So I'll preface my post by saying I don't know enough about shooting to know if a sine wave profile on the case is a good thing or a bad thing.
But I am an en-ga-nerd, and thus have to discuss the metaphysics of a sine wave. So get your popcorn ready. TO is out of season, maybe he's even reading this...
The sine wave is a graphical depiction of an X-Y scale of the changes of an "anything" that follows a specific mathematical pattern. It is NOT a real, physical "thing".
I'll say that again... The sine wave is NOT a real thing, it is a graphical depiction of mathematical formula - nothing more.
So I think that a sine wave is a real physical thing. It shows up in geometry, which I believe is real and the fact that geometry has proofs is just convenient. So either you can define a sine wave from geometry, or if you don't believe geometry is real, how about vibrations? If you look at the motion of a mass vibrating on a spring, you will see that the motion of the mass is sinusoidal with respect to time. A pendulum is a fine example of this type of motion. caveat in both these cases: I'm assuming its a linear vibration problem,the pendulum is at small angles or the mass oscillating is much larger than the spring supporting it).
If you want a spatial example of a sine wave in nature, how about the mode shape of a vibrating string. A string has a number of orthogonal modes which, excluding bending stiffness,why you can't push on a string), are exactly sine waves. If you do forced oscillations, you can isolate a single one of these modes of the string. Again, so long as the vibration amplitudes remain small, its a linear problem which can be solved exactly.
I admit that I believe in math, but personally I just believe that math is a tool for solving useful problems. Perhaps catshooter would agree that a Fourier transform of the powder burn around the circumference of the case would be dominated by the second harmonic. It is unlikely that any of the harmonics would be zero; but the key point is that the overall effect appears to be sinusoidal.
I hope I didn't make anyone get a second bag of popcorn for my logic here. Most mathematical functions have some physical base, at least in my opinion. And I have no idea if its a good thing to have the burn look like that or a bad thing, I just felt like arguing the metaphysics of math for a bit.