I am getting the following random noise type image in areas of low flow (order of 1e-5). I want to know why this happens mathematically. What happens when LIC is computed that causes this in areas of stagnant/low speed flow.
That is completely expected and how LIC works. Everything in LIC is random noise.
LIC works by first creating a random texture. It then smears the texture in the direction of the vectors over the surface. If you look closely at the “lines”, you will see that they are not consistent colors. They shift colors as you follow the stream. This is because it is a random texture blended along the vector lines.
Of course, if the vector is 0, then the initial random texture never gets smeared. That leaves you with the original random field.