigh–Bénard convection.

3) In principal, any wave of one wavelength may be expressed as vortex in the fluid. So, reason of these 6 waves may be 6 prolonged vortexes along the border. These vortexes may be formed by shear layer existing between the central vortex and surroundings of the vortex.

4) Interaction of turbulent flows of atmosphere with surface of Saturn's hard core, surrounded by a thicker liquid metallic hydrogen layer.

5) Influence of Saturn's magnetic field, which is originated by liquid metallic hydrogen layer.

6) Any other crazy idea ...

© Algis Džiugys, December 13th, 2013