There is a good references covering the variations among the the coherence time as a consequence of Doppler shift. The different formulas are a consequence of the definition of the coherence time. Strictly speaking if there is Doppler shift, the wireless channel will vary with time.Since the coherence time is the time interval at which the correlation between the channel responses at the starting of time and end of the time interval must not get smaller than certain threshold, one gets different Tc for different threshold values.
You can your self set the appropriate threshold value for the correlation and get your own empirical formula.
For more information please refer to the link: http://www.ni.com/white-paper/14911/en/