Capturing features of transient boundary layers with a map-based stochastic modeling approach
Authors: Klein Marten , Schmidt Heiko 
Published: March 2024

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&#8211;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.&#160;&#160;References[1] L. Mahrt. Annu. Rev. Fluid Mech. 46:23&#8211;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&#8211;2145, 2023.[4] A. R. Kerstein, and S. Wunsch. Bound.-Lay. Meteorol. 118:325&#8211;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&#8211;136, 2022.[7] L. S. Freire. Bound.-Lay. Meteorol. 184:25&#8211;43, 2022.[8] M. Klein, and H. Schmidt. Adv. Sci. Res. 20:55&#8211;64, 2023.[9] C. Glawe, M. Klein, and H. Schmidt. Proc. Appl. Math. Mech. 23:e202300055, 2023.