EGU22-1432, updated on 27 Mar 2022
EGU General Assembly 2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

A Wavenumber–Frequency Spectrum Model for Sheared Convective Atmospheric Boundary Layer Flows

Naseem Ali1, Juan Pedro Mellado2, and Michael Wilczek1,3
Naseem Ali et al.
  • 1Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg 17, 37077 Göttingen, Germany (
  • 2Department of Earth System Sciences, University of Hamburg, Bundesstraße 55, 20146 Hamburg, Germany (
  • 3Theoretical Physics I, University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany (

Turbulence in the atmospheric boundary layer (ABL) plays an important role in the weather and climate system as it governs the meteorological exchanges of momentum, energy, and moisture between the free atmosphere and the Earth’s surface. Motivated by the need for conceptual physics-based models that parameterize turbulence in the ABL in terms of spectra at all spatio-temporal scales, we explore a linear random advection approach to characterize different scenarios of sheared convective boundary layer flows. As a main result, we obtain the wavenumber–frequency spectrum as a product of the wavenumber spectrum and a Gaussian frequency distribution, whose mean and variance are given by the mean advection and random sweeping velocities, respectively. The applicability of the model is evaluated with direct numerical simulations of the mixed layer and entrainment zone for the streamwise and vertical velocity components as well as buoyancy. To obtain a fully analytical formula for the linear random advection approach, we propose using a von-Kàrmàn wavenumber spectrum parameterized by the characteristic convective velocity and length scales. These scales are height-dependent and vary considerably with the relative balance of buoyancy and shear forces. The comparison of the von-Kàrmàn-based model for velocity and buoyancy to simulation results shows that the main features of the measured spectra are captured by the model. 

How to cite: Ali, N., Mellado, J. P., and Wilczek, M.: A Wavenumber–Frequency Spectrum Model for Sheared Convective Atmospheric Boundary Layer Flows, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1432,, 2022.

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