Turbulent Mixing Processes in the Earth System - Research

Group Leader: Juan Pedro Mellado

The dynamics of the atmosphere and the ocean is the result of the simultaneous interaction among numerous and very diverse complex phenomena. Large-scale dynamics, radiation, clouds and turbulence are a few examples thereof. The last one 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 earth system. It is a common, daily life experience that turbulence enhances mixing rates, and the same is true in the atmosphere and in the ocean. In some zones,  a simple parametrization of that characteristic of turbulence is all we need to obtain a satisfying solution to a particular problem because turbulence is not the controlling mechanism. In some other regions, however, turbulent mixing might become the controlling process and its small-scale details might become relevant -- we are interested in these regions. Examples are the air-water interface, cloud boundaries, the inversion on top of the atmospheric boundary layer or the pycnocline at the bottom of the ocean surface layer, under certain conditions.  We complement in this way large-scale studies of the earth system, like those based on general circulation models or large-eddy simulations, where turbulence needs to be parametrized and is not necessarily the main topic of research.

The tools we use are theory and simulations. We know the set of equations governing the evolution of a fluid or fluids mixture (or a simplified set thereof): the partial differential equations describing the conservation of mass, momentum and energy, and the thermodynamic relations among some of the properties. However, the system is in a turbulent state and there is no explicit analytical solution. For that reason we have to rely on numerical solutions. The level of accuracy that we need in those simulations depends on the problem under investigation. For the small-scale turbulence problems that we are interested in, we need to resolve faithfully the whole spectrum of turbulent scales, and the term direct numerical simulation (DNS) has been coined over the years to refer to this type of approach.

The difficulty of this methodology lies in the fact that we need to cope with a very broad range of spatio-temporal scales embracing almost all of the non-linearly three-dimensional interacting modes, and that requires high-performance computing (HPC). HPC has developed astonishingly during the last decades, and it is playing an increasingly important role in many different research areas, not only in fluid mechanics. However, supercomputers are still far away from allowing us to retain all the details of nature and, at some stage, we need to simplify the problem. 

One possible approach, the one we follow in our research group, is to reduce complexity, to derive simplified archetypal problems that still contain the essential physics that we want to understand from the original system (more on this bottom-up, reductive strategy and on the value of a hierarchy of models in climate research can be found in Held, Bull. Am. Meteorol. Soc., 2005). We focus on a reduced region of the non-dimensional parameter space. Simulations give us then a direct measurement of different turbulent flow properties, like time scales associated with transients, transfer rates, spectra, correlations or distribution functions. But more importantly, we can use that information to understand the dynamics of the problem -- we use them as a tool. In addition, we seek typically scaling laws that allow us to extend the results beyond the particular simulations affordable with the available HPC resources. Turbulence shows some piety in this respect, since some important statistics are known to become approximately independent of the scale separation (domain size) beyond some cross-over value, and HPC resources are reaching this critical value. One way to summarize the strategy, to certain extent, is as follows: What is the simplest problem you can think of that answers a particular question? This is key: DNS is used as a research tool, and not as a brute force solution of nature (see Moin and Mahesh, Ann. Rev. Fluid Mech., 1998).

The current focus of the group is on several aspects of the planetary boundary layer.

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 Phenomena

The region of the atmosphere directly affected by the planet surface extends vertically, though strongly varying, of the order of one kilometer and is called the planetary or 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.