TY - GEN A1 - Klein, Marten A1 - Lignell, David O. A1 - Schmidt, Heiko T1 - Map-Based Modeling of Turbulent Convection: Application of the One-Dimensional Turbulence Model to Planar and Spherical Geometries KW - turbulent convection KW - stochastic modeling KW - boundary layer Y1 - 2018 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_poster_rbc18.pdf UR - https://www.researchgate.net/publication/325155414_Map-Based_Modeling_of_Turbulent_Convection_Application_of_the_One-Dimensional_Turbulence_Model_to_Planar_and_Spherical_Geometries ER - TY - GEN A1 - Klein, Marten A1 - Lignell, David O. A1 - Schmidt, Heiko T1 - Stochastic modeling of transient surface scalar and momentum fluxes in turbulent boundary layers T2 - EMS Annual Meeting 2021, online, 6–10 Sep 2021, EMS2021-79 N2 - 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. KW - one-dimensional turbulence KW - stochastic modeling KW - Ekman flow KW - atmospheric boundary layer KW - roating and stratified fluids Y1 - 2021 UR - https://doi.org/10.5194/ems2021-79 UR - https://www.b-tu.de/media/video/Stochastic-modeling-of-transient-surface-scalar-and-momentum-fluxes-in-turbulent-boundary-layers/8c7baf58c040239649fb7c3b2212c1d5 U6 - https://doi.org/10.5194/ems2021-79 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko A1 - Lignell, David O. T1 - Stochastic modeling of transient surface scalar and momentum fluxes in turbulent boundary layers, EMS Annual Meeting 2021, online, 6–10 Sep 2021 KW - one-dimensional turbulence KW - stochastic modeling KW - Ekman flow KW - atmospheric boundary layer KW - roating and stratified fluids Y1 - 2021 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_poster_ems21.pdf UR - https://www.b-tu.de/media/video/Stochastic-modeling-of-transient-surface-scalar-and-momentum-fluxes-in-turbulent-boundary-layers/8c7baf58c040239649fb7c3b2212c1d5 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko A1 - Lignell, David O. T1 - Stochastic modeling of surface scalar-flux fluctuations in turbulent channel flow using one-dimensional turbulence T2 - International Journal of Heat and Fluid Flow N2 - 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. KW - one-dimensional turbulence KW - stochastic modeling KW - fluctuation modeling KW - passive scalar KW - scalar transfer KW - Schmidt number dependence KW - surface flux Y1 - 2021 UR - https://arxiv.org/abs/2111.15359 U6 - https://doi.org/10.1016/j.ijheatfluidflow.2021.108889 SN - 0142-727X VL - 93 (2022) SP - 1 EP - 19 ER - TY - GEN A1 - Klein, Marten A1 - Freire, Livia S. A1 - Lignell, David O. A1 - Kerstein, Alan R. A1 - Schmidt, Heiko T1 - Ein stochastischer Ansatz zur Modellierung fluktuierender Oberflächenflüsse in turbulenten Grenzschichten T2 - Kurzfassungen der Meteorologentagung DACH N2 - Im Konferenzbeitrag wird auf die Formulierung des stochastischen Modells eingegangen und gezeigt, dass neben Scherspannungen auch Druck-, Coriolis- und Auftriebskräfte berücksichtigt werden können. Das Modell wird beispielhaft als unabhängiges, numerisches Werkzeug angewendet, um fluktuierende Oberflächenflüsse in turbulenten Kanalströmungen sowie stabilen und konvektiven Grenzschichten zu untersuchen. Es werden sowohl glatte, als auch raue bzw. bewachsene (poröse) Oberflächen 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 oberflächennaher, subgitterskaliger Schwankungen in der Lage ist, wandnahe Turbulenzspektren zu reproduzieren und den filterbasierten Modellfehler bei ansonsten fester Gitterauflösung zu verringern. KW - one-dimensional turbulence KW - stochastic modeling KW - turbulent boundary layer KW - turbulent convection KW - rotating and stratified flows Y1 - 2021 UR - https://meetingorganizer.copernicus.org/DACH2022/DACH2022-22.html U6 - https://doi.org/10.5194/dach2022-22 VL - 2022 SP - 1 EP - 1 PB - Copernicus ER - TY - GEN A1 - Lignell, David O. A1 - Behrang, Masoomeh A1 - Kerstein, Alan R. A1 - Wheeler, Isaac A1 - Starick, Tommy A1 - Schmidt, Heiko T1 - Investigation of turbulent mixing of scalars with arbitrary Schmidt numbers using the stochastic Hierarchical Parcel Swapping Model T2 - 77th Annual Meeting of the Division of Fluid Dynamics, November 24–26, 2024; Salt Lake City, Utah N2 - 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. KW - turbulent mixing KW - variable Schmidt number KW - stochastic modeling KW - hierarchical parcel swapping Y1 - 2024 UR - https://meetings.aps.org/Meeting/DFD24/Session/X39.11 PB - American Physical Society ER -