Referee's Report on " A new approach to understanding fluid mixing in process-study

models of stratified fluids " by Hartharn-Evans et al.

The authors proposed a tool for identifying stirring and mixing processes in stratified media. The approaches by Penney et al. (2020) and Grace et al. (2021) were extended and generalized.  Bivariate weighting histograms of fluid variables were used to identify mixing fluid. The weighting was related to the probability a volume of fluid has given properties in a 2D plot.

Two test cases were considered: shoaling internal solitary wave on bottom slope and shear instability in cold temperature stratified water. Unlike Penney et al. (2020) where the density-tracer pair was considered, the authors considered the density-kinetic energy pair. The results of a qualitative analysis of the diagrams are presented.

The developed approach is new and has a perspective used in different geophysical problems. The paper can be worth to be published in Nonlinear Processes in Geophysics after minor revision.

Specific comments

Introduction. It would be useful to include in the review other diagrams of the state and evolution of turbulence in a stratified medium (e. g. Caldwell (J. Geophys. Res. 88 C12, 19) and Gibson (J. Mar. Syst. 21, 1999)).

Fig. 4 caption Explain, please, what is shown in the plates of the middle row.

L 24 Samgorinsky read as Smagorinsky

In the refereed paper, the authors suggest a method of determining how and where the mixing process occurs in water through the paired histograms approach of user-selected variables. Results of numerical simulations from previously published papers by the authors on shoaling internal solitary waves are used. The method allows researchers to identify regions of fluid in physical space that are undergoing mixing. Two specific cases are presented to illustrate the method: (i) shoaling internal solitary waves and (ii) a shear flow instability in water influenced by the nonlinearity of the equation of state. The method is also used to identify how the density and passive tracers are mixed within the core of the Kelvin–Helmholtz instability. By means of the suggested method becomes possible to identify how the different regimes of mixing associated with different types of wave breaking manifest themselves.

The paper is interesting and topical. Apparently, its further development will shed a lite on the onset of turbulence in fluid. It is well-written and well-illustrated; it can be recommended for publication in the NPG. I only have minor remarks that should be attended to before the paper publication.

1. It is not clear to me why the configuration of a flow shown in Fig. 2 was chosen such that it provides a minimum of nonlinearity. As well known, the nonlinearity diminishes when a pycnocline position is in the half-depth.
2. What type of internal solitary waves are realized in that configuration? Apparently, the detail of their shape is not important for this study but still, it would be good to mention what is the most relevant model that describes such solitary waves. Judging by the configuration of stratification and soliton shape shown in Fig. 3a), this is rather a Gardner soliton (see, e.g., Apel et al., JASA, 2007). What is the authors’ opinion on this issue?
3. There are a few typos that should be rectified. For example, the word “much” is repeatedly written in the Abstract. There is a typo in the word “nonlinearity” in the Abstract. And some more typos there are in the text.