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Direct Numerical Simulation of Turbulent Mixing in the Planetary Boundary Layer

Principal Investigator: Juan Pedro Mellado, Max Planck Institute for Meteorology, Hamburg (Germany)
HPC Platform: JUQUEEN of JSC


The planetary boundary layer (PBL) is the lower layer of the troposphere, the layer that directly feels surface effects on time scales smaller than a day. Planetary boundary layers are important in climatology—modulating the fluxes between atmosphere, land and ocean—, and in meteorology—influencing weather conditions—, but key properties remain poorly understood, largely because the PBL is turbulent, and understanding and characterizing the multi-scale nature of turbulence remains challenging. High-performance computing and direct numerical simulations are decisively contributing to advance our understanding of PBL properties.

Direct numerical simulation consists in solving the equations describing the fluid motion without any turbulence model. Currently, we can resolve turbulent motions with sizes varying from 1 km to 1 m, approximately, and although this range of scales is still several orders of magnitude smaller than in nature, it starts to be large enough for results to depend only weakly on it, so that we can extrapolate those results to atmospheric conditions. This approach is helping solve key, long-standing problems.

A key aspect of turbulent mixing in the PBL is how water-vapour properties vary in space and time within the boundary layer, which is relevant, for instance, for vegetation and for clouds. We understand part of the qualitative behaviour of those properties, but we lack a quantitative theory. For instance, surface typically moistens the PBL, whereas mixing with the free troposphere dries it (see mp4-video 1). If surface moistening dominates, the water-vapour content in the PBL increases in time, whereas if drying from the PBL growth into the dry troposphere dominates, the water-vapour content in the PBL decreases. But how does this competition depend on surface and free-troposphere properties?



mp4 video 1: Vertical cross-section of the water vapour content in a convective boundary layer that grows into a dry, linearly stratified troposphere. Green colours indicate moist regions and brown colours indicate dry regions. Small plumes near the surface converge into large-scale updrafts, whereas entrained air at the boundary-layer top converge into large-scale downdrafts, creating large-scale convection cells. (c) Mellado et al.

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Combining theory and three-dimensional simulations, scientists at the Max Planck Institute for Meteorology have expressed this dependence in terms of one single non-dimensional parameter that embeds the combined effect of the surface fluxes of thermal energy and water vapour, and of the vertical variation of temperature and water in the free troposphere [1]. This result greatly simplifies the analysis of the water-vapour properties in the PBL and its parametrization in atmospheric models. As a first application, the authors have provided bulk parametrizations of the mean water vapour and vapour vertical flux, in addition to the vapour fluctuations near the surface and at the top of the boundary layer.

Stratocumulus clouds provide another example of how large-scale simulations are helping understand the interaction between water and turbulence in planetary boundary layers.

Stratocumulus clouds are stratiform clouds that form at the top of shallow planetary boundary layers (see mp4-video 2). Because of their large coverage and high albedo compared to the underlying surface, stratocumulus clouds affect significantly the Earth's radiative balance. However, predicting their evolution remains a long-standing challenge for weather-prediction and climate models, largely because of uncertainties while characterizing cloud-top mixing at meter and sub-meter scales [2]. The role of droplet sedimentation is one such uncertainty. As cloud droplets fall away from the cloud-top boundary, the mixing rate between cloudy air and free-troposphere air decreases, but this effect was considered to be small. Recent work has shown, however, that this effect of droplet sedimentation on cloud-top mixing can be 2 to 3 times larger than previously conjectured and thereby non-negligible [3]. One key implication is that we need to understand better the evolution of the distribution of sizes of cloud droplets near the cloud top, and that is a tremendous challenge because it requires information about the small, dissipative scales of turbulence, on the order of millimetres, and the ability to track billions of cloud droplets, either by measurements in the laboratory or the field, or by large-scale simulations. This is another fascinating example where high-performance computing can break new ground in the coming years.



mp4-video 2: Composite of two vertical cross-sections and a horizontal one at the top showing the liquid mass fraction in a stratocumulus cloud. The white colour represents liquid, grey colour indicating the higher liquid water content induced by radiative cooling. The blue colour represents cloud-free regions. In the vertical planes, we can observe cloud holes penetrating 50 m to 100 m into the cloud bulk. Inside the horizontal plane, we can see the penetration of cloudy updrafts into the upper clear sky. (c) Mellado et al.

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[1] J. P. Mellado, M. Puche, and C. C. van Heerwaarden. Moisture statistics in free convective boundary layers growing into linearly stratified atmospheres. Q. J. R. Meteorol. Soc., 2017.
[2] J. P. Mellado. Cloud-top entrainment in stratocumulus clouds. Annu. Rev. Fluid Mech., 41:145-169, 2017.
[3] A. de Lozar and J. P. Mellado. Reduction of the entrainment velocity by cloud-droplet sedimentation in stratocumulus. J. Atmos. Sci., 74:751-765, 2017.

Scientific Contact:

Juan Pedro Mellado
Max Planck Institute for Meteorology
Bundesstr. 53, D-20146 Hamburg (Germany)
e-mail: juan-pedro.mellado[at]

December 2017