Abstract
A criterion, allowing one to assess conditions likely togenerate gap flows and/or hydraulicjumps in stratified flows over a mountain ridge or a mountain pass,is derived. It is based on the one-dimensional reduced-gravity shallow-watertheory generalized to a three-dimensional orography with moderate streamwisevariations by introducing a variable effective flow cross-section. In this way,the hydraulic jump and gap flow are accommodated within the same model. Theresulting steady hyperbolic problem is shown to require the boundaryconditions to be expressed in terms of Riemann invariants. The latter yield the flow betweentwo given sites in a unique way. In particular, it is possible to relateunambiguously the existence of a hydraulic jump/gap flow and its energydiscontinuity to the boundary conditions. A simple method of flow interpolationand energy discontinuity calculation between two sites is presented.
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References
Armi, L.: 1986, 'The Hydraulics of Two Flowing Layers with Different Densities', J. Fluid Mech. 163, 27-58.
Armi, L.andFarmer, D. M.: 1986, 'Maximal Two-Layer Exchange through a Contraction with Barotropic Net Flow', J. Fluid Mech. 164, 27-51.
Baines: 1984, 'A Unified Description of Two-Layer Flow over Topography', J. Fluid Mech. 184, 127-167.
Banta, R. M.,Darby, L.,Kaufmann, P.,Levinson, D. H.,andZhu, C.-J.: 1999, 'Wind-Flow Patterns in the Grand Canyon as Revealed by Doppler Lidar', J. Appl. Meteorol. 38, 1069-1083.
Banta, R. M.,Olivier, L. D.,Gudiksen, P. H.,andLange R.: 1996, 'Implications of Small-Scale Flow Features to Modeling Dispersion over Complex Terrain', J. Appl. Meteorol. 35, 330-342.
Banta, R. M.,Olivier, L. D.,Neff, W. D.,Levinson, D. H.,andRuffieux, D.: 1995, 'Influence of Canyon-Induced Flows on Flow and Dispersion over Adjacent Plains', Theor. Appl. Climatol. 52, 27-42.
Banta, R. M.,Shepson, P. B.,Bottenheim, J.W.,Anlauf, K. G.,Wiebe, H. A.,Gallant, A.,Biesenthal, T.,Olivier, L. D.,Zhu, C.-J.,McKendry, I. G.,andSteyn, D. G.: 1997, 'Nocturnal Cleansing Flows in a Tributary Valley', Atmos. Environ. 31, 2147-2162.
Drobinski, P.,Dabas, A. M.,Flamant, P. H.,Delaval, A.,Aupierre, M.,Delville, P.,Boitel, C.,Donier, J.-M.,Romand, B.,Loth, C.,andHaeberli, C.: 2000, 'Evidence of Flow-Splitting in the Rhine Valley during the MAP Field Experiment by Ground-Based Doppler Lidar and In-Situ Measurements', in Proceedings of the 9th Conference on Mountain Meteorology [available from AMS], American Meteorological Society, Aspen, Colorado, USA.
Drobinski, P.,Flamant, C.,Dusek, J.,Flamant, P. H.,andPelon, J.: 2001, 'Observational Evidence and Modelling of an Internal Hydraulic Jump at the Atmospheric Boundary-Layer Top during a Tramontane Event', Boundary-Layer Meteorol. 98, 497-515.
Durran, D. R.: 1999, Numerical Methods for Wave Equations in Geophysical Fluid Dynamics, Springer, 465 pp.
Farmer, D. M.andArmi, L.: 1986: 'Maximal Two-Layer Exchange over a Sill and through the Combination of a Sill and Contraction with Barotropic Net Flow', J. Fluid Mech. 164, 53-76.
Farmer, D. M.andArmi, L.: 1999: 'Stratified Flow over Topography: The Role of Small-Scale Entrainment and Mixing in Flow Establishement', Proc.-Royal Soc., Math. Phys. Eng. Sci. 455, 3221-3258.
Finnigan, T. D.,Vine, J. A.,Jackson, P. L.,Allen, S. E.,Lawrence, G. A.,andSteyn, D. G.: 1994, 'Hydraulic Physical Modeling and Observations of a Severe Gap Wind', Mon. Wea. Rev. 122, 2677-2687.
Flamant, C.andPelon, J.: 1996, 'Atmospheric Boundary-Layer Structure over the Mediterranean during a Tramontane Event', Quart. J. Roy. Meteorol. Soc. 122, 1741-1778.
Guyon, E.,Hulin, J. P.,andPetit, L.: 1991, Hydrodynamique Physique, Inter Editions, CNRS Editions, Paris.
Houghton, D. D.andKasahara, A.: 1968, 'Nonlinear Shallow Fluid Flow over an Isolated Ridge', Comm. Pure Appl. Math. XXI, 1-23.
Jackson, P. L.andSteyn, D. G.: 1994a, 'Gap Winds in a Fjord. Part I: Observations and Numerical Simulation', Mon. Wea. Rev., 122, 2645-2665.
Jackson, P. L.andSteyn, D. G.: 1994b, 'Gap Winds in a Fjord. Part II: Hydraulic Analog', Mon. Wea. Rev. 122, 2666-2676.
Levinson, D. H.andBanta, R. M.: 1995, 'Observations of a Terrain-Forced Mesoscale Vortex and Canyon Drainage Flows along the Front Range of Colorado', Mon. Wea. Rev. 123, 2029-2050.
Long, R. R.: 1953, 'Some Aspects of the Flow of Stratified Fluids. I. A Theoretical Investigation', Tellus 5, 42-58.
Long, R. R.: 1954, 'Some Aspects of the Flow of Stratified Fluids. II. Experiments with a Two-Fluid System', Tellus 6, 97-115.
Neiman, P. J.,Hardesty, R. M.,Shapiro, M. A.,andCupp, R. E.: 1988, 'Doppler Lidar Observations of a Downslope Windstorm', Mon. Wea. Rev. 116, 2265-2275.
Post, M. J.andNeff, W. D.: 1986, 'Doppler Lidar Measurements of Winds in a Narrow Mountain Valley', Bull. Amer. Meteorol. Soc. 116, 2265-2275.
Scorer, R. S.: 1952, 'Mountain-Gap Winds: A Study of Surface Wind at Gibraltar', Quart. J. Roy. Meteorol. Soc. 78, 53-61.
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Drobinski, P., Dusek, J. & Flamant, C. Diagnostics Of Hydraulic Jump And Gap Flow In Stratified Flows Over Topography. Boundary-Layer Meteorology 98, 475–495 (2001). https://doi.org/10.1023/A:1018703428762
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DOI: https://doi.org/10.1023/A:1018703428762