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The Influence of WENO Schemes on Large-Eddy Simulations of a Neutral Atmospheric Boundary Layer

Aaron WangaThe Pennsylvania State University, University Park, Pennsylvania

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Ying PanaThe Pennsylvania State University, University Park, Pennsylvania

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Paul M. MarkowskiaThe Pennsylvania State University, University Park, Pennsylvania

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Abstract

This work explores the influence of weighted essentially nonoscillatory (WENO) schemes on Cloud Model 1 (CM1) large-eddy simulations (LES) of a quasi-steady, horizontally homogeneous, fully developed, neutral atmospheric boundary layer (ABL). An advantage of applying WENO schemes to scalar advection in compressible models is the elimination of acoustic waves and associated oscillations of domain-total vertical velocity. Applying WENO schemes to momentum advection in addition to scalar advection yields no further advantage but has an adverse effect on resolved turbulence within LES. As a tool designed to reduce numerically generated spurious oscillations, WENO schemes also suppress physically realistic instability development in turbulence-resolving simulations. Thus, applying WENO schemes to momentum advection reduces vortex stretching, suppresses the energy cascade, reduces shear-production of resolved Reynolds stress, and eventually amplifies the differences between the surface-layer mean wind profiles in the LES and the mean wind profiles expected in accordance with the filtered law of the wall (LOTW). The role of WENO schemes in adversely influencing surface-layer turbulence has inspired a concept of anti-WENO (AWENO) schemes to enhance instability development in regions where energy-containing turbulent motions are inadequately resolved by LES grids. The success in reproducing the filtered LOTW via AWENO schemes suggests that improving advection schemes is a critical component toward faithfully simulating near-surface turbulence and dealing with other “terra incognita” problems.

Significance Statement

Turbulent motions are produced through instability development. Advection schemes designed to avoid generating spurious oscillations in flow fields involving sharp gradients may also suppress the development of physically realistic instabilities. This work explores the influence of advection schemes on numerical simulations that resolve turbulent motions. Recommendations are made concerning the use of advection schemes in simulating atmospheric turbulence, which is almost always accompanied with thermodynamic processes involving sharp temperature and moisture gradients. In addition, an advection-scheme-based concept is proposed to reproduce turbulent motions that are inadequately resolved by simulation grids.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Aaron Wang, auw317@psu.edu

Abstract

This work explores the influence of weighted essentially nonoscillatory (WENO) schemes on Cloud Model 1 (CM1) large-eddy simulations (LES) of a quasi-steady, horizontally homogeneous, fully developed, neutral atmospheric boundary layer (ABL). An advantage of applying WENO schemes to scalar advection in compressible models is the elimination of acoustic waves and associated oscillations of domain-total vertical velocity. Applying WENO schemes to momentum advection in addition to scalar advection yields no further advantage but has an adverse effect on resolved turbulence within LES. As a tool designed to reduce numerically generated spurious oscillations, WENO schemes also suppress physically realistic instability development in turbulence-resolving simulations. Thus, applying WENO schemes to momentum advection reduces vortex stretching, suppresses the energy cascade, reduces shear-production of resolved Reynolds stress, and eventually amplifies the differences between the surface-layer mean wind profiles in the LES and the mean wind profiles expected in accordance with the filtered law of the wall (LOTW). The role of WENO schemes in adversely influencing surface-layer turbulence has inspired a concept of anti-WENO (AWENO) schemes to enhance instability development in regions where energy-containing turbulent motions are inadequately resolved by LES grids. The success in reproducing the filtered LOTW via AWENO schemes suggests that improving advection schemes is a critical component toward faithfully simulating near-surface turbulence and dealing with other “terra incognita” problems.

Significance Statement

Turbulent motions are produced through instability development. Advection schemes designed to avoid generating spurious oscillations in flow fields involving sharp gradients may also suppress the development of physically realistic instabilities. This work explores the influence of advection schemes on numerical simulations that resolve turbulent motions. Recommendations are made concerning the use of advection schemes in simulating atmospheric turbulence, which is almost always accompanied with thermodynamic processes involving sharp temperature and moisture gradients. In addition, an advection-scheme-based concept is proposed to reproduce turbulent motions that are inadequately resolved by simulation grids.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Aaron Wang, auw317@psu.edu
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