Reply to “Comment on Tailleux, R. Neutrality Versus Materiality: A Thermodynamic Theory of Neutral Surfaces. Fluids 2016, 1, 32.”

Rémi Tailleux

doi:10.3390/fluids2020020

Abstract

McDougall, Groeskamp and Griffies (MGG) strongly criticise all aspects of Tailleux (2016) that challenge the current conventional wisdom about the use of neutral density concepts for studying and parameterising lateral ocean stirring and mixing. However, their claim that most of Tailleux (2016)’s results or conclusions are incorrect is easily shown to originate: (1) from mistakingly confusing Tailleux’s Eulerian arguments for Lagrangian ones; (2) from their irrational belief that only one particular kind of quasi-material surface is somehow endorsed by Nature and hence relevant to the description of stirring and mixing—namely the locally-defined neutral tangent planes—stating at one point: “why should the ocean care about human constructed density variables”? MGG appear to overlook the simple fact that solutions of the Navier–Stokes equations—which synthesise our ideas about how Nature works—never require the introduction of any form of quasi-material or quasi-neutral density variable. This implies that the empirical isopycnal/isentropic stirring property is necessarily an emergent property of the Navier–Stokes equations, and hence that all forms of isopycnal surfaces—both neutral and not—are necessarily all human constructs. To establish the relevance of any particular construct to the actual ocean, an explicit model of stirring is needed to elucidate the nature of the dynamical/energetics constraints on lateral stirring. Even in the simplest model of stirring, neutral stirring represents only one possible mode out of a continuum of stirring modes responsible for lateral stirring in the ocean, without any evidence that it should dominate over the other ones. To help clarify the issues involved, it is proposed to regard the rigorous study of ocean stirring and mixing as relying on at least five distinct stages, from defining a model of stirring to constructing physically-based mixing parameterisations in numerical ocean models.

Highlights

That challenge the current conventional wisdom about the use of neutral density concepts for studying and parameterising lateral ocean stirring and mixing
Tailleux’s Eulerian arguments for Lagrangian ones; (2) from their irrational belief that only one particular kind of quasi-material surface is somehow endorsed by Nature and relevant to the description of stirring and mixing—namely the locally-defined neutral tangent planes—stating at one point: “why should the ocean care about human constructed density variables”? MGG appear to overlook the simple fact that solutions of the Navier–Stokes equations—which synthesise our ideas about how Nature works—never require the introduction of any form of quasi-material or quasi-neutral density variable
There is no physical basis for such a claim, which is disproved by all published theoretical models of stirring, such as that first considered by Eckart [2] or that based on the discrete view of stirring analysed in [1] and in the present response) of lateral (MGG used ‘neutral’ in place of ‘lateral’; this is either an oversight or a deliberate attempt to mislead the reader into thinking that the two terms are interchangeable, which is not the case) mixing in the ocean”

Summary

Introduction

That challenge the current conventional wisdom about the use of neutral density concepts for studying and parameterising lateral ocean stirring and mixing. Apart from the Eulerian versus Lagrangian points of contention discussed above, MGG raise a number of interesting issues pertaining to the Human versus Nature approach to lateral stirring surfaces that seems to underscore—if needed—the irrational basis of neutral density theory as it is currently formulated or advocated in [3].

Results

Conclusion