The scales of Sindhu Bhairavi are as follows :
Aarohanam (Ascending) : S R2 G2 M1 G2 P D1 N2 S’
Avarohanam (Descending) : N2 D1 P M1 G2 R1 S N2 S
This is a janya raga, derived from Natakapriya (see below), 10th on the Melakarta scale. However, some say that Sindhu Bhairavi as sung now is a derivative of 8th Melakarta Hanumatodi and 20th Melakarta Natabhairavi asboth R1 and R2 are used in this raga. I have also read that there it is not a raga which can be so classified because all 12 notes can be used (some sparingly). I understand that the raga has origins in the Middle East.
In Carnatic concerts, this raga is not often used for elaborations but for light numbers or bhajans towards the end. It is indeed quite regularly sung. The beautiful Thillana by Lalgudi Jayaraman will be familiar to all as also Swati Thirunal’s Bhaja Bhaja Manasa and Vishveshvar Darshan Kar, Iduvo Thillai by Gopalakrishna Bharati.
For Tamil speakers, here is a lec-dem by Charulata Mani on this raga.
Note : The 12 notes in the octave are named as below. Please note that C is used as Sa for the sake of simplicity as the scale is relative in Carnatic Music. Also note that the scales paint only a superficial picture of the raga as the gamakas(ornamentations) are a very important part of a raga.