Numerical simulation and analysis of transient Ekman boundary layers using a stochastic turbulence model

Atmospheric boundary layers (ABLs) govern the atmosphere–surface coupling and are therefore of fundamental relevance for Earth’s weather and climate system. Key challenges in modeling and simulation of ABLs arise from the emerging spatio-temporal variability that manifests itself by fluctuating transport processes and intermittency on multiple scales (e.g. [1,2]). Observed flow features are the result of interacting inertial, Coriolis, buoyancy, and viscous forces, acting on all relevant scales of the turbulent flow. Small-scale processes, even if nonuniversal in nature, are usually not resolved due to cost constraints but modeled based on justified physical or empirical relations with the resolved scales, neglecting expensive backscatter (e.g. [3]). This issue is addressed here by a stochastic forward model, the so-called one-dimensional turbulence (ODT) model [4], which allows to preserve small-scale information in a feasible manner. In the ABL, ODT autonomously evolves flow profiles for prescribed initial and boundary conditions. Turbulent advection is modeled by a stochastically sampled sequence of mapping events that punctuate the deterministic advancement of molecular-diffusive processes and Coriolis forces. The model aims to reproduce turbulent cascade phenomenology, resolved along a notional vertically oriented line-of-sight, respecting fundamental physical conservation principles. The dynamical complexity of the model arises from a physically based feedback of the evolving flow state on the stochastic sampling procedure.

In this study, ODT is utilized as standalone tool for the numerical simulation of fluctuating wind velocity and temperature profiles in temporally developing neutral and stably stratified ABLs [5]. Comparison with available reference data shows that the model is able to reasonably reproduce conventional low-order but also detailed flow statistics for fixed model parameters. The model exhibits scale-selective buoyancy damping, but is unable to completely capture the relaminarization under prescribed, but developing, very stable conditions. This can be attributed to the model’s resistance against leaving the fully developed turbulent state. Forthcoming research addresses fluctuations and intermittency effects. For the latter, an event-based clustering approach is presented that aims to identify turbulent cascade events across flow regimes, yielding new possibilities for the analysis and prediction of turbulent time series.

References

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[5] M. Klein, and H. Schmidt. Adv. Sci. Res. 19:117–136, 2022.