<p>Katabatic flows over sloping terrain exhibit low-level jets, with turbulent transport becoming dominant over local shear production near the jet maximum, challenging the applicability of classical similarity theory developed for horizontal terrain. This study investigates the influence of slope angle on local similarity scaling in katabatic flows using one-dimensional Reynolds-averaged Navier–Stokes (RANS) simulations with first- and second-order turbulence closures. The strengths and limitations of these models are assessed against observations from the Pasterze Glacier, the Vatnajökull ice cap, the MATERHORN experiment, and the Val Ferret field campaigns. The second-order closure reproduces the observed mean jet structure and momentum fluxes more accurately and is therefore used to analyse turbulence dynamics and similarity relations. A characteristic height scale, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$z_{TM}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>z</mi> <mrow> <mi mathvariant="italic">TM</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>, is proposed to identify the region where the recently-proposed slope-adjusted stability parameter of Hang et al. (<CitationRef CitationID="CR32">2021</CitationRef>) collapses the local dimensionless momentum gradients across observations and simulations. The observed dimensionless temperature gradient exhibits larger scatter, whereas the simulations show a more consistent trend. Overall results indicate that RANS provides an efficient and viable framework for studying katabatic flows, with the second-order closure resolving processes that the first-order closure does not represent but are essential to katabatic dynamics, and that flux–gradient relations based on the slope-adjusted stability parameter collapse the dimensionless momentum gradient well below <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$z_{TM}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>z</mi> <mrow> <mi mathvariant="italic">TM</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>, while non-local transport processes limit flux–gradient relations near and above the jet peak.</p>

Numerical Analysis of Slope Effect on Local Similarity Functions for Katabatic Flows

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2026年7月4日

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Yicheng Li,
Marco G. Giometto,
Chaoxun Hang,
Holly J. Oldroyd

摘要

Katabatic flows over sloping terrain exhibit low-level jets, with turbulent transport becoming dominant over local shear production near the jet maximum, challenging the applicability of classical similarity theory developed for horizontal terrain. This study investigates the influence of slope angle on local similarity scaling in katabatic flows using one-dimensional Reynolds-averaged Navier–Stokes (RANS) simulations with first- and second-order turbulence closures. The strengths and limitations of these models are assessed against observations from the Pasterze Glacier, the Vatnajökull ice cap, the MATERHORN experiment, and the Val Ferret field campaigns. The second-order closure reproduces the observed mean jet structure and momentum fluxes more accurately and is therefore used to analyse turbulence dynamics and similarity relations. A characteristic height scale, $z_{TM}$ $z_{TM}$ , is proposed to identify the region where the recently-proposed slope-adjusted stability parameter of Hang et al. (2021) collapses the local dimensionless momentum gradients across observations and simulations. The observed dimensionless temperature gradient exhibits larger scatter, whereas the simulations show a more consistent trend. Overall results indicate that RANS provides an efficient and viable framework for studying katabatic flows, with the second-order closure resolving processes that the first-order closure does not represent but are essential to katabatic dynamics, and that flux–gradient relations based on the slope-adjusted stability parameter collapse the dimensionless momentum gradient well below $z_{TM}$ $z_{TM}$ , while non-local transport processes limit flux–gradient relations near and above the jet peak.