Turbulent Mixing Processes in the Earth System - Research

Group Leader: Juan Pedro Mellado


The dynamics of the atmosphere and of the ocean results from the interaction among very diverse complex phenomena, such as large-scale motion, chemistry, radiation, clouds, and turbulence. Turbulence is the focus of this Max Planck Research Group. Our goal is to improve our current understanding of geophysical turbulence and its role in the susceptibility and predictability of the earth system.


Daily life experience, e.g., stirring up the milk in a cup of coffee, teaches us that turbulence enhances mixing rates. The same is true in the atmosphere and in the ocean. In some regions,  a simple parametrization of that enhancement of mixing rates is sufficient to represent the effect of turbulence on the dynamics of those regions. However, in some other regions, such as near the surface, at cloud boundaries, or inside the inversion on top of the atmospheric boundary layer, turbulence might act as a controlling process and its details become relevant---we are interested in these regions.


The tools that we use in our research are theory and simulations. The level of accuracy that we need in those simulations depends on the problem under investigation. For the small-scale turbulence phenomena that we are interested in, we need to resolve faithfully almost the entire range of turbulent scales. This approach is referred to as direct numerical simulation, and it has become feasible only in recent years thanks to progress in supercomputing. Still, we need to simplify the problem at some stage, and our approach is to reduce complexity while retaining a broad range of spatial and temporal scales. We derive simplified archetypal problems that still contain the essential physics that we want to understand from the original system, and exploit dimensional analysis to reduce the number of independent parameters that define the problem. Simulations give us then a direct measurement of turbulent flow properties, such as mean values, transfer rates, spectra, correlations or probability distribution functions, and we can use that information to understand the dynamics of the system in terms of dominant balances, scaling laws and parametrizations, or time scales associated with transients. Scaling laws are particularly valuable because they allow us to extend the results beyond the specific simulations that we perform, and draw conclusions that are applicable to the atmosphere and to the ocean.

Buoyancy Reversal

If we pour water on top of an ice surface, a turbulent mixing layer may develop next to the ice, even though the temperature of the water gets colder as we approach that ice and therefore the configuration should be, apparently, stable. The reason is that the density of water has a non-linear variation with the temperature such that the maximum density occurs at about 4°C and not at 0°C, causing intermediate regions to be heavier than those in contact with the ice. Such a phenomenon is called buoyancy reversal.


In the context of atmospheric flows, buoyancy reversal may occur at the cloud interfaces. Local evaporation of cloud droplets as environmental dry air is entrained, cools down the mixture because the corresponding amount of latent heat must be absorbed. If this evaporative cooling is strong enough, and that is determined by the local thermodynamic conditions inside and outside the cloud, buoyancy reversal appears. This mechanism may influence the overall mixing of the cloud and therefore the cloud development, which is the motivation for current research in this area. In the case of the cloud-top shown to the right, this process leads to the buoyancy reversal instability and turbulence issues from the cloud-top, advancing into the cloud below.

Clouds as Multi-Phase Flows

Our planet is such that water may appear in the form of gas, liquid and solid, and clouds may develop. Clouds constitute disperse and dilute multi-phase turbulent flows in which the suspended particles are liquid droplets and ice crystals, and the carrier gas is a mixture of dry air and water vapor, water undergoing phase transition. Turbulent multiphase flows constitute an area of active research by themselves. In the earth system, the problem is even more complex because of the link to radiation processes, hydrological cycles, and aerosol transport. It is well established that clouds is one of the most important topics to be addressed in the coming years, since they are a major source of uncertainty in climate and weather prediction.


In our group we aim at the first part of the problem, namely, at the description and analysis of small-scale processes associated with turbulent multi-phase flows and the simulation of them. The focus is on how to extend current continuum formulations of the system to incorporate part of the complex phenomena associated with phase transition and intertial effects, on the limitations of it as well as possible alternatives.

Boundary Layer Turbulence

The region of the atmosphere directly affected by the planet surface extends vertically, though strongly varying, of the order of one or two kilometers, and it is called the planetary boundary layer, or the atmospheric boundary layer. It contains many interesting turbulent phenomena.

On the one hand, there are processes associated with the buoyancy in which the major forcing mechanism is heat transfer from the surface. Next to this lower boundary, cellular patterns like the one shown to the left of this text are often observed. The relatively warmer regions organize themselves into ascending layers and transport away the heat that has been transfered from the ground to the air mass that descends in between. In the upper region of the boundary layer, the interaction of turbulent motions and the stable inversion dictates the rate at which free-atmosphere air is entrained into the boundary layer, controlling the boundary layer growth. Although the understanding of this system has significantly increased during the last decades, some details of those small-scale processes at the lower and upper regions of the boundary layer are still obscure.

A second situation is that in which the main forcing mechanism is a mean horizontal wind. In that case, the strong shear that forms next to the surface is the cause of turbulent motion, and the flow structure next to the ground changes notoriously, from the cellular pattern mentioned before to the elongated structures observed in the picture to the right. The interaction of this turbulent flow with a stable background stratification is particularly important and difficult. As the surface cools down, the turbulent kinetic energy diminishes because of the increasingly heavier parcels of fluid that are transported upwards. A point might be reached in which turbulent mixing is inhibited in an intermittent way, modifying the cooling rates of the surface. This is another problem that has attracted and attracts the attention of the scientific community and we are currently looking at it in our research group.