## depression near Greenland – logarithmic spirals in nature

Logarithmic spirals frequently occur in nature.  Is this such a manifestation?

The general equation for a logarithmic spiral is as follows.

$r=ae^{b\theta}$

Changing the variables $a$ and $b$ produces spirals of different qualities.  The $a$ is really an enlargement scale factor but the $b$ controls how the spiral grows per revolution.

If $b=0.2$ is more representative of an ammonite then $b=0.75$ seems to be our Greenland depression.

Wouldn’t it be nice to take the equations for atmospheric fluid dynamics and show this explicitly.  Unfortunately this is beyond the scope of this blog: here we have circular motion on the surface of a rotating sphere in an elliptical orbit … . The way to go with this would be to take the basic baratropic equations and then perform a scale analysis to disregard ‘small’ terms.  At this point the pure mathematician get frustrated with approximations and goes into a sulk.  We are left with contemplating the beautiful images though…