Turbulent flow in the inner layer of a katabatic jet along a steep alpine slope
Authors: Brun Christophe , Charrondière Claudine , Hopfinger Emil , Cohard Jean-Martial , Sicart Jean-Emmanuel 
Published: March 2022

&lt;p&gt;&lt;span&gt;Katabatic winds are generated by the combination of a &lt;/span&gt;&lt;span&gt;vertical&lt;/span&gt; &lt;span&gt;density gradient, slope and gravity, when the surface radiative budget is negative. We presently analyse some results of a campaign led in the French Alps in 2019 (Charrondi&amp;#232;re et al. 2022) in order to study katabatic flows over a steep snowy alpine slope of about 30&amp;#176;, that develop during winter anticyclonic conditions. In the topographic and meteorological configuration of the experiment, these downslope flows have a jet shape, with a maximum wind speed height zj very close to the surface, at about 30 cm height.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;A 3D pitot type sensor allowed measurements of wind speed down to 3 cm height above the surface, at a high sampling frequency of 1250 Hz. Sonic anemometers placed on a fixed bracket allowed to capture for the first time the 3D velocity of the katabatic flows (f=20 Hz) in the topographic coordinate system, whereas previous studies are in the streamline coordinate system. &lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;We focus mainly on the inner region of the jet, below zj. The turbulent momentum flux is decreasing with height, and its variation can be derived from a simplification of the along-slope momentum equation where the gravity term balances&lt;/span&gt;&lt;span&gt; the turbulent m&lt;/span&gt;&lt;span&gt;omentum flux gradient to first order, as shown in Denby and Smeets (2000)&lt;/span&gt;&lt;span&gt;.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;We compare the inner region of the jet with a &lt;/span&gt;&lt;span&gt;neutral turbulent bou&lt;/span&gt;&lt;span&gt;ndary layer in terms of wind speed profile, and derive a correction of the classical log-law that considers the gravity effect on the along-slope velocity. This correction is different from the well-known Monin-Obukhov stability correction, which is negligible &lt;/span&gt;&lt;span&gt;for&lt;/span&gt;&lt;span&gt; the present flow &lt;/span&gt;&lt;span&gt;because of relative low turbulent sensible heat fluxes compared to turbulent momentum fluxes&lt;/span&gt;&lt;span&gt;.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;We also show that the slope-normal velocity is negative and as high as 10-15% of the maximum wind speed in the inner region of the jet. The slope-normal momentum equation behavior in this region of the jet is consistent with the observa&lt;/span&gt;&lt;span&gt;tions and confirms that a gravity source term directs the flow to the ground. &lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;We finally analyze the impact of gravity on the temperature equation: the mean temperature profile and the turbulent sensible heat flux are also modified by it. All these modifications have implications on the turbulent Prandtl number, which behaves differently from what we expect on a &lt;/span&gt;&lt;span&gt;neutral&lt;/span&gt;&lt;span&gt; turbulent boundary layer &lt;/span&gt;&lt;span&gt;co&lt;/span&gt;&lt;span&gt;ole&lt;/span&gt;&lt;span&gt;d at the surface&lt;/span&gt;&lt;span&gt;.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;Charrondi&amp;#232;re, C., Brun, C., Cohard, JM. &lt;em&gt;et al.&lt;/em&gt; Katabatic Winds over Steep Slopes: Overview of a Field Experiment Designed to Investigate Slope-Normal Velocity and Near-Surface Turbulence. &lt;em&gt;Boundary-Layer Meteorol&lt;/em&gt; &lt;strong&gt;182, &lt;/strong&gt;29&amp;#8211;54 (2022).&amp;#160;&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;Denby B, Smeets CJPP (2000) Derivation of turbulent flux profiles and roughness lengths from&amp;#160;&lt;/span&gt;&lt;span&gt;katabatic flow dynamics. Journal of Applied Meteorology 39(9):1601&amp;#8211;1612&lt;/span&gt;&lt;/p&gt;