Despite whatever be the shape of object that you drop in water, it be 1D, 2D, 3D, they all produce ripples in a circular pattern, is this pattern followed under water as well (in terms of density changes, like compressions and rarefactions) I assume it to be semispherical under water but have no proof, and why is this pattern so in the first place?
I know the question is there. My Actual question is written in bold above. Does it have to do with energy?
You can also see the exact same phenomenon when you see a bubble. Bubbles always occupy spherical spaces. This occurs due to the fact that a ripple expands in every direction at a constant rate so naturally the resultant shape the ripple encloses is a circle. This might also be related to the fact that for any given area, the smallest perimeter is bounded by a circle! and for any given volume, the sphere has the least surface area.
The simplest answer is that this has to do with symmetry. In the immediate vicinity of the droplet, the water is isotropic. Therefore there is no preferred direction. In more rigorous terms, the density-density correlation function for liquid water is rotationally and translationally invariant.
Now, if one were to change the geometry of the problem in some way, then one no longer has to have the droplet expand in a circular pattern. This is what happens in a solid. If you take a look at the image below, you can see a six-fold pattern emerge (especially in image G below). This is because the solid in question is graphene which has a honeycomb lattice and a corresponding six-fold rotational symmetry. The image is from the paper: The Effective Fine-Structure Constant of Freestanding Graphene Measured in Graphite
