@misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Modeling simultaneous momentum and passive scalar transfer in turbulent annular Poiseuille flow}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {22}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {1}, issn = {1617-7061}, doi = {10.1002/pamm.202200272}, abstract = {Simultaneous momentum and passive scalar transfer in weakly heated pressure-driven turbulent concentric annular pipe flow is numerically investigated using the cylindrical formulation of the stochastic one-dimensional turbulence (ODT) model,which is utilized here as standalone tool. In the present study, we focus on the model calibration for heated annular pipes based on recent reference direct numerical simulations (DNS) from Bagheri and Wang (Int. J. Heat Fluid Flow 86, 108725,2020; Phys. Fluids 33, 055131, 2021). It is shown that the model is able to individually capture scalar and momentum transfer, but not both equally well at the same time. We attribute this to less dissimilar scalar and momentum transport in the model at the low Reynolds number investigated. It is argued that the model prefers a fully developed turbulent state due to its construction. Nevertheless, it is demonstrated that ODT is able to reasonably capture the radial inner-outer asymmetry of the scalar and momentum boundary layers which yields better predictive capabilities than wall-function-based approaches.}, language = {en} } @misc{GaoSchmidtKleinetal., author = {Gao, Tianyun and Schmidt, Heiko and Klein, Marten and Liang, Jianhan and Sun, Mingbo and Chen, Chongpei and Guan, Qingdi}, title = {One-dimensional turbulence modeling of compressible flows. I. Conservative Eulerian formulation and application to supersonic channel flow}, series = {Physics of Fluids}, volume = {35}, journal = {Physics of Fluids}, number = {3}, issn = {1089-7666}, doi = {10.1063/5.0125514}, abstract = {Accurate but economical modeling of supersonic turbulent boundary layers is a standing challenge due to the intricate entanglement of temperature, density, and velocity fluctuations on top of the mean-field variation. Application of the van Driest transformation may describe well the mean state but cannot provide detailed flow information. This lack-in modeling coarse and fine-scale variability is addressed by the present study using a stochastic one-dimensional turbulence (ODT) model. ODT is a simulation methodology that represents the evolution of turbulent flow in a low-dimensional stochastic way. In this study, ODT is extended to fully compressible flows. An Eulerian framework and a conservative form of the governing equations serve as the basis of the compressible ODT model. Computational methods for statistical properties based on ODT realizations are also extended to compressible flows, and a comprehensive way of turbulent kinetic energy budget calculation based on compressible ODT is put forward for the first time. Two canonical direct numerical simulation cases of supersonic isothermal-wall channel flow at Mach numbers 1.5 and 3.0 with bulk Reynolds numbers 3000 and 4880, respectively, are used to validate the extended model. A rigorous numerical validation is presented, including the first-order mean statistics, the second-order root mean square statistics, and higher-order turbulent fluctuation statistics. In ODT results, both mean and root mean square profiles are accurately captured in the near-wall region. Near-wall temperature spectra reveal that temperature fluctuations are amplified at all turbulent scales as the effects of compressibility increase. This phenomenon is caused by intensified viscous heating at a higher Mach number, which is indicated by the steeper profiles of viscous turbulent kinetic energy budget terms in the very near-wall region. The low computational cost and predictive capabilities of ODT suggest that it is a promising approach for detailed modeling of highly turbulent compressible boundary layers. Furthermore, it is found that the ODT model requires a Mach-number-dependent increase in a viscous penalty parameter Z in wall-bounded turbulent flows to enable accurate capture of the buffer layer.}, language = {en} } @misc{GaoSchmidtKleinetal., author = {Gao, Tianyun and Schmidt, Heiko and Klein, Marten and Liang, Jianhan and Sun, Mingbo and Chen, Chongpei and Guan, Qingdi}, title = {One-dimensional turbulence modeling of compressible flows: II. Full compressible modification and application to shock-turbulence interaction}, series = {Physics of Fluids}, volume = {35}, journal = {Physics of Fluids}, number = {3}, issn = {1089-7666}, doi = {10.1063/5.0137435}, abstract = {One-dimensional turbulence (ODT) is a simulation methodology that represents the essential physics of three-dimensional turbulence through stochastic resolution of the full range of length and time scales on a one-dimensional domain. In the present study, full compressible modifications are incorporated into ODT methodology, based on an Eulerian framework and a conservative form of the governing equations. In the deterministic part of this approach, a shock capturing scheme is introduced for the first time. In the stochastic part, one-dimensional eddy events are modeled and sampled according to standard methods for compressible flow simulation. Time advancement adjustments are made to balance comparable time steps between the deterministic and stochastic parts in compressible flows. Canonical shock-turbulence interaction cases involving Richtmyer-Meshkov instability at Mach numbers 1.24, 1.5, and 1.98 are simulated to validate the extended model. The ODT results are compared with available reference data from large eddy simulations and laboratory experiments. The introduction of a shock capturing scheme significantly improves the performance of the ODT method, and the results for turbulent kinetic energy are qualitatively improved compared with those of a previous compressible Lagrangian ODT method [Jozefik et al., "Simulation of shock-turbulence interaction in non-reactive flow and in turbulent deflagration and detonation regimes using one-dimensional turbulence," Combust. Flame 164, 53 (2016)]. For the time evolution of profiles of the turbulent mixing zone width, ensemble-averaged density, and specific heat ratio, the new model also yields good to reasonable results. Furthermore, it is found that the viscous penalty parameter Z of the ODT model is insensitive to compressibility effects in turbulent flows without wall effects. A small value of Z is appropriate for turbulent flows with weak wall effects, and the parameter Z serves to suppress extremely small eddy events that would be dissipated instantly by viscosity.}, language = {en} } @misc{KleinSchoepsMedinaMendezetal., author = {Klein, Marten and Sch{\"o}ps, Mark Simon and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Numerical simulation and analysis of transient Ekman boundary layers using a stochastic turbulence model}, series = {EGU General Assembly 2023}, journal = {EGU General Assembly 2023}, publisher = {EGU - European Geophysical Union}, address = {Vienna, Austria}, doi = {10.5194/egusphere-egu23-9116}, language = {en} } @misc{GlaweKleinSchmidt, author = {Glawe, Christoph and Klein, Marten and Schmidt, Heiko}, title = {ODT augmented RaNS}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {368}, language = {en} } @misc{MedinaMendezSharmaSchmidtetal., author = {Medina M{\´e}ndez, Juan Al{\´i} and Sharma, Sparsh and Schmidt, Heiko and Klein, Marten}, title = {Towards the use of a reduced order and stochastic turbulence model for assessment of far-field sound radiation: low Mach number jet flows}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {413 -- 414}, language = {en} } @misc{SharmaAytonKleinetal., author = {Sharma, Sparsh and Ayton, Lorna and Klein, Marten and Schmidt, Heiko}, title = {Estimation of ODT-resolved acoustic sources in high Reynolds number turbulent jets}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {414 -- 415}, language = {en} } @misc{PolasanapalliKleinSchmidt, author = {Polasanapalli, Sai Ravi Gupta and Klein, Marten and Schmidt, Heiko}, title = {SGS modeling in lattice Boltzmann method for non-fully resolved turbulent flows}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {363 -- 364}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Effects of Reynolds number on turbulent concentric coaxial pipe flow using stochastic modeling}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {365}, language = {en} } @misc{Klein, author = {Klein, Marten}, title = {Map-based stochastic modeling of multiscale transfer processes in turbulent flows}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {362}, abstract = {The detailed modeling of turbulent mixing has remained a numerical challenge for a number of applications, ranging from chemically reacting flows to noise prediction in technical flows, and encompassing convection on multiple scales in the geophysical context, among others. Complications arise from the dynamical complexity of turbulence that manifests itself by emergent small-scale flow features, scaling cascades, and intermittency due to prescribed forcings, boundary and initial conditions. In order to robustly predict, for example, the occurrence of catalytic reactions, generation of mixing noise, or the heat transfer across a layer of fluid, it is crucial to represent the physical redistribution processes in the flow with a proper account of participating time and length scales. This yields scale-locality and causality constraints that can usually only be fully addressed by direct numerical simulation (DNS) based on the discretized three-dimensional (3-D) Navier-Stokes equations, which is a very costly undertaking and limited to moderate or low turbulence intensities. In order to over- come the fundamental limitations of statistical turbulence models and numerical cost of DNS, so-called map-based stochastic turbulence models have been developed and increasingly applied to various mutiphysical flows over the last couple of decades. These models utilize onedimensional (1-D) generalized Baker's maps in order to distinguish advective filamentation from molecular diffusion processes, resolving all relevant scales of the flow along a single physical coordinate. Baker's maps are probabilistically sampled with respect to size, location, and time of occurrence which introduces dynamical complexity into the bottom-up modeling approach. When the sampling is based on the evolving flow state, a self-contained reduced- order model with predictive capabilities for turbulent flows can be formulated. In the talk, I will summarize the map-based stochastic modeling strategy with an emphasize on the so-called One-Dimensional Turbulence (ODT) model. After that, I will discuss some recent advances in the field, demonstrating the applicability of the approach across flow configurations. I will address in more detail the flow physics representation by means of entrainment and passive scalar mixing in turbulent jets, as well as heat flux and wall shear stress fluctuations in heated channels and stably-stratified atmospheric boundary layers.}, language = {en} } @misc{GlaweKleinSchmidt, author = {Glawe, Christoph and Klein, Marten and Schmidt, Heiko}, title = {Stochastic deconvolution of wall statistics in Reynolds-averaged Navier-Stokes simulations based on one-dimensional turbulence}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {23}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {3}, issn = {1617-7061}, doi = {10.1002/pamm.202300055}, pages = {9}, abstract = {Reynolds-averaged Navier-Stokes simulation (RaNS) is state-of-the-art for numerical analysis of complex flows at high Reynolds number. Standalone RaNS may yield a reasonable estimate of the wall-shear stress and turbulent drag if a proper wall-function is prescribed, but detailed turbulence statistics cannot be obtained, especially at the wall. This lack in modeling is addressed here by a stochastic deconvolution strategy based on a stochastic one-dimensional turbulence (ODT) model. Here, a one-way coupling strategy is proposed in which a forcing term is computed from the balanced RaNS solution that is in turn utilized in the ODT model. The temporally developing ODT solution exhibits turbulent perturbations but relaxes toward the local RaNS solution due to resolved molecular-diffusive processes. It is demonstrated that the approach is able to recover the distribution of positive wall-shear stress fluctuations in turbulent channel flow. When formulated as post-processing tool, it is suggested that RaNS can be enhanced by ODT providing economical means for local high-fidelity numerical modeling based on a low-fidelity flow solution.}, language = {en} } @misc{MedinaMendezKleinSchmidt, author = {Medina M{\´e}ndez, Juan Ali and Klein, Marten and Schmidt, Heiko}, title = {Investigating dissipative roughness effects on turbulent drag using a stochastic turbulence model}, series = {18th European Turbulence Conference (ETC18), 4-6 September 2023, Valencia}, journal = {18th European Turbulence Conference (ETC18), 4-6 September 2023, Valencia}, address = {Valencia}, pages = {1}, language = {en} } @misc{MedinaMendezSharmaSchmidtetal., author = {Medina M{\´e}ndez, Juan Ali and Sharma, Sparsh and Schmidt, Heiko and Klein, Marten}, title = {Toward the use of a reduced-order and stochastic turbulence model for assessment of far-field sound radiation: Low Mach number jet flows}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {23}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {3}, issn = {1617-7061}, doi = {10.1002/pamm.202300186}, pages = {9}, language = {en} } @misc{KleinKesslerSchmidt, author = {Klein, Marten and Kessler, Robert William and Schmidt, Heiko}, title = {On the influence of a wavy leading edge on the aerodynamic drag of a wing: A numerical parameter study}, series = {STAB Jahresbericht 2023}, volume = {21/2023}, journal = {STAB Jahresbericht 2023}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft (STAB)}, address = {G{\"o}ttingen, Germany}, pages = {110 -- 111}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Investigating heat transfer properties of tubular heat exchangers with a stochastic turbulence model}, series = {1st EIZ (Energie-Innovationszentrum) Annual Meeting, 24-25 April 2024, Cottbus, Germany}, journal = {1st EIZ (Energie-Innovationszentrum) Annual Meeting, 24-25 April 2024, Cottbus, Germany}, address = {Cottbus, Germany}, pages = {2}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Features of turbulent boundary layers in heated concentric coaxial pipe flow at high Reynolds and low Prandtl numbers}, series = {ICTAM 2024}, journal = {ICTAM 2024}, address = {Daegu, South Korea}, doi = {10.13140/RG.2.2.30075.12323}, pages = {1}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Investigating Prandtl number effects in heated concentric coaxial pipe flow at high Reynolds number}, series = {1st European Fluid Dynamics Conference (EFDC1), 16-20 September 2024, Aachen, Germany}, journal = {1st European Fluid Dynamics Conference (EFDC1), 16-20 September 2024, Aachen, Germany}, address = {Aachen, Germany}, pages = {1}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Theoretical analysis and stochastic modeling of turbulent heat transfer in annular pipe flows}, series = {77th Annual Meeting of the Division of Fluid Dynamics, November 24-26, 2024; Salt Lake City, Utah}, journal = {77th Annual Meeting of the Division of Fluid Dynamics, November 24-26, 2024; Salt Lake City, Utah}, publisher = {American Physical Society}, abstract = {Heat transfer in annular pipes is determined by the thermal and momentum boundary layer at the cylindrical inner and outer walls, respectively. The relative contributions are expressed by a local Nusselt number that depends on the radius ratio, the Prandtl number, and the Reynolds number. Direct numerical simulation (DNS) has been used previously to infer closure relations constrained to weakly turbulent flow due to numerical resource requirements. Here, stochastic one-dimensional turbulence (ODT) is utilized as a standalone tool as an alternative to DNS. ODT offers full-scale resolution along a representative radial domain, providing predictive capabilities relative to a calibrated reference case at a radically reduced cost. On average, ODT obeys radial balance equations compatible with the Navier-Stokes equations. Separating the boundary layer into a diffusion and a mixing-length dominated region in cylindrical geometry yields wall-curvature corrections at the inner wall. The proposed expressions can be used to enhance prescribed wall functions, for example, in Reynolds-averaged Navier-Stokes simulations.}, language = {en} } @misc{KleinZenkerStaricketal., author = {Klein, Marten and Zenker, Christian and Starick, Tommy and Schmidt, Heiko}, title = {Stochastic modeling of multi-stream mixing based on one-dimensional turbulence}, series = {77th Annual Meeting of the Division of Fluid Dynamics}, journal = {77th Annual Meeting of the Division of Fluid Dynamics}, publisher = {American Physical Society}, abstract = {Measurements of multiple scalar mixing in a turbulent jet show a strong location dependence of the scalar fluctuations and mixing processes. Mixing is quantitatively described by the state space of scalar fluctuations in terms of a joint probability density function (JPDF). The JPDF evolves in the downstream and radial directions and has non-Gaussian shape which is a burden for mixing modeling since factoring into marginal distribution functions is not permissible. Stochastic simulations based on one-dimensional turbulence (ODT) are able to reasonably reproduce the JPDF and its spatial evolution by a parabolic marching problem that circumvents constraints of the underlying elliptic problem. The model reproduces the inertial-advective range (exponent -5/3) and predicts the emergence of the viscous-advective range (exponent -1) at higher wavenumbers as the Schmidt number increases. The model offers full-scale resolution at affordable cost providing means to reasonably capture state-space statistics of turbulent mixing.}, language = {en} } @misc{KleinMedinaMendezSchoepsetal., author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Sch{\"o}ps, Mark Simon and Schmidt, Heiko and Glawe, Christoph}, title = {Towards physics-based nowcasting of the instantaneous wind velocity profile using a stochastic modeling approach}, series = {STAB Jahresbericht 2024 zum 24. DGLR-Fachsymposium der STAB, 13. - 14. November 2024, Regensburg}, journal = {STAB Jahresbericht 2024 zum 24. DGLR-Fachsymposium der STAB, 13. - 14. November 2024, Regensburg}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft, STAB}, address = {Regensburg [et al.]}, pages = {162 -- 163}, abstract = {The primary objective of this contribution is to provide an overview of the regime-spanning forward modeling capabilities offered by the stochastic one-dimensional turbulence model. The focus is on the applicability of the model and its validation for neutral and stable atmospheric boundary layer flows as a prerequisite for future applications to challenging atmospheric conditions.}, language = {en} } @misc{VallemKleinSchmidt, author = {Vallem, Rishindra and Klein, Marten and Schmidt, Heiko}, title = {Capabilities and limitations of smoothed particle hydrodynamics for the simulation of two-phase flow instabilities}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {24/2024}, journal = {Proceedings in Applied Mathematics and Mechanics}, publisher = {Wiley}, address = {Weinheim}, issn = {1617-7061}, doi = {10.1002/pamm.202400206}, pages = {15}, abstract = {Smoothed particle hydrodynamics (SPH) is a mesh-free, Lagrangian particle-based method that is able to simulate multiphase flows in an economical manner. However, its ability to capture the flow regimes and regime transitions in two phase (liquid-gas) internal flows, such as pipe or channel flows is not yet generally established. To address this lack in understanding, we first examine a laminar rising bubble case in order to evaluate the fluid-fluid interface representation and transient interface evolution by the solver. With a focus towards the transition mechanism from a stratified flow regime to a slug flow regime, we investigate the Kelvin-Helmholtz instability (KHI) both qualitatively and quantitatively, initially focusing on a low density ratio () and then extending it to a high density ratio (). For the low density ratio, we conduct an analysis of the temporal evolution and demonstrate that the SPH solver captures the initial exponential growth in qualitative agreement with inviscid linear stability theory (LST) and reference numerical data for shear-dominated flow with Richardson number . By conducting eight additional simulations for various for the high density ratio, we demonstrate that the numerically obtained parameter value for instability is around , which is in reasonable agreement with the theoretically expected value of . Based on the SPH results obtained for the range , we suggest a simple parameterization of the reduction of the effective growth rate proportional to .}, language = {en} } @misc{KleinKesslerSchmidt, author = {Klein, Marten and Kessler, Robert William and Schmidt, Heiko}, title = {Numerical investigation of drag reduction effects on a track bicycle fork using wings with a wavy leading edge}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {24}, journal = {Proceedings in Applied Mathematics and Mechanics}, publisher = {Wiley}, issn = {1617-7061}, doi = {10.1002/pamm.202400178}, pages = {1 -- 14}, abstract = {Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulations (LES) of the flow around wings with a wavy leading edge (WLE) are conducted in order to assess the capabilities of a passive flow control strategy for drag reduction. The intended application is indoor track cycling with controlled flow conditions. A section of a single fork rod is investigated in order to make the numerical simulations feasible. The present study reveals that net drag reduction is possible by a nonsinusoidal modification of the leading edge of the wing. However, the drag reduction effect remains limited to a few percent. While RANS and LES yield the same drag coefficient for a reference case, RANS underestimates the drag reduction effect for a longer wing and the WLE cases, but exhibits otherwise a qualitatively similar trend as the LES. With the aid of RANS, an optimal geometry is obtained defined by the wavelength-to-chord length ratio of and the amplitude-to-chord length ratio of . Corresponding LES results give an indication of the origin of drag reduction by a hampered vortex shedding. The generation of smaller and more streamwise oriented vortical flow structures at the trailing edge and behind the WLE wing is correlated with significantly reduced lift fluctuations and drag reduction.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Capturing features of transient boundary layers with a map-based stochastic modeling approach}, publisher = {Copernicus GmbH}, doi = {10.5194/egusphere-egu24-15560}, pages = {2}, abstract = {Atmospheric boundary layers (ABLs) exhibit transient processes on various time and length scales, with a scale separation between the large-scale forcing and the small-scale response. Some crucial but standing challenges in modeling and simulation of ABL flows lie in the detailed representation of boundary layer turbulence (e.g. [1]). This includes intermittent and transient processes and the resulting turbulent and laminar response mechanisms. State-of-the-art subgrid-scale models utilize statistical closures for an averaged resolved flow state on the basis of the Monin-Obhukov similarity theory (MOST) to represent scalar fluxes and momentum fluxes (e.g. [2]). Fluctuations are not resolved in MOST. Instead, their ensemble effect is parameterized by the resolved large scales, neglecting backscatter from the unresolved small scales. Data-driven stochastic approaches aim to incorporate fluctuations and the spontaneous occurrence of instabilities, but at the expense of ad hoc forcings (e.g. [3]). The mentioned limitations can be removed by a physically compatible representation of turbulent fluctuations. This is addressed here by utilization of a map-based stochastic approach that is based on the one-dimensional turbulence (ODT) model [4]. ODT autonomously evolves vertical flow profiles for prescribed initial and boundary conditions, and physical forcings. The model captures turbulent cascade phenomenology and aims to resolve all relevant turbulent scales along a physical coordinate. Turbulent advection is modeled by a stochastically sampled sequence of spatial mapping events that punctuate the deterministic advancement due to viscous and Coriolis forces. The offered dynamical complexity removes the need for artificial forcings. In the contribution, key results from recent and ongoing studies related to the reduced-order modeling of ABL flows will be presented. First, surface scalar and momentum fluxes in turbulent channels are discussed emphasizing the correctly predicted inapplicability of the Reynolds analogy [5]. Second, the influence of system rotation and stratification is discussed for low-order velocity statistics and the participating turbulent scales [6,7]. Third, results for nonequilibrium conditions are presented for a transient ABL that exhibits turbulent bursts in response to an oscillatory geostrophic forcing [8]. Last, some preliminary results on the stochastic deconvolution of averaged data [9] will be presented focusing on the additional physical insight that is offered by the model. References [1] L. Mahrt. Annu. Rev. Fluid Mech. 46:23-45, 2014. [2] I. Stiperski, and M. Calaf. Phys. Rev. Lett. 130:124001, 2023. [3] V. Boyko, and N. Vercauteren. Q. J. R. Meteorol. Soc. 149(755):2125-2145, 2023. [4] A. R. Kerstein, and S. Wunsch. Bound.-Lay. Meteorol. 118:325-356, 2006. [5] M. Klein, H. Schmidt, and D. Lignell. Int. J. Heat Fluid Flow 93:108889, 2022. [6] M. Klein, and H. Schmidt. Adv. Sci. Res. 19:117-136, 2022. [7] L. S. Freire. Bound.-Lay. Meteorol. 184:25-43, 2022. [8] M. Klein, and H. Schmidt. Adv. Sci. Res. 20:55-64, 2023. [9] C. Glawe, M. Klein, and H. Schmidt. Proc. Appl. Math. Mech. 23:e202300055, 202}, language = {en} }