This is a style originally intended for Kathak. To my knowledge it's not very often used for Kathak and I've only occasionally seen it used by dancers from Jaipur Gharana. It is quite simple in reality; it involves a bun and a plait and that's it!
I began by simply dividing the hair in two and tying the first half into a ponytail, creating a half-pony.
I then used a doughnut to make this into a bun (check out my Le Beignet. post on how to use a hair doughnut)...
...and secured it with a hairnet.
You can see that the bun isn't too high up on the head, this is because I did it with Kathak in mind rather than Bharatanatyam.
I've added a mix of ornaments here to substitute not having any that were meant for dance. Here I've used plastic flowers, a brooch and an earring.
This is the final product, but where did the long red thing come from I hear you ask... sorry! I forgot to take pictures of that stage! All I did was plait a paranda in to the second half of the hair and then wrapped the flowers around the plait. There are some links on how to tie a paranda on my That long thing with tassels post.
As you can see the lower bun creates a look more suited for Kathak, naturally the fringe would normally need to be pinned or gelled back.
Many Kathak dancers who use this style pin the plait to their dresses so it hangs at the front.
This same style can very easily be used for Bharatanatyam if you tie the bun higher and add a few more flowers.