Dear Mrugesh,

The following links can help you.

 http://www.flow3d.com/wp-content/uploads/2014/08/Computational-Modelling-of-Free-Surface-Flow-in-Intake-Structures-using-FLOW-3D-Software.pdf

 https://www.academia.edu/7208352/Predicting_Free-surface_Vortices_with_Single-phase_Simulations

 https://en.wikipedia.org/wiki/Vortex

 https://math.berkeley.edu/~chorin/C80.pdf

With my best regards

Prof. Bachir ACHOUR

Yes it is ifluence y earth rotation and in which hemisphere you are in..please read papers on geophysics

Mrugesh, my additional advice, on top of what has been indicated by previous comments, is the following: 

Whenever you want to simulate instabilities or secondary flows which are generally challenging to trigger and sustain numerically due to round-off or dissipation errors, it is fundamental to use structured meshes. Dissipative non-structured meshes may turn extremely difficult or computationally too expensive (too many nodes) to let these low-intensive phenomenon to be reproduced in the simulations.

Dear Mrugesh Joshi,

The bath sink vortex is not due to the Coriolis acceleration of the earth. This effect is much to small to cause this. The bath sink vortex is due to the flow in the  viscous boundary layers at the bottom of the bath. A small asymmetry in the geometry of the bath or of the downstream pipe system, will determine the direction of rotation of this vortex. So calculations should include the boundary layers and a small asymmetry in the system in order to provide meaningful results.

There is a nice book on vortices "Vortex Flow in Nature and Technology: Hans J. Lugt ".

Good luck, Mico

I think Avraham is right

There was a recent attempt of numerical simulation in JFM: J. Fluid Mech. (2010), vol. 656, pp. 177–188. And a lot of experimental activity in both hemispheres in 60s (see references in JFM paper). The conclusion was that it is possible but extremely difficult to exclude all factors but Coriolis force. One of the main troubles was the residual motion of water after the bath was filled. They had to wait several hours and still it survived.

Mister Avraham Hirschberg is absolutelly right!!!

Absolutely agree with Avraham Hirschberg. Coriolis effect is very very small compared to other effects, especially in asymmetery of geometrical and physical boundaty conditions. Just try that in your bathroom !

As said Avaham the effects are poor, but if you include this force into the equations they should be as a mass force (like density x gravity acceleration) in a noninertial frame of reference with relative velocity V and include the rotational angular velocity omega. For the Earth this velocity is omega = 2 Pi /(24x3600) rad/s. The Coreolis force is then calculated as -2 density x omega x V and treated in composition with density x gravity. If the sink stands over the Earth the velocity V=0 (negligible). If you are over an airplane or a ship velocity V means something, more for a tornado or hurricane. Another aspect is the latitude, because passing over the Equator the vectorial product gives zero (vectors are paralell) on a movil on the Earth, and in the Poles are maximum. Finally, conservatión principles as linear momentum (Navier-Stokes) should be applied to relative velocity field. See for example eq.(19), Chap.V, sec.1.1 of A. Granados, Mecanica y Termodinamica de Sistemas Materiales Coninuos, USB, 2015 (optionally, "Mechanics of Continuous Material System", ec.(9), sec.II.2, here in ResearchGate) (optionally, "Mecánica de Sistemas Materiales Continuos desde Marcos de Referencia No Inerciales", ec.(17) & (18), sec.2.2.3 here in ResearchGate). This is for a sink with a geometry pecfectly symmetric, otherwise there are other aspects as said before, including initial and boundary conditions.

Coriolis force appears when the dynamics is referred to a rotating frame (see a text such as that of mine: Analytical Engineering Mechanics. The motion through a sink, is seen through a fixed frame of reference (fixed observer). Hence the question of Coriolis force does not arise, even if earth's rotation is considered  as it is negligible. The effect is appreciable in the case of huge scale such as cyclones.

Acceleration of Coriolis seen as an inertial force tends to maintain the fluid at rest respect to an absolute or inertial frame around the Earth. Thus tends to rotate the fluid clockwise in the north hemisphere and counterclockwise in the south hemisphere (seen from above, ie. from outside de Earth to the center). This may be corroborated in a toilet (if the symmetry is satisfied)

I am afraid not. The toilet is too small a system compared to cyclones. If Coriolis force had to be taken in to account for every rotatory motion on earth, then all solutions of dynamical problems have to be revisited. See my text: Analytical Engineering Mechanics.