Modeling transitional boundary layers over smooth and rough sufaces with a map-based stochastic modeling approach

Challenges in the numerical simulation of atmospheric flows persist in representing surface roughness effects and near-wall turbulence. While Monin-Obhukov similarity theory (MOST) is extensively used in many numerical solvers due to it's simplicity and efficiency, its limitations are well known, prominently under very stable stratification and over rough surfaces (e.g., [1, 2]). The binding element is the atmospheric surface layer that exhibits strong variability in structure and thickness. Emerging dynamical features, in particular intermittency and laminar-turbulent transitions, present core challenges for advanced surface-flux parameterization. Here, an idealized Atmospheric Boundary Layer (ABL), the so-called Ekman Boundary Layer (EBL) is numerically analyzed to address some of the aforementioned challenges utilizing the dimensionally reduced, stochastic One-Dimensional Turbulence (ODT) model. ODT was applied previously as a stand-alone tool to stratified EBL flows over (almost) smooth and very rough surfaces [3, 4, 5], demonstrating predictive capabilities relevant for developing advanced wall models. Recently, the model has been utilized to obtain homogeneous roughness parameterizations for various types of surfaces in channel flow, demonstrating forward modeling capabilities for the Reynolds shear stress otherwise prescribed, e.g., in widely used Reynolds-averaged Navier-Stokes models [6]. In the contribution, the model's capabilities to capture turbulent-laminar regime transitions are discussed and ongoing work on parameterization for dynamic effects associated with roughness-induced drag is presented. References[1] M. Optis, A. Monahan, F. C. Bosveld (2016). Limitations and breakdown of Monin–Obukhov similarity theory for wind profile extrapolation under stable stratification. Wind Energy, 19, 1053–1072. https://doi.org/10.1002/we.1883[2] J. Kostelecky, C. Ansorge (2025). Surface roughness in stratified turbulent Ekman flow. Boundary-Layer Meteorology, 191, 5. https://doi.org/10.1007/s10546-024-00895-5[3] A. R. Kerstein, S. Wunsch (2006). Simulation of a Stably Stratified Atmospheric Boundary Layer Using One-Dimensional Turbulence. Boundary-Layer Meteorology, 118, 325-356. https://doi.org/10.1007/s10546-005-9004-x[4] L. S. Freire, M. Chamecki (2018). A one-dimensional stochastic model of turbulence within and above plant canopies. Agricultural and Forest Meteorology, 250-251, 9-23. https://doi.org/10.1016/j.agrformet.2017.12.211[5] M. Klein, H. Schmidt (2022). Exploring stratification effects in stable Ekman boundary layers using a stochastic one-dimensional turbulence model. Advances in Science and Research, 19, 117-136. https://doi.org/10.5194/asr-19-117-2022[6] J. A. Medina Méndez, M. Klein, J. W. R. Peeters, H. Schmidt (2026). International Journal of Heat and Fluid Flow, 117, 110113. https://doi.org/10.1016/j.ijheatfluidflow.2025.110113