Here's my try - There are several sections added together:
First start with a Normalized Object Texture Co-ordinate, offset by a mapping node. This will make the lines of the wave point towards the "center", but be offset like the reference image.
The next section uses the Distance output of a Voronoi texture node to make the "Vortex points" so to speak - more than one turbulent area.
The next section "Warps" the lines slightly with a noise texture so they look more "flowing"
The section after that adds a pixilation look to the waves (optional, depending on how low-fi you're going for).
This all goes into a wave texture, that is then "Quantized" by using several constant steps in a ColorRamp for the colors.
Lastly, there is a "Movement" Section (if you plan on animating), I used a value node to control the location of a Mapping Node connected to the input of the Voronoi texture. I used a math node to slow it down a little. If you want this to move as you animate, type #frame into the Value box.
(actual animation looks quite a lot better - I had to cut it way down to meet upload file-size requirements)