Interesting question but, my opinion as a non-expert in clouds physics, is that is very difficult to give an univocal aswer ... first of all, I doubt that it makes sense to consider in general a cloud as a passive tracer to control (and to visualize) the turbulent velocity field and see the turbulence as the cause and the response of the coulds as passive effect. I think more about a complex two-way problem where the vapour mass in the cloud can have effect in the thermodynamics sense and acts also by means of the buoyancy on the turbulence. Maybe if we assume only the large scale dynamics (not exactly haotic as you wrote...) we could approssimate more a cloud as a tracer and modelling the effects acting on smaller scales.

However, the Kolmogorov (length and time) scales define only the smallest lenght in which turbulence dissipate the kinetic energy. That is more towards the microscopic action than the macroscopic one.

Filippo Maria Denaro Thank you so much for your answer.

Turbulent flow in the atmosphere encompasses a very wide range of scales. The smaller scale affects the stochastic coagulation of cloud droplets, while larger scale eddies influence the topology of the cloud edge and largely control the entrainment of ambient air.

After focusing our attention on a shallow convection, we will see that even this relatively simple system is associated with a rather complicated and non-stationary turbulence. For this reason, most research in this area is done using numerical simulation. In computer models of small convective clouds, we can observe the complex billowing forms resulting from the Kelvin-Helmholtz instability that develops at the interface of the cloud. The multi-scale nature of vortices linked to this instability is very well confirmed by the observations.

An interesting aspect of the aesthetically pleasing forms of convective clouds is their interaction with the larger-scale flow manifested by momentum and thermodynamic properties transport in the vertical direction. We are still trying to parameterize this effect in the large-scale models developed for numerical weather prediction. Perhaps in the near future, the topological arguments will help us to organize existing knowledge on the role of convective clouds in shaping the weather patterns on a larger scale.

Cloud systems associated with the synoptic-scale weather system are also affected by turbulence, although the main factor determining their intriguing shapes is large-scale transport, often leading to patterns reminiscent of chaotic advection.

The complete systematization of the influence of turbulence on the cloud field is a complex task that is still waiting for authoritative wording.

Unresolved turbulence by current meteorological models are responsible for forecast error in the cloud fraction. Meteorologists refer that to "dirty ridge" when you have a zone of high pressure and the forecast calls for not much clouds but the reality is that the sky is cloudy almost all day. This is due to the fact that model at the scale of the tile have little upward motion whereas locally you can have rising small bubbles producing condensation and low-level clouds (as strato-cumulus). This is an example where presence of local turbulence produce clouds by mixing. Representation of small-scale turbulence is still poor in NWP models.

Alain Robichaud

That is an intriguing issue. A turbulence model can fail for several reasons but first we should consider the formulation for the resolved variable to analyse the reasons for a lack in the model. As you are considering a turbulence model "at a scale of the tile" I suppose that you are talking about a formulation like LES, where you suppose to have a scale separation (large vs. small). The problem you addressed is due to the fact that someway the problem is not well-posed. The modelling of the small scales is something that uses the large resolved variable to provide a contribution (in integral sense) which still acts on to the large scales. As you see, there is no at all idea of a "little upward motion" that characterizes the model. In other words, what you would ask for is a model that describes a phenomenon that starts to small unresolved scales and then affects the large scale. That is somehow a counterpart of an inverse energy cascade that is not described by pure dissipative models. Actually, one can also debate about the well-posed model if the main driving force acts at scales that are, a priori, not resolved. Maybe the problem is not in the turbulence model but in the mathematical governing PDE that should describe such physics using, explicitly, some forcing term.

Then, a further question would be in the fact that an improved turbulence model gives a input to the "cloud model", are we sure that such a model works properly? I mean, if we would be able to perform a DNS of the turbulent field, would be able to describe correctly the cloud physics with the present models?

Filippo,

I am not an expert of turbulence. I just shared an observation that I have seen over decades by using NPW models. And in weather offices, they refer to it as dirty ridge. Now, I do not see how can a model having 10 km resolution can reproduce turbulence at the scale of few hundred meters even with the best subgrid representation for turbulence.

Best regards

Alain,

from an ideal point of view, if we were able to resolve the full range of lenght scales (Direct Numerical Simulation) there is no model at all since there is not unresolved subgrid contribution. However, performing a DNS in a simple 3D box of 10 km of edge at a physical Re number seems still utopia.

But in principle, a DNS realized over a smaller box lenght could likely produce a meaningful turbulence allowing to analyse and assess the validity of the models cloud.

Conversely, in a modelled simulation, if the driving force starts from the unresolved subgrid scales there is no specific fault due to the SGS model but rather in the fact that the scale separation is supposed at a wrong lenght. The backward effect from small to large scale can be described in some advanced SGS models but they suppose a fully developed turbulence which is not the case of this physics.

Cloud modeling requires a simulation describing the interaction between the cloud droplet spectrum and turbulent flow. Mathematically, we have to solve the Smoluchowski equation (stochastic coagulation equation with terms describing condensation and evaporation) coupled to Navier - Stokes equations. This simulation is difficult and can only be attempted for a limited part of the cloud

The situation is further complicated by the fact that the turbulent flow structure in the cloud is very anisotropic, which requires simulations of most of the cloud volume (this is still not possible due to the limited computing power). Perhaps we need a better mathematical description of turbulence in the cloud to answer the fundamental questions of cloud physics?

As far as the reality of numerical weather prediction is concerned, we currently use a rather simplistic parameterizations of mixing based on J. Smagorinsky’s ideas (diffusivity proportional to the deformation) and various forms of the bulk moist thermodynamics (all these assumptions are probably justified on the grids with a horizontal resolutions of the order of 10 km).

Perhaps experiments with realistic cloud models will eventually lead to better parameterizations required when the resolution of the numerical weather prediction models will increase.

Please look the attachment, may be it will be interesting for you.

M. A. Zatevakhin

that is a very interesting approach, that is the idea of using LES formulation to get quite well resolved large scale. However I am inclined to think that small scales are rather relevant and have a relevance that is difficult to take into account in a SGS model.

Furthermore, you paper tried to describe a boundary layer dynamics and that requires a strong constraint on the vertical resolution that has to be at the level of the DNS. Conversely, seems your grid is quite coarse in the vertical direction.

To complicate much more the problem, the buoyancy driven flow requires a congruent coupled SGS approach since, in condition of statistical energy equilibrium, production of kinetic energy due to gravity should equate the dissipation. That is one of the problem highlighed, for example, in a hystorical Lilly's paper on Tellus and then on PoF.

I have worked on such LES modelling some years ago and it is really a challenging task. But I definitely agree that LES is quite mature to be used instead of the hystorycal RANS formulations.

Indeed there are some problems, but the objective was to see phenomenon using first non-zero approach. And figures 7...9 demonstrate the effect.

Academic resources on atmospheric dispersion are provided on the project references:

SINGLE PHASE AND MULTIPHASE TURBULENT FLOWS (SMTF) IN NATURE AND ENGINEERING APPLICATIONS | Jamel Chahed | 3 publications | Research Project (researchgate.net)