Abstract
In a valley sheltered from strong synoptic effects, the dynamics of the valley atmosphere at night is dominated by katabatic winds. In a stably stratified atmosphere, these winds undergo temporal oscillations, whose frequency is given by \(N \sin {\alpha }\) for an infinitely long slope of constant slope angle \(\alpha \), \(N\) being the buoyancy frequency. Such an unsteady flow in a stably stratified atmosphere may also generate internal gravity waves (IGWs). The numerical study by Chemel et al. (Meteorol Atmos Phys 203:187–194, 2009) showed that, in the stable atmosphere of a deep valley, the oscillatory motions associated with the IGWs generated by katabatic winds are distinct from those of the katabatic winds. The IGW frequency was found to be independent of \(\alpha \) and about \(0.8N\). Their study did not consider the effects of the background stratification and valley geometry on these results. The present work extends this study by investigating those effects for a wide range of stratifications and slope angles, through numerical simulations for a deep valley. The two oscillatory systems are reproduced in the simulations. The frequency of the oscillations of the katabatic winds is found to be equal to \(N\) times the sine of the maximum slope angle. Remarkably, the IGW frequency is found to also vary as \(C_\mathrm{w}N\), with \(C_\mathrm{w}\) in the range \(0.7\)–\(0.95\). These values for \(C_\mathrm{w}\) are similar to those reported for IGWs radiated by any turbulent field with no dominant frequency component. Results suggest that the IGW wavelength is controlled by the valley depth.
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References
Ball FK (1956) The theory of strong katabatic winds. Aust J Phys 9:373–386
Bastin S, Drobinski P (2005) Temperature and wind velocity oscillations along a gentle slope during sea-breeze events. Boundary-Layer Meteorol 114:573–594
Buettner KJK, Thyer N (1965) Valley winds in the mount rainier area. Arch Meteorol Geophys Bioklimatol 14:125–147
Catalano F, Cenedese A (2010) High-resolution numerical modeling of thermally driven slope winds in a valley with strong capping. J Appl Meteorol Climatol 49:1859–1880
Cerasoli CP (1978) Experiments on buoyant-parcel motion and the generation of internal gravity waves. J Fluid Mech 86:247–271
Chemel C, Staquet C, Largeron Y (2009) Generation of internal gravity waves by a katabatic wind in an idealized alpine valley. Meteorol Atmos Phys 103:187–194
Deardorff JW (1980) Stratocumulus-capped mixed layers derived from a three-dimensional model. Boundary-Layer Meteorol 18:495–527
Dohan K, Sutherland BR (2003) Internal waves generated from a turbulent mixed region. Phys Fluids 15:488–498
Fedorovich E, Shapiro A (2009) Structure of numerically simulated katabatic and anabatic flows along steep slopes. Acta Geophys 57:981–1010
Fleagle RG (1950) A theory of air drainage. J Meteorol 7:227–232
Gryning SE, Mahrt L, Larsen S (1985) Oscillating nocturnal slope flow in a coastal valley. Tellus 37A:196–203
Helmis CG, Papadopoulos KH (1996) Some aspects of the variation with time of katabatic flow over simple slope. Q J R Meteorol Soc 122:595–610
Lighthill JM (1978) Waves in Fluids. Cambridge University Press, UK, 504 pp.
Mahrt L (1982) Momentum balance of gravity flows. J Atmos Sci 39:2701–2711
Mahrt L, Richardson S, Seaman N, Stauffer D (2010) Non-stationary drainage flows and motions in the cold pool. Tellus A 62:698–705
McNider RT (1982) A note on velocity fluctuations in drainage flows. J Atmos Sci 39:1658–1660
Monti P, Fernando HJS, Princevac M, Chan WC, Kowalewski TA, Pardyjak ER (2002) Observations of flow and turbulence in the nocturnal boundary layer over a slope. J Atmos Sci 59:2513–2534
Mori M, Kobayashi T (1996) Dynamic interaction between observed nocturnal drainage winds and a cold air lake. J Meteorol Soc Jpn 74:247–258
Mowbray DE, Rarity DSH (1967) The internal wave pattern produced by a sphere moving vertically in a density stratified liquid. J Fluid Mech 30:489–495
Noilhan J, Planton S (1989) A simple parametrization of land surface processes for meteorological models. Mon Weather Rev 117:536–549
Peck L (1996) Temporal and spatial fluctuations in ground cover surface temperature at a Northern New England site. Atmos Res 41:131–160
Poulos G, Zhong S (2008) An observational history of small-scale katabatic winds in mid-latitudes. Geogr Compass 2. doi:10.1111/j.1749-8198.2008.00,166.x
Princevac M, Hunt J, Fernando HJS (2008) Slopes in wide valleys: hydraulic theory and observations. J Atmos Sci 65:627–643
Rampanelli G, Zardi D, Rotunno R (2004) Mechanism of up-valley winds. J Atmos Sci 61:3097–3111
Renfrew IA (2004) The dynamics of idealized katabatic flow over a moderate slope and ice shelf. Q J R Meteorol Soc 130:1023–1045
Simpson JE (1994) Sea breeze and local winds. Cambridge University Press, UK, 234 pp.
Skyllingstad ED (2003) Large-eddy simulation of katabatic flows. Boundary-Layer Meteorol 106:217–243
Taylor JR, Sarkar S (2007) Internal gravity waves generated by a turbulent bottom ekman layer. J Fluid Mech 590:331–354
van Gorsel E, Vogt R, Christen A, Rotach M (2004) Low frequency temperature and velocity oscillations in katabatic winds. In: Proceedings of the 27th international conference on alpine meteorology, 19–23 May 2003, Brig
Viana S, Terradellas E, Yagüe C (2010) Analysis of gravity waves generated at the top of a drainage flow. J Atmos Sci 67:3949–3966
Voisin B (2007) Added mass effects on internal wave generation. In: Proceedings of the fifth international symposium on environmental hydraulics, 4–7 Dec 2007, Tempe
Voisin B, Ermanyuk VE, Flor JB (2011) Internal wave generation by oscillation of a sphere, with application to internal tides. J Fluid Mech 666:308–357
von Görtler H (1943) über eine schwingungserscheinung in flüssigkeiten mit stabiler dichteschichtung. Z Angew Math Mech 23:65–71
Whiteman CD (2000) Mountain meteorology: fundamentals and applications. Oxford University Press, New York, 355 pp.
Whiteman CD, Muschinski A, Zhong S, Fritts D, Hocj SW, Hahnenbreg M, Yao W, Hohreiter V, Behn M, Cheon Y, Clements CB, Horst TW, Brown WOJ, Oncley SP (2008) METCRAX 2006: meteorological experiments in Arizona’s meteor crater. B Am Meteorol Soc 89:1665–1680
Wu J (1969) Mixed region collapse with internal wave generation in a density-stratified medium. J Fluid Mech 35:531–544
Xue M, Droegemeier KK, Wong V (2000) The advanced regional prediction system (ARPS)—a multi-scale non hydrostatic atmospheric simulation and prediction model. Part I: model dynamics and verification. Meteorol Atmos Phys 75:161–193
Yu Y, Cai XM (2006) Structure and dynamics of katabatic flow jumps: idealised simulations. Boundary-Layer Meteorol 118:527–555
Acknowledgments
The PhD Grant of YL was funded by the French Région Rhône-Alpes as part of the ‘Cluster Environnement’. YL and CS also acknowledge financial support from the French ‘Institut national des sciences de l’Univers’ (INSU) as part of the LEFE/IDAO Program. Time-consuming computations were performed thanks to the French IDRIS national supercomputing facilities.
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Largeron, Y., Staquet, C. & Chemel, C. Characterization of Oscillatory Motions in the Stable Atmosphere of a Deep Valley. Boundary-Layer Meteorol 148, 439–454 (2013). https://doi.org/10.1007/s10546-013-9825-y
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DOI: https://doi.org/10.1007/s10546-013-9825-y