@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{LignellBehrangKersteinetal., author = {Lignell, David O. and Behrang, Masoomeh and Kerstein, Alan R. and Wheeler, Isaac and Starick, Tommy and Schmidt, Heiko}, title = {Investigation of turbulent mixing of scalars with arbitrary Schmidt numbers using the stochastic Hierarchical Parcel Swapping Model}, 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 = {Hierarchical Parcel Swapping (HiPS) is a stochastic model of turbulent mixing. HiPS is based on a binary tree structure consisting of nodes emanating from the top of the tree and terminating in parcels at the base of the tree containing fluid properties. Length scales decrease geometrically with increasing tree level, and corresponding time scales follow inertial range scaling. Turbulent mixing is modeled by swapping subtrees at different tree levels. Swaps involving single parcels result in micromixing that changes scalar states. Swaps are implemented as a Poisson process at rates corresponding to level time scales. HiPS is extended to simulation of multiple scalars with arbitrary diffusivities, considering transport in the inertial, viscous-advective, and inertial-diffusive ranges. Fundamental analysis of particle dispersion is presented with comparisons to theoretical results and DNS data in the inertial and viscous ranges. Scalar energy spectra are analysed in the three ranges and reproduce known scaling exponents. Scalar dissipation statistics are analysed and reproduce the experimental and theoretical lognormal distribution with negative skewness represented by a stretched-exponential function. DNS data are used to evaluate empirical coefficients, facilitating quantitative applications. The physical fidelity demonstrated with HiPS suggests its use as a low-cost subgrid model for coarse-grained flow simulation, for which parcel-pair mixing is a common treatment.}, language = {en} } @misc{KleinMedinaMendezSchmidt, author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Resolving the electrostatic boundary layer in a turbulent electrohydrodynamic flow with a map-based stochastic modeling approach}, series = {1st European Fluid Dynamics Conference - Daily Scientific Program}, journal = {1st European Fluid Dynamics Conference - Daily Scientific Program}, address = {Aachen}, pages = {1}, abstract = {Electrohydrodynamically (EHD) enhanced wall-bounded turbulent flows are encountered in various technical applications ranging from air-cleaning devices (like precipitators) to electrolyte flows (like redox flow batteries). The multi-physical processes governing the flow properties, however, are not yet very well understood. This is due the inaccessibility to and limitations of measurement equipment and numerical resolution requirements imposed by the electrostatic charge boundary layer that interacts on different time scales with the turbulent boundary layer. Recent advances in measurement techniques allow to resolve the exponential electrostatic charge boundary layer in a charged particle-ladden, weakly turbulent gas flow [1], which is qualitatively compatible with direct numerical simulation (DNS) results for a weakly turbulent flow of an electrolyte [2] at low Reynolds (Re) number. The challenge that remains is the extrapolation to highly turbulent flow conditions. Charged particles are heavy compared with fluid molecules and can be treated as a high Schmidt (Sc) number scalar, which is a burden for DNS. In this contribution, it is demonstrated that this burden can be overcome for the transient boundary layer evolution by utilizing a radically reduced, map-based stochastic one-dimensional turbulence (ODT) model. The model predicts a significant enhancement of the skin friction drag due to turbulence-induced screening layer depletion [3], as summarized in Fig. 1. In the talk, features of the instantaneous and mean velocity and electrostatic boundary layer will be presented. The plausibility of the model prediction is evaluated on a physical basis, encompassing details of the model formulation and the emerging hydrodynamic and electrokinetic properties of the boundary layer. References [1] W. Xu, S. Jantaˇc, T. Matsuyama, and H. Grosshans. arXiv:2306.06970, 2023. (Accepted for publication by Exp. Fluids.) [2] R. Ostilla-M´onico, and A. A. Lee. Faraday Discuss., 199:159-173, 2017. [3] M. Klein, J. A. Medina M´endez, and H. Schmidt. Tech. Mech., 43:111-127, 2023.}, 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} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Investigating Reynolds number effects in turbulent concentric coaxial pipe flow using stochastic one-dimensional turbulence modeling}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {23}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {4}, issn = {1617-7061}, doi = {10.1002/pamm.202300167}, pages = {1 -- 8}, abstract = {The present study numerically investigates turbulent momentum transfer in concentric coaxial (annular) pipe flow with small radius ratios (𝜂 = 𝑅𝑖∕𝑅𝑜 = 0.1,0.04,0.02). To model the flow, a stochastic one-dimensional turbulence (ODT) model formulated for cylindrical geometry is used that provides full-scale resolution along a representative radial coordinate. The present investigation extends the model validation by Tsai et al. (PAMM,22:e202200272, 2023), to radius ratios smaller than 0.1 and addresses boundary layers with strong span-wise curvature effects. The focus is on the assessment and analysis of statistical flow features in the vicinity of the inner cylinder wall, particularly in cases with small radius ratios. Following Boersma \& Breugem (Flow Turbul. Com-bust.,86:113-127, 2011), classical boundary-layer and mixing-length theory is utilized to analyze the model predictions. The results demonstrate that the ODT model captures leading-order curvature and mixing-length effects by its physics-compatible construction. Utilizing the model for extrapolation to high Reynolds numbers inaccessible to conventional high-fidelity numerical approaches shows that curvature effects persist and nonlocally affect the entire boundary layer. The model results provide support for a spanwise-curvature-modified wall function.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Capturing features of turbulent Ekman-Stokes boundary layers with a stochastic modeling approach}, series = {Advances in Science and Research}, volume = {20}, journal = {Advances in Science and Research}, issn = {1992-0636}, doi = {10.5194/asr-20-55-2023}, pages = {55 -- 64}, abstract = {Atmospheric boundary layers (ABLs) exhibit transient processes on various time scales that range from a few days down to seconds, with a scale separation of the large-scale forcing and the small-scale turbulent response. One of the standing challenges in modeling and simulation of ABLs is a physically based representation of complex multiscale boundary layer dynamics. In this study, an idealized time-dependent ABL, the so-called Ekman-Stokes boundary layer (ESBL), is considered as a simple model for the near-surface flow in the mid latitudes and polar regions. The ESBL is driven by a prescribed temporal modulation of the bulk-surface velocity difference. A stochastic one-dimensional turbulence (ODT) model is applied to the ESBL as standalone tool that aims to resolve all relevant scales of the flow along a representative vertical coordinate. It is demonstrated by comparison with reference data that ODT is able to capture relevant features of the time-dependent boundary layer flow. The model predicts a parametric enhancement of the bulk-surface coupling in the event of a boundary layer resonance when the flow is forced with the local Coriolis frequency. The latter reproduces leading order effects of the critical latitudes. The model results suggest that the bulk flow decouples from the surface for high forcing frequencies due to a relative increase in detached residual turbulence.}, 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{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{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{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{KleinMedinaMendezSchmidt, author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Simulating Volatile Wind Energy: Stochastic Forward Modeling and Machine Learning}, publisher = {Innovation Hub 13, TH Wildau}, address = {Wildau}, pages = {1}, abstract = {The transformation of the energy sector is based on the integration of various renewable sources, such as wind and solar energy. One of the key challenges for the integration of these sources into the existing power grid is their erratic and sometimes discontinuous availability (volatility). Wind energy is one of the most relevant sources of CO2 neutral electric energy, but volatile due to fluctuating wind fields on multiple scales. This has already been realized so that senors provide real-time information on the scale of individual wind turbines. However, fore- casting remains an unresolved problem since numerical weather prediction models cannot provide the necessary level of detail. New modeling strategies are required that integrate turbine-scale and meso-scale information for accurate site-specific short-term prediction. Present and forthcoming research aims to incorporate fluctuations on multiple levels of fidelity, depending on the abstraction layer}, language = {en} } @misc{KleinZenkerStaricketal., author = {Klein, Marten and Zenker, Christian and Starick, Tommy and Schmidt, Heiko}, title = {Stochastic modeling of three-scalar mixing in a coaxial jet using one-dimensional turbulence}, series = {12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12), Osaka, Japan (Online), July 19-22, 2022}, journal = {12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12), Osaka, Japan (Online), July 19-22, 2022}, pages = {1 -- 6}, abstract = {Modeling complex mixing processes is a standing challenge for a number of applications ranging from chemical to mechanical and environmental engineering. Here, the gas-phase turbulent mixing in a three-stream concentric coaxial jet is investigated as a canonical problem. Reynolds-averaged Navier-Stokes simulations (RANS) suggest that the gas-phase mixing can be accurately modeled by air doped with passive scalars, for which small-scale resolving numerical simulations are performed with the one-dimensional turbulence (ODT) model as stand-alone tool. We show that both the spatial (S-ODT) and temporal (T-ODT) model formulations yield qualitatively similar results exhibiting reasonable to good agreement with available reference experiments, Reynolds-averaged and large-eddy simulations, as well as mixing models. This is demonstrated for low-order statistics, like the scalar variance and dissipation, but also the two-scalar joint probability density functions that can not be obtained with RANS. Our results suggest that S-ODT has better capabilities than T-ODT to model the mixing processes in the jet which we attribute to the account of local advective time scales.}, language = {en} } @misc{KleinMedinaMendezSchmidt, author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Modeling electrohydrodynamically enhanced drag in channel and pipe flows using One-Dimensional Turbulenc}, series = {Proceedings of the Conference on Modelling Fluid Flow (CMFF'22)}, journal = {Proceedings of the Conference on Modelling Fluid Flow (CMFF'22)}, editor = {Vad, Janos}, publisher = {University of Technology and Economics, Department of Fluid Mechanics}, address = {Budapest, Hungary}, isbn = {978-963-421-881-4}, pages = {82 -- 91}, abstract = {The joint modeling of flow hydrodynamics and electrokinetics is a relatively unexplored area of turbulent flow research. We address a lack of available models for electrohydrodynamic (EHD) turbulent flow utilizing a lower-order approach, the stochastic One-Dimensional Turbulence (ODT) model. ODT is constructed on the principles of the direct energy cascade of Navier-Stokes turbulence, with key emphasis on the accurate resolution of the small molecular transport scales within a notional line-of-sight. We investigate two canonical flow configurations to demonstrate the applicability of the model in the simulation of EHD flows. First, we investigate EHD effects in zero-pressure-gradient turbulent boundary layers by two-way coupled model application to plane Couette flow of a dilute electrolyte. Second, we apply the one-way coupled model to EHD-enhanced gas flow through a vertical pipe with an inner concentric electrode, where electric fields are generated by means of a corona discharge and the corresponding effect of a continuum ionic charge density field.}, language = {en} } @misc{SharmaKleinSchmidt, author = {Sharma, Sparsh and Klein, Marten and Schmidt, Heiko}, title = {Features of far-downstream asymptotic velocity fluctuations in a round jet: A one-dimensional turbulence study}, series = {Physics of Fluids}, volume = {34}, journal = {Physics of Fluids}, number = {8}, issn = {1089-7666}, doi = {10.1063/5.0101270}, language = {en} } @misc{KleinMedinaMendezSchmidt, author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Modeling electrohydrodynamically enhanced drag in channel and pipe flows using one-dimensional turbulence}, series = {Conference on Modelling Fluid Flow (CMFF'22)}, journal = {Conference on Modelling Fluid Flow (CMFF'22)}, address = {Budapest, Hungary}, pages = {1 -- 8}, language = {en} } @misc{KleinTsaiSchmidt, author = {Klein, Marten and Tsai, Pei-Yun and Schmidt, Heiko}, title = {Stochastic modeling of heat and momentum transfer in annular pipe flow: A one-dimensional turbulence study with comparison to DNS and LES}, series = {STAB Jahresbericht 2022}, volume = {23}, journal = {STAB Jahresbericht 2022}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft (STAB)}, address = {G{\"o}ttingen, Germany}, language = {en} } @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 = {92nd Annual Meeting of GAMM}, journal = {92nd Annual Meeting of GAMM}, publisher = {Gesellschaft f{\"u}r angewandte Mathematik und Mechanik e.V.}, address = {Aachen, Germany}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic modeling of transient Ekman flow at arbitrary Reynolds number driven by horizontal bottom wall oscillation}, series = {EMS Annual Meeting 2022, Abstracts}, volume = {19}, journal = {EMS Annual Meeting 2022, Abstracts}, publisher = {Copernicus}, address = {Bonn, Germany}, doi = {10.5194/ems2022-617}, language = {en} } @misc{SharmaKleinSchmidt, author = {Sharma, Sparsh and Klein, Marten and Schmidt, Heiko}, title = {Modelling turbulent jets at high-Reynolds number using one-dimensional turbulence}, series = {AIAA AVIATION 2021 FORUM}, journal = {AIAA AVIATION 2021 FORUM}, publisher = {American Institute of Aeronautics and Astronautics, Inc.}, isbn = {978-1-62410-610-1}, doi = {10.2514/6.2021-2104}, language = {en} } @misc{KleinFreireLignelletal., author = {Klein, Marten and Freire, Livia S. and Lignell, David O. and Kerstein, Alan R. and Schmidt, Heiko}, title = {Ein stochastischer Ansatz zur Modellierung fluktuierender Oberfl{\"a}chenfl{\"u}sse in turbulenten Grenzschichten}, series = {Kurzfassungen der Meteorologentagung DACH}, volume = {2022}, journal = {Kurzfassungen der Meteorologentagung DACH}, publisher = {Copernicus}, doi = {10.5194/dach2022-22}, pages = {1 -- 1}, abstract = {Im Konferenzbeitrag wird auf die Formulierung des stochastischen Modells eingegangen und gezeigt, dass neben Scherspannungen auch Druck-, Coriolis- und Auftriebskr{\"a}fte ber{\"u}cksichtigt werden k{\"o}nnen. Das Modell wird beispielhaft als unabh{\"a}ngiges, numerisches Werkzeug angewendet, um fluktuierende Oberfl{\"a}chenfl{\"u}sse in turbulenten Kanalstr{\"o}mungen sowie stabilen und konvektiven Grenzschichten zu untersuchen. Es werden sowohl glatte, als auch raue bzw. bewachsene (por{\"o}se) Oberfl{\"a}chen betrachtet. Anhand neuer Ergebnisse wird demonstriert, dass der Modellansatz in der Lage ist, Referenzdaten zufriedenstellend zu reproduzieren und extrapolieren. Daneben werden aktuelle Arbeiten zur Kopplung des stochastischen Modellansatzes mit Large-Eddy-Simulationen vorgestellt. Es wird gezeigt, dass die stochastische Modellierung oberfl{\"a}chennaher, subgitterskaliger Schwankungen in der Lage ist, wandnahe Turbulenzspektren zu reproduzieren und den filterbasierten Modellfehler bei ansonsten fester Gitteraufl{\"o}sung zu verringern.}, language = {de} } @misc{KleinMaierSchmidt, author = {Klein, Marten and Maier, Roland Erich and Schmidt, Heiko}, title = {Stochastic modeling of transient neutral and stably-stratified Ekman boundary layers}, series = {Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)}, volume = {21}, journal = {Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)}, publisher = {Wiley}, address = {Weinheim}, doi = {10.1002/pamm.202100146}, pages = {1 -- 3}, abstract = {Neutral and stably-stratified Ekman boundary layers (EBLs) are numerically investigated with a stochastic one-dimensional turbulence (ODT) model. EBLs achieve the bulk-surface coupling in Earth's atmosphere. They are numerically challenging due to transient and non-universal turbulence properties even at small scales. ODT addresses this problem by distinguishing turbulent-advective from molecular-diffusive transport processes for a vertical column along which all relevant scales of the flow are resolved. We demonstrate the model's capabilities for economical, accurate, and stratification regime independent simulation of EBLs for the wind-turning angle. ODT reproduces and extrapolates reference direct numerical simulation results consistent with observations. We conclude that ODT may be useful for modeling of atmospheric surface layers.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Investigating Schmidt number effects in turbulent electroconvection using one-dimensional turbulence}, series = {Proc. Appl. Math. Mech.}, volume = {21}, journal = {Proc. Appl. Math. Mech.}, publisher = {Wiley}, address = {Weinheim}, doi = {https://doi.org/10.1002/pamm.202100147}, pages = {1 -- 3}, abstract = {Turbulent electroconvection denotes a fluctuating multiphysical flow in which hydrodynamics and electrokinetics interact on multiple scales. The dynamical processes at work are entangled down to the molecular-diffusive scales that are determined by the Schmidt (Sc) and Reynolds (Re) number. Turbulence properties are generally nonuniversal which leads to high numerical resolution requirements. We address the numerical challenges associated with accuracy and feasibility by utilizing a stochastic one-dimensional turbulence (ODT) model. Here, ODT is applied to turbulent Couette flow of dilute electrolytes as canonical problem for turbulent electroconvection. For Sc ⩾ O(10), ODT predicts an increase of the skin friction drag due to electrohydrodynamically (EHD) enhanced small-scale eddy production once the flow is sufficiently turbulent.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic modeling and simulation of turbulent boundary layers in annular channel flow using one-dimensional turbulence}, series = {STAB Jahresbericht 2021}, volume = {2021}, journal = {STAB Jahresbericht 2021}, editor = {Wagner, Claus}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft, STAB}, address = {G{\"o}ttingen}, pages = {39 -- 40}, abstract = {In our contribution to the STAB workshop we will present the ODT model formulation with an emphasis on turbulent eddy energetics and map-based advection modeling in radial direction. After that, we will address ODT's capabilities for simulation of turbulent boundary layers in planar and annular channel flows in terms of conventional turbulence statistics and bulk quantities. Last, we will address the effects of radius ratio and Reynolds number variations.}, language = {en} } @misc{KleinSchmidtLignell, author = {Klein, Marten and Schmidt, Heiko and Lignell, David O.}, title = {Stochastic modeling of surface scalar-flux fluctuations in turbulent channel flow using one-dimensional turbulence}, series = {International Journal of Heat and Fluid Flow}, volume = {93 (2022)}, journal = {International Journal of Heat and Fluid Flow}, issn = {0142-727X}, doi = {10.1016/j.ijheatfluidflow.2021.108889}, pages = {1 -- 19}, abstract = {Accurate and economical modeling of near-surface transport processes is a standing challenge for various engineering and atmospheric boundary-layer flows. In this paper, we address this challenge by utilizing a stochastic one-dimensional turbulence (ODT) model. ODT aims to resolve all relevant scales of a turbulent flow for a one-dimensional domain. Here ODT is applied to turbulent channel flow as stand-alone tool. The ODT domain is a wall-normal line that is aligned with the mean shear. The free model parameters are calibrated once for the turbulent velocity boundary layer at a fixed Reynolds number. After that, we use ODT to investigate the Schmidt (Sc), Reynolds (Re), and Peclet (Pe) number dependence of the scalar boundary-layer structure, turbulent fluctuations, transient surface fluxes, mixing, and transfer to a wall. We demonstrate that the model is able to resolve relevant wall-normal transport processes across the turbulent boundary layer and that it captures state-space statistics of the surface scalar-flux fluctuations. In addition, we show that the predicted mean scalar transfer, which is quantified by the Sherwood (Sh) number, self-consistently reproduces established scaling regimes and asymptotic relations. For high asymptotic Sc and Re, ODT results fall between the Dittus-Boelter, Sh ∼ Re^(4/5) Sc^(2/5), and Colburn, Sh ∼ Re^(4/5) Sc^(1/3), scalings but they are closer to the former. For finite Sc and Re, the model prediction reproduces the relation proposed by Schwertfirm and Manhart (Int. J. Heat Fluid Flow, vol. 28, pp. 1204-1214, 2007) that yields locally steeper effective scalings than any of the established asymptotic relations. The model extrapolates the scalar transfer to small asymptotic Sc ≪ Re_τ^(-1) (diffusive limit) with a functional form that has not been previously described.}, language = {en} } @misc{KleinLignellSchmidt, author = {Klein, Marten and Lignell, David O. and Schmidt, Heiko}, title = {Stochastic modeling of transient surface scalar and momentum fluxes in turbulent boundary layers}, series = {EMS Annual Meeting 2021, online, 6-10 Sep 2021, EMS2021-79}, journal = {EMS Annual Meeting 2021, online, 6-10 Sep 2021, EMS2021-79}, doi = {10.5194/ems2021-79}, abstract = {Turbulence is ubiquitous in atmospheric boundary layers and manifests itself by transient transport processes on a range of scales. This range easily reaches down to less than a meter, which is smaller than the typical height of the first grid cell layer adjacent to the surface in numerical models for weather and climate prediction. In these models, the bulk-surface coupling plays an important role for the evolution of the atmosphere but it is not feasible to fully resolve it in applications. Hence, the overall quality of numerical weather and climate predictions crucially depends on the modeling of subfilter-scale transport processes near the surface. A standing challenge in this regard is the robust but efficient representation of transient and non-Fickian transport such as counter-gradient fluxes that arise from stratification and rotation effects. We address the issues mentioned above by utilizing a stochastic one-dimensional turbulence (ODT) model. For turbulent boundary layers, ODT aims to resolve the wall-normal transport processes on all relevant scales but only along a single one-dimensional domain (column) that is aligned with the vertical. Molecular diffusion and unbalanced Coriolis forces are directly resolved, whereas effects of turbulent advection and stratification are modeled by stochastically sampled sequence of mapping (eddy) events. Each of these events instantaneously modifies the flow profiles by a permutation of fluid parcels across a selected size interval. The model is of lower order but obeys fundamental conservation principles and Richardson's 1/4 law by construction. In this study, ODT is applied as stand-alone tool in order to investigate nondimensional control parameter dependencies of the scalar and momentum transport in turbulent channel, neutral, and stably-stratified Ekman flows up to (friction) Reynolds number Re = O(104). We demonstrate that ODT is able to capture the state-space statistics of transient surface fluxes as well as the boundary-layer structure and nondimensional control parameter dependencies of low-order flow statistics. Very good to reasonable agreement with available reference data is obtained for various observables using fixed model set-ups. We conclude that ODT is an economical turbulence model that is able to not only capture but also predict the wall-normal transport and surface fluxes in multiphysics turbulent boundary layers.}, language = {en} } @misc{KleinSchmidtLignell, author = {Klein, Marten and Schmidt, Heiko and Lignell, David O.}, title = {Stochastic modeling of transient surface scalar and momentum fluxes in turbulent boundary layers, EMS Annual Meeting 2021, online, 6-10 Sep 2021}, pages = {1}, language = {en} } @misc{KleinZenkerSchmidt, author = {Klein, Marten and Zenker, Christian and Schmidt, Heiko}, title = {Map-based stochastic modeling of turbulent mixing in transient shear flows}, series = {MATH+ CECAM Discussion Meeting on Generalized Langevin Equations}, journal = {MATH+ CECAM Discussion Meeting on Generalized Langevin Equations}, pages = {1}, abstract = {Map-based stochastic modeling distinguishes molecular-diffusive from turbulent-advective transport processes in fluid flows. In the one-dimensional turbulence (ODT) model, a stochastic point process with energetically constrained rejection sampling of discrete eddy events is used to economically model the effects of turbulence on all relevant scales of the flow. Here I will discuss the model formulation and its application to passive scalar mixing in a confined jet. [1] M. Klein, C. Zenker, H. Schmidt (2019) Chem. Eng. Sci. 204:186-202}, language = {en} } @misc{RakhiKleinMedinaMendezetal., author = {Rakhi, Rakhi and Klein, Marten and Medina M{\´e}ndez, Juan Ali and Schmidt, Heiko}, title = {One-dimensional turbulence modelling of incompressible temporally developing turbulent boundary layers with comparison to DNS}, series = {Journal of Turbulence}, volume = {20}, journal = {Journal of Turbulence}, number = {8}, issn = {1468-5248}, doi = {10.1080/14685248.2019.1674859}, pages = {506 -- 543}, abstract = {The incompressible temporally developing turbulent boundary layer (TBL) is analysed using the map-based stochastic one-dimensional turbulence (ODT) model. The TBL is a canonical flow problem, which is, in the present study, formed by a planar moving wall and a free stream at rest. An understanding of this idealised flow is of fundamental relevance for the numerical analysis of turbulent boundary-layer-type flows. In the present ODT simulations, the flow variables are resolved on all scales along a wall-normal, one-dimensional domain. These variables are evolved by a deterministic and a stochastic process. The latter models the effect of turbulent advection and pressure fluctuations, whereas the former represents molecular diffusion. The model is appropriate for high Reynolds numbers for which the turbulence field exhibits a broad range of scales and is notionally featureless. We show that ODT is able to capture salient features of the TBL by comparing the various statistics with available reference direct numerical simulation (DNS) results for different bulk Reynolds numbers in the range 250 ≤ Reb ≤ 2000 using fixed model parameters. The influence of the model parameters is analysed for Reb = 1000 and optimal parameter values are provided. The results discussed in this paper suggest that ODT is an economical and reasonably accurate approach for the simulation of transient turbulent boundary-layer-type flows.}, language = {en} } @misc{KleinLignellSchmidt, author = {Klein, Marten and Lignell, David O. and Schmidt, Heiko}, title = {Map-Based Modeling of Turbulent Convection: Application of the One-Dimensional Turbulence Model to Planar and Spherical Geometries}, pages = {1}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Map-based Modeling of Turbulent Boundary Layers Subject to Rotation and Stratification}, pages = {1}, language = {en} } @inproceedings{RiepinMoebiusMuesgens, author = {Riepin, Iegor and M{\"o}bius, Thomas and M{\"u}sgens, Felix}, title = {Integrated Electricity and Gas Market Modeling - Effects of Gas Demand Uncertainty}, series = {15th International Conference on the European Energy Market (EEM), 27-29 June 2018, Lodz, Poland}, booktitle = {15th International Conference on the European Energy Market (EEM), 27-29 June 2018, Lodz, Poland}, publisher = {IEEE}, address = {Piscataway, NJ}, isbn = {978-1-5386-1488-4}, doi = {10.1109/EEM.2018.8469790}, pages = {5}, abstract = {This paper develops an integrated fundamental investment model which considers both the gas and electricity sector. Furthermore, we adopt the theory of stochastic programming with recourse in the combined model to account for uncertainty in the gas market. This approach enables us to analyze how uncertain gas demand in other sectors affects decisions to invest in electricity generation capacities. We find an overall decrease and a reallocation of investments in gas-fired power plants. We also quantify the expected costs of ignoring uncertainty.}, language = {en} }