1 Oscillating motions in the stable atmosphere of a deep valley Y. Largeron 1, C. Staquet 1 and C. Chemel 2 1. LEGI, Grenoble, France 2. NCAS-Weather, University of Hertfordshire, UK OGOA workshop, Lyon, May 2013

2 Katabatic wind After sunset the ground surface cools (infra-red emission) → formation of a cold layer of air along the sloping surface → this cold layer flows down by gravity

3 Katabatic wind oscillations time Potential temperature measured on the valley floor with microwave profiler, night sept. (Van Gorsel et al. 2004) Riviera valley (Switzerland) Mesoscale Alpine Program-MAP (2000)  Temporal oscillations in the katabatic wind? Or internal gravity waves? Height above the ground

4 Numerical simulations ARPS code (Advanced Regional Prediction System) Idealized 3D topography Constant Brunt-Vaisala frequency (8 runs: from 2 K/km to 15 K/km)‏ T air - T ground = 3 o Soil model Horiz. resolution: 200 m/100 m/50 m, vert. resolution : 5 m (bottom)‏ For horiz. resolution 200 m : 121 (x) x 103 (y) x 140 (z) grid points Computation starts at 22:00 on dec. 21st (45 o latitude) ‏

5 Oscillations in the katabatic wind Along-slope velocity versus coordinate normal to the slope at t=95 min Along-slope velocity versus time at 12 m above ground level

6 Oscillations in the katabatic wind Mechanism of oscillations: the katabatic wind flows down in a stable medium (along a cooling ground )‏ Fluid particle model of McNider (1982) for a simple slope  in a constant N fluid: the wind velocity should oscillate at frequency N sin  (  :slope angle) Along-slope velocity at a given location in the katabatic wind Results consistent with in situ measurements (e.g. Gryning et al. 85, Helmis & Papadopulos 96, Monti et al. 02)‏  = N sin   =44°  21°  = N sin 

7 Group velocity Oscillations in the katabatic wind But... dispersion relation of internal gravity waves:  = N sin  where  is the angle of the wave group velocity with horizontal. Could these oscillations of frequency N sin  be associated with waves whose group velocity is along the slope? We found no phase propagation in the katabatic wind: these oscillations are temporal oscillations only Wave vector 

8 Emission of internal gravity waves by the katabatic wind Phase lines of w in (x,z) plane at t=25 minat t=45 min The waves are emitted at the nose of the katabatic wind, where a hydraulic jump occurs (e.g. Renfrew 2004). The phase lines have the same inclination  along the slope → the wave frequency does not depend upon the slope angle.

9 (z=2200m) Emission of internal gravity waves by a katabatic flow Frequency of the wave field 1. No dependence upon the slope angle sin 

10 Emission of internal gravity waves by a katabatic flow Frequency of the wave field 2. No dependence of  /N upon N  /N  0.9 cf. Wu 69, Cerasoli 78, Sutherland & Linden 02, Jacobitz & Sarkar 02, Dohan & Sutherland 03  /N averaged along the valley axis versus N‏

11 Emission of internal gravity waves Wavelengths of the wave field → the wavelengths are of the order of the depth of the valley Compute cx from figure; x =c x T  x  1400 m. z can be read from the figure : z  1300 m. Vertical velocity plotted at y=15 km, z=800 m Vertical velocity plotted at y=15 km, x=-0.6 km

12 Conclusions Two distinct systems of oscillation in the stably-stratified atmospheric boundary layer of a valley: In the katabatic wind, at frequency  sin  temporal oscillations of the wind only (not a trapped wave field)‏ Emission of an internal gravity wave field by the katabatic wind, at frequency  and wavelengths  depth of the valley  Chemel C., Staquet C., Largeron Y., 2009 Generation of internal gravity waves by katabatic winds in an alpine valley. Meteorology and Atmospheric Physics, 103, 179.  Largeron Y., Staquet C., Chemel C., 2013 Characterization of oscillating motions in the stable atmosphere of a deep valley. Boundary-Layer Meteorology (in press).

13 Questions How does wave emission occur ? What does set the wave frequency ? And the wave amplitude ?

14 Oscillations in the katabatic wind “ We found no phase propagation in the katabatic wind: these oscillations are temporal oscillations only » (t,z) diagram of the vertical velocity over 3 hours in the katabatic flow