It was shown by Oberlack and Rosteck [ Discr. Cont. Dyn. Sys. S, 3, 451 2010] that the infinite set of multipoint correlation (MPC) equations of turbulence admits a considerable extended set of Lie point symmetries compared to the Galilean group, which is implied by the original set of equations of fluid mechanics. Specifically, a new scaling group and an infinite set of translational groups of all multipoint correlation tensors have been discovered. These new statistical groups have important consequences for our understanding of turbulent scaling laws as they are essential ingredients of, e.g., the logarithmic law of the wall and other scaling laws, which in turn are exact solutions of the MPC equations. In this paper we first show that the infinite set of translational groups of all multipoint correlation tensors corresponds to an infinite dimensional set of translations under which the Lundgren-Monin-Novikov (LMN) hierarchy of equations for the probability density functions (PDF) are left invariant. Second, we derive a symmetry for the LMN hierarchy which is analogous to the scaling group of the MPC equations. Most importantly, we show that this symmetry is a measure of the intermittency of the velocity signal and the transformed functions represent PDFs of an intermittent (i.e., turbulent or nonturbulent) flow. Interesting enough, the positivity of the PDF puts a constraint on the group parameters of both shape and intermittency symmetry, leading to two conclusions. First, the latter symmetries may no longer be Lie group as under certain conditions group properties are violated, but still they are symmetries of the LMN equations. Second, as the latter two symmetries in its MPC versions are ingredients of many scaling laws such as the log law, the above constraints implicitly put weak conditions on the scaling parameter such as von Karman constant $\kappa$ as they are functions of the group parameters. Finally, let us note that these kind of statistical symmetries are of much more general type, i.e., not limited to MPC or PDF equations emerging from Navier-Stokes, but instead they are admitted by other nonlinear partial differential equations like, for example, the Burgers equation when in conservative form and if the nonlinearity is quadratic.

In this work, direct numerical simulation (DNS) of the stratocumulus cloud-top mixing layer is used to test various approaches to estimate the turbulence kinetic energy (TKE) dissipation ra... AbstractIn this work, direct numerical simulation (DNS) of the stratocumulus cloud-top mixing layer is used to test various approaches to estimate the turbulence kinetic energy (TKE) dissipation ra...

The Next Generation of Earth Modeling Systems (nextGEMS) project aimed to produce multidecadal climate simulations, for the first time, with resolved kilometer-scale (km-scale) processes in the ocean, land, and atmosphere. In only 3 years, nextGEMS achieved this milestone with the two km-scale Earth system models, ICOsahedral Non-hydrostatic model (ICON) and Integrated Forecasting System coupled to the Finite-volumE Sea ice-Ocean Model (IFS-FESOM). nextGEMS was based on three cornerstones: (1) developing km-scale Earth system models with small errors in the energy and water balance, (2) performing km-scale climate simulations with a throughput greater than 1 simulated year per day, and (3) facilitating new workflows for an efficient analysis of the large simulations with common data structures and output variables. These cornerstones shaped the timeline of nextGEMS, divided into four cycles. Each cycle marked the release of a new configuration of ICON and IFS-FESOM, which were evaluated at hackathons. The hackathon participants included experts from climate science, software engineering, and high-performance computing as well as users from the energy and agricultural sectors. The continuous efforts over the four cycles allowed us to produce 30-year simulations with ICON and IFS-FESOM, spanning the period 2020–2049 under the SSP3-7.0 scenario. The throughput was about 500 simulated days per day on the Levante supercomputer of the German Climate Computing Center (DKRZ). The simulations employed a horizontal grid of about 5 km resolution in the ocean and 10 km resolution in the atmosphere and land. Aside from this technical achievement, the simulations allowed us to gain new insights into the realism of ICON and IFS-FESOM. Beyond its time frame, nextGEMS builds the foundation of the Climate Change Adaptation Digital Twin developed in the Destination Earth initiative and paves the way for future European research on climate change.

In this work we study different techniques to estimate basic properties of turbulence, that is its characteristic velocity and length scale from low-resolution data. The methods are based on statistics of the signals like the velocity spectra, second-order structure function, number of signal’s zero-crossings and the variance of velocity derivative. First, in depth analysis of estimates from artificial velocity time series is performed. Errors due to finite averaging window, finite cut-off frequencies and different fitting ranges are discussed. Next, real atmospheric measurement data are studied. It is demonstrated that differences between results of the methods can indicate deviations from the Kolmogorov’s theory or the presence of external intermittency, that is the existence of alternating laminar/turbulent flow patches.

Turbulent flows featuring additional scalar fields, such as chemical species or temperature, are common in environmental and industrial applications. Their physics is complex because of a broad range of scales involved; hence, efficient computational approaches remain a challenge. In this paper, we present an overview of such flows (with no particular emphasis on combustion, however) and we recall the major types of micro-mixing models developed within the statistical approaches to turbulence (the probability density function approach) as well as in the large-eddy simulation context (the filtered density function). We also report on some trends in algorithm development with respect to the recent progress in computing technology.

In this work we show how to retrieve information about temporal changes of turbulence in the atmosphere based on in situ wind velocity measurements performed by aircraft. We focus on the stratocumulus-topped boundary layer high-resolution data taken by a helicopter-borne platform Airborne Cloud Turbulence Observation System (ACTOS). We calculate two nondimensional indicators, the dissipation factor and the integral-to-Taylor-scale ratio, and study their dependence on the Taylor-scale-based Reynolds number. By analyzing these results, we can identify regions where turbulence is in its stationary state and regions where turbulence decays in time or, on the contrary, becomes stronger. We can also detect nonequilibrium turbulence states, which indicate the presence of rapidly changing external conditions. Significance Statement: The purpose of this work is to retrieve new information on turbulence in the atmosphere. We consider data from a field study based on in situ observations from a measurement payload below a slow-flying helicopter. We show that it is possible to retrieve information on temporal tendencies in a given region from such measurements. We attempt to estimate whether turbulence is in its stationary state, or possibly, turbulence decays due to insufficient production, or, on the contrary, becomes stronger. Such information provide useful knowledge of small-scale processes in the atmospheric boundary layer and can be used to improve their parameterizations.