|I read the extensive response to reviewers that the authors prepared and the revised manuscript. Some improvements were made, but there are still some major flaws that need to be addressed.|
1) The authors claim that they solve the “Navier-Stokes equations” (abstract, line 4). Recalling one of my previous comments, I think that they should use a different terminology, “Reynolds-averaged Navier-Stokes (RANS) equation”, also in the abstract and not only in the introduction, in order to avoid misunderstanding with DNS models.
2) Eq. 6 is not correct yet: first of all, dQ/dt should read dQ/dr (the error is a copy&paste from Zijlema and Stelling, 2008)...
Second, the equation 6 is not integrated over the depth only, but also over a sector of amplitude y1-y0. I do not understand why this is necessary, and in any case the notation is confusing, the variable y is not defined and there is no reference to fig. 3 where a diagram is shown that is absolutely obscure, if not even wrong (e.g., y should be a tangential coordinate, not orthogonal to r).
Why not introducing the equation integrated only over the depth? By the way, the kinematic boundary condition at the free surface has to be specified.
In fact, the other equations are not presented as integrated over alpha, and only when discretized the “alpha terms” appear (section 2.3).
3) The sentence “In non-turbulent thermohaline systems, stability largely depends on density gradients and molecular heat and salt diffusion rates, which in turn are highly dependent on temperature and salinity” (l. 145-146) is not entirely correct. While I completely agree with the first part, the second part is an overstatement. Stability “highly” depends on the difference between heat and salt diffusion rates, but not on their dependence on temperature and salinity. Most of the models do not even consider this dependence and assume constant values for the two (different!) molecular diffusion coefficients.
4) I do not understand why the simulation of cases 1 and 2 (section 3.1) was stopped after 2 hours (l. 377).
Similar for cases 3 and 4 (section 3.2): “From the current results, we cannot tell whether the system converges after 2 h to a system where the salt flux exceeds the heat flux” (l. 430-431).
The fact that the simulations are short makes the authors hypothesize a subsequent behavior, which is not known. Why not running longer simulations?
5) The authors replied in the following way to my previous that the “standard” turbulence model cannot be taken as “perfect” in transitional (laminar/turbulent) double-diffusive systems: “Further, the referee points out his belief that a standard k-epsilon model is not suitable for these conditions. We would like to ask the referee to better explain why he has this belief for these applications” (p. 7 of their replies).
However, they seem to agree with my comment in the revised manuscript. For instance, “… might indicate that the standard k-epsilon model does not function for systems with high density gradients” (l. 385-386); “The poor performance of the standard k-epsilon model also appears” (l. 392); “confirming that the standard k-epsilon model suppresses the onset of double-diffusive convection” (l. 403-404); “… caused by a defective turbulence modelling for systems of large density gradients” (l. 498).
Frankly speaking, I do not understand such a different opinion in their reply to reviewers and in the manuscript.
6) In line with the comment above about the modelling of turbulence fluxes in systems with high density gradients, it is worth recalling that the actual requirements are quite simple: a model is needed that predict no turbulence in stable regions (hence molecular diffusion) and significantly higher convective fluxes in unstable regions. A few models that exploit this kind of simplified behavior have been proposed and, recently, Toffolon et al. (2015) showed how it is even possible to reproduce – by means of an minimal model of that kind – the formation of double-diffusive staircases. This considerations can be used in the discussion at l. 409-417.
7) When analyzing the case of salt fingers (section 3.2), the authors write: “The numerical results … confirm that salt-fingers are formed over the interface (Fig. 11)” (l. 419-420). I do not see what they refer to in figure 11.
Are they referring to the vertical stripes? In axisymmetric conditions, these are not fingers, they are circles (as I already noted in my previous review).
8) As a whole, it seems that the quantitative comparison (sections 3.1 and 3.2) is not so satisfactory.
9) I do not see why an axisymmetric 2-D model should be presented as “quasi 3-D”.
- At the free surface (l. 153), a kinematic boundary condition is required as well.
- (l. 419), “Case 4”: (Tu = 85.0°) not (Tu = 71.2°).
Toffolon, M., A. Wüest, and T. Sommer (2015), Minimal model for double diffusion and its application to Kivu, Nyos and Powell Lake, J. Geophys. Res. Oceans, 120, 6202–6224, doi:10.1002/2015JC010970