# Comment on Tailleux, R. Neutrality versus Materiality: A Thermodynamic Theory of Neutral Surfaces. Fluids 2016, 1, 32

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## Abstract

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## 1. Overarching Comments on Tailleux

- Tailleux [7] misunderstands or misinterprets the justification, as published by Griffies [4], McDougall and Jackett [5], and McDougall et al. [6], that the energetic lateral mixing of mesoscale eddies occurs in the locally-referenced potential density surface. For example, Tailleux [7] quotes McDougall et al. [6] as implying that the individual fluid motions in mesoscale eddies move across the locally-referenced potential density surface. In contrast, McDougall et al. [6] discuss these motions only as part of a reductio ad absurdum proof. That is, McDougall et al. [6] specifically conclude, based on ocean measurements, that this dianeutral motion is NOT what occurs in the ocean. Moreover, inexplicably, Tailleux [7] asserts that while individual motions are diabatic, their average is adiabatic. This is incorrect. Rather, if individual motions are diabatic, then the average of many such motions exhibits dianeutral diffusion.
- Tailleux [7] states that, (1) in order for an adiabatic and isohaline displacement of a fluid parcel over a distance $\delta \mathbf{x}$ to be neutral, then $\mathbf{d}\cdot \delta \mathbf{x}=0$ (his Equation (1), where $\mathbf{d}$ is the normal vector to the neutral tangent plane); and (2) then goes on to state that $-\text{\hspace{0.17em}}\mathbf{d}\cdot \delta \mathbf{x}$ (his Equation (7)) is the buoyant force experienced by fluid parcels after such an adiabatic and isohaline displacement. Both of these statements are generally incorrect. Indeed, we consider these two incorrect equations to be at the core of the errors that permeate Tailleux [7]. The reason these equations are generally incorrect is that they ignore the unsteady nature of baroclinic motion. These two equations are only correct if the ocean hydrography is in a steady state. This is the case for a hydrographic atlas, but is it not appropriate for discussions of the underlying physics and energetics of epineutral mixing. For such discussions, it is crucial to properly account for unsteadiness of the flow during baroclinic instability and the associated release of available potential energy.
- Tailleux [7] asserts that “adiabatic and isohaline parcel exchanges can only be meaningfully defined on material surfaces of the form $\gamma \left({S}_{\mathrm{A}},\text{\hspace{0.17em}}\mathrm{\Theta}\right)$”. We disagree with this statement. There is no fundamental reason that the ocean should oblige in this regard. Rather, we oceanographers should examine ocean mixing in terms of known physical processes that occur at the in situ pressure of the mixing. (Tailleux [7] uses potential temperature and an undefined type of salinity. Since Absolute Salinity and Conservative Temperature are the recommended salinity and temperature variables for use in oceanographic publications (see Valladares et al. [9] and Intergovernmental Oceanographic Commission (IOC) et al. [10]), we have adopted these variables in this paper).

## 2. Comments on Section 1 of Tailleux

## 3. Comments on Section 2 of Tailleux

## 4. Comments on Section 3 of Tailleux

## 5. Comments on Section 6 of Tailleux

#### 5.1. Tailleux’s First Conclusion

#### 5.2. Tailleux’s Second Conclusion

#### 5.3. Tailleux’s Third Conclusion

#### 5.4. Tailleux’s Fourth Conclusion

#### 5.5. Tailleux’s Seventh Conclusion

#### 5.6. Tailleux’s Eighth Conclusion

#### 5.7. Tailleux’s Ninth Conclusion

#### 5.8. Tailleux’s Eleventh Conclusion

#### 5.9. Tailleux’s Twelfth Conclusion

#### 5.10. Tailleux’s Thirteenth Conclusion

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Neutral Trajectories at Finite Amplitude

## References

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**Figure 1.**Sketch illustrating the two dianeutral advection processes, thermobaricity and cabbeling. Panels (

**a**) and (

**b**) show a neutral trajectory and a vertical cast in physical space and in ${S}_{\mathrm{A}}-\mathrm{\Theta}$ space, respectively. The Absolute Salinity and Conservative Temperature of the ocean’s environment at the locations A–E in panel (

**a**), are depicted in panel (

**b**). When parcels A and B mix with one another (in the appropriate mass ratio) they produce water parcel E. This mixing between parcels A and B occurs at the pressure of point D, but the mixing occurs between parcels A and B and not with the ocean properties at this location. The potential density surface of parcel D with respect to the pressure at point D, is shown.

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**MDPI and ACS Style**

McDougall, T.J.; Groeskamp, S.; Griffies, S.M.
Comment on Tailleux, R. Neutrality versus Materiality: A Thermodynamic Theory of Neutral Surfaces. *Fluids* 2016, *1*, 32. *Fluids* **2017**, *2*, 19.
https://doi.org/10.3390/fluids2020019

**AMA Style**

McDougall TJ, Groeskamp S, Griffies SM.
Comment on Tailleux, R. Neutrality versus Materiality: A Thermodynamic Theory of Neutral Surfaces. *Fluids* 2016, *1*, 32. *Fluids*. 2017; 2(2):19.
https://doi.org/10.3390/fluids2020019

**Chicago/Turabian Style**

McDougall, Trevor J., Sjoerd Groeskamp, and Stephen M. Griffies.
2017. "Comment on Tailleux, R. Neutrality versus Materiality: A Thermodynamic Theory of Neutral Surfaces. *Fluids* 2016, *1*, 32" *Fluids* 2, no. 2: 19.
https://doi.org/10.3390/fluids2020019