# Waves and turbulence in katabatic winds

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## Abstract

The measurements taken during the Vertical Transport and Mixing Experiment (VTMX, October, 2000) on a northeastern slope of Salt Lake Valley, Utah, were used to calculate the statistics of velocity fluctuations in a katabatic gravity current in the absence of synoptic forcing. The data from ultrasonic anemometer-thermometers placed at elevations 4.5 and 13.9 m were used. The contributions of small-scale turbulence and waves were isolated by applying a high-pass digital (Elliptical) filter, whereupon the filtered quantities were identified as small-scale turbulence and the rest as internal gravity waves. Internal waves were found to play a role not only at canonical large gradient Richardson numbers \((\overline{\hbox {Ri}_\mathrm{g} } >1)\), but sometimes at smaller values \((0.1 < \overline{\hbox {Ri}_\mathrm{g}}<1)\), in contrast to typical observations in flat-terrain stable boundary layers. This may be attributed, at least partly, to (critical) internal waves on the slope, identified by Princevac et al. [1], which degenerate into turbulence and help maintain an active internal wave field. The applicability of both Monin-Obukhov (MO) similarity theory and local scaling to filtered and unfiltered data was tested by analyzing *rms* velocity fluctuations as a function of the stability parameter z/L, where L is the Obukhov length and z the height above the ground. For weaker stabilities, \(\hbox {z/L}<1\), the MO similarity and local scaling were valid for both filtered and unfiltered data. Conversely, when \(\hbox {z/L}>1\), the use of both scaling types is questionable, although filtered data showed a tendency to follow local scaling. A relationship between z/L and \(\overline{\hbox {Ri}_\mathrm{g} }\) was identified. Eddy diffusivities of momentum \(\hbox {K}_\mathrm{M}\) and heat \(\hbox {K}_\mathrm{H}\) were dependent on wave activities, notably when \(\overline{\hbox {Ri}_\mathrm{g} } > 1\). The ratio \(\hbox {K}_{\mathrm{H}}/\hbox {K}_{\mathrm{M}}\) dropped well below unity at high \(\overline{\hbox {Ri}_\mathrm{g} }\), in consonance with previous laboratory stratified shear layer measurements as well as other field observations.

## Keywords

Katabatic winds Mixing Stratified flows MOST Eddy diffusivity## Notes

### Acknowledgments

The data analysis was performed with the support of Office of Naval Research Award # N00014-11-1-0709, Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program.

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