An expression for the rate of change of neutral density following a fluid parcel (the material derivative) is derived and checked numerically. This expression can be used to quantify the degree to which neutral density varies even under purely adiabatic and isohaline motions. We also present an approximate form of neutral density, namely a rational function of only two variables, either salinity and conservative temperature or salinity and potential temperature.
McDougall, Trevor J., and David R. Jackett. 2005. "The material derivative of neutral density." Journal of Marine Research 63, (1). https://elischolar.library.yale.edu/journal_of_marine_research/75