Measuring dispersion in circular data stats noob here.
I have a (circular) dataset with values in [0, 2pi]. I need some kind of a measure of how disperse or diverse the dataset is. I have looked a bit into non circular (regular) data, and I happened to come across coefficient of variation as a non-dimensional measure of dispersion in a dataset.
My question is: can I modify the coefficient of variation in my case as (circular stddev) / (circular mean) and use it as a dispersion measure?

Short answer is No. A coefficient of variation such as you define it is not just useless, it is meaningless.
For example, two datasets that are 350, 0, 10 degrees and 170, 180, 190 degrees have (I suggest) equal dispersion by any standard BUT dividing any measure of dispersion by the mean makes no sense, even if it is a vector mean. In other words, the mean can easily be zero.
(In this example, and rarely, the vector mean and the ordinary mean coincide for each dataset.)
More generally, the position of the mean depends on a convention about what is zero direction. In geography and Earth sciences, North as a bearing is usually zero, but there could be excellent grounds for using another direction as zero. The same goes for time of day, time of year and any other circular outcome space.
But a positive answer is that several measures of dispersion are defined for circular data. The range can often be useful, defined as the complement of the largest gap on the circle. So, the two toy examples above both have range 20 degrees: that is obvious enough for 170, 180, 190 and obvious when you think about it for the other example. The mean resultant length is more nearly standard. (It has many other names, including vector strength and consistency.)
There is an entire literature on circular statistics with several dedicated monographs, for all that many statistical people never have cause to know about it.
