Vortex-Merging

When two vortices come at certain distance and revolve around a common center, each vortex exerts a centripetal force on the other vortex, which makes them to join together and merge into single one. This visualization can help in understanding the patterns of black hole merging at larger scale and the amount of energy released by this cosmic process. It can also help the Air Traffic Control (ATC) to decide the time-interval between take-off for two airplanes, so as to minimize the turbulence effect caused by first airplane.  A spectral method (based on Fourier collocation method) was developed to solve Navier-Stokes equations with projection scheme for pressure. Please look through the book by Roger & Pyret to know more about this method. The objective of the work was to visualize merging process of two symmetric vortices with an initial Gaussian profile. These vortices were given an angular velocity in anti-clockwise direction at a particular Reynolds number. The merging process for different mass of vortices was captured through the in-house solver.

Details of the Project :

Timeline --- May-July 2017

Supervisor --- Dr. A. Sameen, Professor, Department of Aerospace Engineering, Indian Institute of Technology  Madras. 

Main Objectives of the study - 

1. To develop a robust spectral element method-based numerical solver for Navier-Stokes solution.

2. To understand the  merging phenomenon in terms of time and distance between vortices by varying the Reynolds number and radius of vortices.

Details of study  - 

The Simulations were carried out on a 64 x 64 grid with a time step size of 0.001. Domain size was 2Pi x 2Pi and periodic boundary conditions were applied on all four boundaries. Reynolds numbers used for the study were 100, 500, 1000 and 10000. Initial distance between the centers of vortices was 2.0 and core size was 0.4 (All units Non-Dimensional).

Significant Outcomes - 

We focus on the two-dimensional dynamics of two identical co-rotating vortices having a smooth vorticity distribution. Although such a configuration is a very simplified representation of the near wake of a realistic aircraft, it contains all the ingredients necessary to explore and understand the physics involved in vortex merging. The description of the overall merging process can be done by separating it in four stages, as given below.

1. Before merging , i.e. when the vortices are far apart, the two vortices rotate around each other with a common center with a constant angular velocity.

2. Attainment of critical ratio and advection stage: In this stage, due to the strains induced by two vortices on each other, they tend to combine with each other and start moving closely towards each other along with their rotary motion.

3. Diffusion stage leading to a axisymmetric vortex center.

4. Diffusion of the final stage vortex and merging of two vortices into a single one which after vortex diminishes.