I take the audience on a scientific journey from the physics of neutron stars to cosmology and further on to turbulence and its role for oceaongraphy and climate modeling. Scientific highlights on this journey include an exact equation of state for neutron stars, results on cosmology, and a general turbulence model which has guided the modeling of transport processes in oceanography which is needed in climatology. From short encounters to longterm collaborations famous physicists are part of this story, including P.A.M. Dirac, W. Heisenberg, I. Rabi, J.A. Wheeler and many others.

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Workshop: Modelling of geophysical and stellar flows (2023)

The atmospheres of most stars have at least some level of magnetic activity. This is modulated by variability, which manifests itself as varying magnetic strength across the stellar surface and in time as well as in the form of different magnetic behaviour of different stars. This is moreover intertwined with all the other physical effects occurring in the atmospheres of stars, in particular convection, radiative transfer and turbulence. In the case of the Sun, magnetic fields are known to be ubiquitous, at an average level of roughly 1 hG across its surface, which - inter alia - has an impact on its inferred temperature stratification and chemical abundance. It is especially interesting to understand solar magnetism, for example its main magnetic cycle, also in comparison to other stars, given the Sun's driving influence on life on Earth and as the base energy input for terrestrial climate. Knowledge of stellar activity is also crucial for improved exoplanet detection and characterisation. Our team is focussing on different aspects of stellar atmosphere physics, from the viewpoint of numerical (magneto-)hydrodynamic simulations. Recent examples include the production of models for stars of spectral type F to A, and the study of hard turbulence as possible driver of synchronised swaying atmospheric motions akin to the still unexplained effect of solar supergranulation.

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Workshop: Modelling of geophysical and stellar flows (2023)

The overall understanding of solar and stellar convection has been questioned during the last decade or so with helioseismic results suggesting that the convective amplitudes at large horizontal scales in the Sun might be much lower than indicated by current simulations or mixing length estimates. A manifestation of this ``convective conundrum'' is that global simulations struggle to reproduce a solar-like differential rotation with a fast equator and slow poles with nominally solar parameters. A major contributor to this is that giant cell convection, with characteristic length scale comparable to the depth of the convection zone, is excited in simulations but appears to be much weaker in the Sun. A possible solution to this conundrum is that a large fraction of the solar convection zone is in fact stably stratified due to plumes originating near the surface and piercing the whole convection zone, such that giant cells are not excited. Non-rotating numerical simulations lend support to such non-local scenario of convection and lead to sizeable Schwarzschild-stable, yet convecting, layers in deep convection zones. Another possibility is that convection is rotationally constrained such that horizontal extent of convection cells is significantly reduced. New results from hydrodynamic rotating Cartesian convection simulations are presented that seek to capture the rotationally constrained convection near the base of the solar convection zone. The current results indicate that in models corresponding to the deep parts of the solar convection zone, the subadiabatic and overshoot layers are somewhat shallower than in the non-rotating case. Furthermore, these simulations suggest that deep convection in the Sun is not strongly rotationally constrained and that rotational suppression of large scale flows is weak.

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Workshop: Modelling of geophysical and stellar flows (2023)

In 1D stellar evolution models, the process of convection is often described using the mixing length theory (MLT). However, MLT does not account for the non-locality of convection, and an ad hoc implementation of overshooting is needed. The Kuhfuss theory is one of the theories that attempts to derive a more complete picture of turbulent convection. In this theory, non-locality is not implemented artificially, but is included in the theory. Both versions of the Kuhfuss theory, the 1-equation model as well as the 3-equation model, are implemented in the stellar evolution code GARSTEC and have already been tested on convective cores on the main sequence before (Ahlborn et al. 2022). Following these promising results for convection in stellar cores, we tested the Kuhfuss theory for convective envelopes. We applied the 1-equation model of the Kuhfuss convection theory to a stellar model calibrated to the Sun. Using helioseismic measurements of quantities of the convective envelope and interior structure, we quantified the differences and improvements from the Kuhfuss theory compared to MLT. We furthermore followed the evolution of stars to the red giant branch to study the influence of the Kuhfuss theory on the location of the red giant branch bump, which is known to be sensitive to the description and depth of convective overshooting. In the future, these cases will also be studied using the full 3-equation Kuhfuss model.

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Workshop: Modelling of geophysical and stellar flows (2023)

Observations of stars with convectively burning cores have shown that the size of these cores is substantially underestimated. The increase of the convective core size, known as overshooting, has profound effects on the stellar structure and evolution, e.g. affecting age estimates, luminosities or nucleosynthetic yields of stars. Here, we applied a turbulent convection theory to model the evolution of intermediate and high-mass stars. We predict the emergence of an overshooting zone and modifications to the thermal stratification. The application of a turbulent convection theory is a crucial step towards a more realistic description of convection in stellar models. The predictions of the turbulent convection model may be tested against a variety of different observations, e.g. spectroscopic observations of massive stars, asteroseismic observations or observations of detached binary systems. Finally, the predictions of the turbulent convection model can be compared to hydrodynamic simulations of turbulent convection.

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Workshop: Modelling of geophysical and stellar flows (2023)

In this presentation I shall provide an overview of our current understanding of modelling energy exchange between stellar convection and oscillations in stars supporting solar-type oscillations. Stellar calculations, adopting a 1D, non-local, time-dependent convection model, are calibrated against seismic observations and 3D-simulation results. These stellar models are tested against data from the Sun and from Kepler main-sequence stars. This provides insight into the physical processes that determine energy transport in the outer stellar layers and to a better understanding of the so-called surface effects of pulsation frequencies.

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Workshop: Modelling of geophysical and stellar flows (2023)

While all of the stars change their brightness during their lifetimes, there are many among them that do this on a human timescale (from less than a day to years) due to external or internal reasons. We call those stars classical variables, which exhibit a strong, stable radial pulsation with periods from 0.3-100 days. In these cases, the outer envelope of the star periodically expands and shrinks due to an effect tied to hydrogen and helium ionisations called the kappa mechanism. They are important to astronomers because their period is proportional to their average brightness, making them perfect distance indicators. Since the first electronic computers became available, astronomers have applied them to model the structure and dynamics of these (and every other) types of stars. The first attempts neglected convection and turbulence, considering only radiative energy transport. However, it soon turned out that we could not adequately describe pulsation without convection. Moreover, the different improved forms of static mixing length theory were also inadequate. Hence, massive research was started to create a time-dependent theory that can describe convection correctly in a one-dimensional approximation. These efforts revealed some hidden features of the phenomena but could not answer all of the questions raised. Since convection and non-radial pulsation are genuinely multi-dimensional phenomena, multi-D models seem inevitable, but this approach requires high computational performance, which was not available decades ago. Today, though we have better equipment, numerical modelling of turbulent convection in stars is still a great challenge due to the many magnitudes of scale it involves, especially in classical pulsators. In this talk, I highlight some of the achievements of this journey and show the recent developments and future aspects of turbulent RHD modelling in classical pulsating stars.

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Workshop: Modelling of geophysical and stellar flows (2023)

We speak about numerical issues and results regarding the simulation of solar granulation flows and the pulsation-convection interaction in Cepheids in 3D and 2D, respectively.

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Workshop: Modelling of geophysical and stellar flows (2023)

In intention of this talk is to show how research on a rather specific topics from stellar astrophysics, the study of atmospheres of A-type stars, has led myself to numerous collaborations with researchers working in other fields such as meteorology, oceanography, numerical mathematics, and high preformance computing. To explain "turbulence" in the context of solar and stellar astrophysics, a short introduction into simulations of solar granulation will be given (much more details will follow in Herbert Muthsam's talk) followed by how turbulent convection is detected and modelled in A-type stars. Various modelling approaches have been used in this context: mixing lenth theory, two-point closure models, Reynolds stress models, and numerical simulations. The latter lead to the necessity to develop improved time integration methods which have first been probed in studies of semi-convection (diffusive convection). Studies in meteorology inspired new models for higher order moments required for Reynolds stress models. Finally, some result on the modelling of convective overshooting is presented which has been inspired by work that will be discussed in detail in other talks during the workshop (by Felix Ahlborn, Teresa Braun, Petri Käpylä).

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Workshop: Modelling of geophysical and stellar flows (2023)

Three examples from geophysical fluid dynamics will showcase mathematical modelling as the "art of judicious simplification": The computational prediction of two seasonal to decadal phenomona, the "quasi-biennial oscillation" (QBO) and the "El Niño Southern Oscillation" (ENSO) became possible only after theoreticians had captured their essential causal structures in convincing reduced mathematical models. With our own research, we aim to similarly untangle the mechanisms behind the "rapid intensification" (RI) of tropical storms during their transition to hurricane strength.

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Pauli Symposium on Turbulence in Stellar & Geophysical flows (2023)

Turbulence closure models (parameterization schemes) currently used in numerical models of the atmosphere are discussed. The focus is on truncated one-equation turbulence kinetic energy (TKE) closure schemes that are arguably the present-day draft horses of operational meteorology, e.g., numerical weather prediction. Advantages and shortcomings of one-equation TKE schemes are outlined in the context of various operational constraints. A TKE scalar variance (TKESV) closure scheme is considered in some detail. The TKESV scheme carries transport equations (with due regard for the time-rate-of-change and third-order transport terms) for both the TKE and the variances and covariance of scalar quantities (e.g., temperature and humidity) that characterize turbulence potential energy. It is argued that the TKESV scheme has considerable advantages over the TKE scheme in terms of the essential physics but it can still meet severe operational requirements. Careful consideration is given to a number of tricky parameterization issues, including the pressure-scrambling effects in the Reynolds-stress and scalar-flux equations and the influence of clouds on turbulent mixing. An assumed PDF (probability distribution function) closure approach is briefly outlined. Finally, realizability of turbulence closures is considered within a more general framework of the problem of moments of the probability theory.

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Pauli Symposium on Turbulence in Stellar & Geophysical flows (2023)

The three principal dynamical regimes of the atmosphere and the ocean are: i) small-scale turbulence down to the smallest space and time scales ii) internal gravity waves over a wide range of spatial scales iii) geostrophically balanced eddying motion at the largest space and time scales. All regimes are of turbulent character and need parameterisations in ocean components of climate models because of the lack of coarse grid resolution. A few aspects of closures for gravity wave turbulence are presented and closures for eddies in the ocean are discussed.

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Pauli Symposium on Turbulence in Stellar & Geophysical flows (2023)

Stellar evolution models provide the foundation of several methods applied to study the evolutionary properties of stars and stellar populations, both Galactic and extragalactic. The accuracy of the results obtained with these techniques is tied to the accuracy of the stellar models, and in this context the correct treatment of turbulent convection is crucial. Unfortunately, the modelling of turbulent convection in stellar evolution computations is still affected by sizable uncertainties. The aim of this talk is to highlight the effect of turbulent convection on the most important stellar model predictions in the context of the study of stellar systems like star clusters and galaxies, and the (simple) prescriptions we currently use (out of necessity).

• Thematic program: Mathematics – Magnetism - Materials (2023/2024)
• Event: Pauli Symposium on Turbulence in Stellar & Geophysical flows (2023)

In a viscous fluid, the energy dissipation is the signature of the breaking of the time-reversal symmetry (hereafter TSB) t->-t, u-> -u, where u is the velocity. This symmetry of the Navier-Stokes equations is explicitly broken by viscosity. Yet, in the limit of large Reynolds numbers, when flow becomes turbulent, the non-dimensional energy dissipation per unit mass becomes independent of the viscosity, meaning that the time-reversal symmetry is spontaneously broken. Natural open questions related to such observation are: what is the mechanism of this spontaneous symmetry breaking? Can we associate the resulting time irreversibility to dynamical processes occurring in the flow? Can we devise tools to locally measure this time irreversibility? In this talk, I first show that the TSB is indeed akin to a spontaneous phase transition in the Reversible Navier-Stokes equations, a modification of the Navier-Stokes equation suggested by G. Gallavotti to ensure energy conservation and relevance of statistical physics interpretation. I then discuss a mechanism of the TSB in Navier-Stokes was first suggested by L. Onsager in 1949, in which quasi-singularities or singularities create a non-viscous dissipation. I exhibit the tools to track these quasi-singularities. I show how the application of these tools to velocity measurements in a turbulent swirling flow allows to detect Eulerian and Lagrangian signatures of irreversibility. This enables me to evidence the structures that are responsible for irreversibility and associate them with peculiar properties of the local velocity field or trajectories.

• Thematic program: Models in Plasmas, Earth and Space Science (2023/2024)
• Event: Pauli Symposium on Turbulence in Stellar & Geophysical flows (2023)