Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-20T07:00:59.490Z Has data issue: false hasContentIssue false
  • English
  • Français

Separation of upslope flow over a uniform slope

Published online by Cambridge University Press:  23 June 2015

C. M. Hocut ,
D. Liberzon  and
H. J. S. Fernando
C. M. Hocut
Affiliation:
Environmental Fluid Dynamics Laboratories, Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA
D. Liberzon
Affiliation:
Environmental Fluid Dynamics Laboratories, Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA
H. J. S. Fernando*
Affiliation:
Environmental Fluid Dynamics Laboratories, Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA Department of Aerospace and Mechanical Engineering, University of Notre Dame, IN 46556, USA
*
†Email address for correspondence: Harindra.J.Fernando.10@nd.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Motivated by the importance of understanding mountain weather during periods of thermal convection, a laboratory study was conducted to investigate the separation of an upslope (anabatic) flow on a two-dimensional heated mountainous slope in the absence of a background mean flow. Three flow regimes were identified. In the first, at slope angles ${\it\beta}$ larger than a critical value ${\it\beta}_{c}\approx 20^{\circ }$, the separated flow generated a rising plume completely fed by the anterior upslope flow. For this case, a simple model based on a balance between the opposing vorticities of baroclinicity and shear was proposed to predict the location of the separation point relative to the mountain base. The model also predicts the velocity and length scales at separation as well as those of the rising plume after separation. In the second regime, $10^{\circ }<{\it\beta}\leqslant {\it\beta}_{c}$, the volume flow of the separated plume was not fully supplied by the upslope flow, requiring entrainment of additional ambient fluid at the base of the plume source. The third regime occurred when ${\it\beta}\leqslant 10^{\circ }$, wherein the plume almost completely engulfed the slope, similar to a buoyant plume emanating from a source of finite dimensions, thus overshadowing the upslope flow. Measurements of the separation point conducted during the MATERHORN field research program were consistent with the results of the laboratory experiments and modelling.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Geophysical and Geological Flows: Meteorology Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 775 , 25 July 2015 , pp. 266 - 287
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, T. & Brown, A. R. 2006 Modeling of turbulent form drag in convective conditions. Boundary-Layer Meteorol. 118, 421–429.Google Scholar
Apsley, D. D. & Castro, I. P. 1997 A limited-length-scale $k{-}{\it\varepsilon}$ model for the neutral and stably-stratified atmospheric boundary layer. Boundary-Layer Meteorol. 83, 75–98.CrossRefGoogle Scholar
Baines, P. G. 1995 Topographic Effects in Stratified Flows. Cambridge University Press.Google Scholar
Baines, P. G. & Manins, P. C. 1989 The principles of laboratory modeling of stratified atmospheric flows over complex terrain. J. Appl. Meteorol. 28, 1213–1225.Google Scholar
Banta, R. M. 1984 Daytime boundary-layer evolution over mountainous terrain. Part I: observations of the dry circulations. Mon. Weath. Rev. 112, 340–356.Google Scholar
Barry, R. G. 1992 Mountain Weather & Climate. Routledge.Google Scholar
Belcher, S. E. & Hunt, J. C. R. 1998 Turbulent flow over hills and waves. Annu. Rev. Fluid Mech. 30, 507–538.CrossRefGoogle Scholar
Berman, N. S., Boyer, D. L., Brazel, A. J., Brazel, S. W., Chen, R. R., Fernando, H. J. S. & Fitch, M. J. 1995 Synoptic classification and physical model experiments to guide field studies in complex terrain. J. Appl. Meteorol. 34, 719–730.Google Scholar
Blumen, W. 1990 Atmospheric Processes over Complex Terrain, Meteorological Monographs, vol. 23. American Meteorological Society Google Scholar
Boyer, D. L. & Davies, P. A. 2000 Laboratory studies of orographic effects in rotating and stratified flows. Annu. Rev. Fluid Mech. 32, 165–202.CrossRefGoogle Scholar
Britter, R. E., Hunt, J. C. R. & Richards, K. J. 1981 Air flow over a two-dimensional hill: studies of velocity speed-up, roughness effects and turbulence. Q. J. R. Meteorol. Soc. 107, 91–110.Google Scholar
Carruthers, D. J., Ellis, A., Hunt, J. C. R. & Chan, P. W. 2014 Modeling of wind shear downwind of mountain ridges at Hong Kong International Airport. Meteorol. Appl. 21 (1), 94–101; (special issue).Google Scholar
Chao, W. C. 2012 Correction of excessive precipitation over steep and high mountains in a GCM. J. Atmos. Sci. 69, 1547–1561.Google Scholar
Chen, C. C., Labhabi, A., Chang, H. C. & Kelly, R. E. 1991 Spanwise pairing of finite-amplitude longitudinal vortex rolls in inclined free-convection boundary layers. J. Fluid Mech. 231, 73–111.Google Scholar
Chen, R. R., Berman, N. S., Boyer, D. L. & Fernando, H. J. S. 1996 Physical model of diurnal heating in the vicinity of a long mountain. J. Atmos. Sci. 53, 62–85.Google Scholar
Chen, R. R., Berman, N. S., Boyer, D. L. & Fernando, H. J. S. 1999 Physical model of nocturnal drainage flow in complex terrain. Contrib. Atmos. Phys. 72, 219–242.Google Scholar
Colomer, J., Boubnov, B. M. & Fernando, H. J. S. 1999 Turbulent convection from isolated sources. Dyn. Atmos. Oceans 30, 125–148.Google Scholar
Crook, N. A. & Tucker, D. F. 2005 Flow over heated terrain. Part I: Linear theory and idealized numerical simulations. Mon. Weath. Rev. 133, 2552–2564.CrossRefGoogle Scholar
De Wekker, S. F. 2008 Observational and numerical evidence of depressed convective boundary layer height near a mountain base. J. Appl. Meteorol. Climatol. 47, 1017–1026.Google Scholar
Dörnbrack, A. & Schumann, U. 1993 Numerical simulation of turbulent convective flow over wavy terrain. Boundary-Layer Meteorol. 65, 323–355.CrossRefGoogle Scholar
Doyle, J. D. & Durran, D. R. 2007 Rotor and subrotor dynamics in the lee of three-dimensional terrain. J. Atmos. Sci. 64, 4202–4221.CrossRefGoogle Scholar
Ellis, A. W., Hildebrandt, M. L., Thomas, W. M. & Fernando, H. J. S. 2000 Analysis of the climatic mechanisms contributing to the summertime transport of lower atmospheric ozone across metropolitan Phoenix, Arizona, USA. Clim. Res. 15, 13–31.Google Scholar
Fernando, H. J. S. 2010 Fluid dynamics of urban atmospheres in complex terrain. Annu. Rev. Fluid Mech. 42, 365–389.CrossRefGoogle Scholar
Fernando, H. J. S., Lee, S. M., Anderson, J., Princevac, M., Pardyjak, E. & Grossman-Clarke, S. 2001 Urban fluid mechanics: air circulation and contaminant dispersion in cities. Environ. Fluid Mech. 1, 107–164.Google Scholar
Fernando, H. J. S. & Pardyjak, E. R. 2013 Field studies delve into the intricacies of mountain weather. Eos 94 (36), 313–315.Google Scholar
Fernando, H. J. S., Pardyjak, E., Di Sabatino, S., Chow, F. K., Fernando, H. J. S., Pardyjak, E. R., Di Sabatino, S., Chow, F. K., De Wekker, S. F. J., Hoch, S. W., Hacker, J., Pace, J. C., Pratt, T., Pu, Z., Steenburgh, J. W., Whiteman, C. D., Wang, Y., Zajic, D., Balsley, B., Dimitrova, R., Emmitt, G. D., Higgins, C. W., Hunt, J. C. R., Knievel, J. C., Lawrence, D., Liu, Y., Nadeau, D. F., Kit, E., Blomquist, B. W., Conry, P., Coppersmith, R. S., Creegan, E., Felton, M., Grachev, A., Gunawardena, N., Hang, C., Hocut, C. M., Huynh, G., Jeglum, M. E., Jensen, D., Kulandaivelu, V., Lehner, M., Leo, L. S., Liberzon, D., Massey, J. D., McEnerney, K., Pal, S., Price, T., Sghiatti, M., Silver, Z., Thompson, M., Zhang, H. & Zsedrovits, T. 2015 The MATERHORN – unraveling the intricacies of mountain weather. Bull. Am. Meteorol. Soc. (in press); doi:10.1175/BAMS-D-13-00131.1.Google Scholar
Fernando, H. J., Zajic, D., Di Sabatino, S., Dimitrova, R., Hedquist, B. & Dallman, A. 2010 Flow, turbulence, and pollutant dispersion in urban atmospheres. Phys. Fluids 22 (5), 051301.Google Scholar
Geerts, B., Miao, Q. & Demko, J. C. 2008 Pressure perturbations and upslope flow over a heated, isolated mountain. Mon. Weath. Rev. 136, 4272–4288.Google Scholar
Gong, W. & Ibbetson, A. 1989 A wind tunnel study of turbulent flow over model hills. Boundary-Layer Meteorol. 49, 113–148.Google Scholar
Hanley, K. E., Kirshbaum, D. J., Belcher, S. E., Roberts, N. M. & Leoncini, G. 2011 Ensemble predictability of an isolated mountain thunderstorm in a high resolution model. Q. J. R. Meteorol. Soc. 137, 2124–2137.CrossRefGoogle Scholar
Hewer, F. E. 1998 Non-linear numerical model predictions of flow over an isolated hill of moderate slope. Boundary-Layer Meteorol. 87, 381–408.Google Scholar
Hunt, J. C. R. 1991 Industrial and environmental fluid mechanics. Annu. Rev. Fluid Mech. 23, 1–42.Google Scholar
Hunt, J. C. R., Fernando, H. J. S. & Princevac, M. 2003 Unsteady thermally driven flows on gentle slopes. J. Atmos. Sci. 60, 2169–2182.Google Scholar
Hunt, J. C. R., Leibovich, S. & Richards, K. J. 1988 Turbulent shear flows over low hills. Q. J. R. Meteorol. Soc. 114, 1435–1470.Google Scholar
Jackson, P. S. & Hunt, J. C. R. 1975 Turbulent wind flow over low hills. Q. J. R. Meteorol. Soc. 101, 929–955.CrossRefGoogle Scholar
Kline, S. J. & McClintock, F. A. 1953 Describing uncertainties in single-sample experiments. Mech. Engng 75, 3–8.Google Scholar
Krettenauer, K. & Schumann, U. 1989 Direct numerical simulation of thermal convection over a wavy surface. Meteorol. Atmos. Phys. 41, 165–179.CrossRefGoogle Scholar
Lehner, M. & Whiteman, C. D. 2012 The thermally driven cross-basin circulation in idealized basins under varying wind conditions. J. Appl. Meteorol. 51, 1026–1045.Google Scholar
Lewis, H. W., Mobbs, S. D., Vosper, S. B. & Brown, A. R. 2008 The effect of surface heating on hill-induced flow separation. Boundary-Layer Meteorol. 129, 269–287.Google Scholar
Lighthill, M. J. 1963 Introduction: boundary layer theory. In Laminar Boundary Theory (ed. Rosenhead, L.), pp. 46–113. Oxford University Press.Google Scholar
List, E. J. 1982 Turbulent jets and plumes. Annu. Rev. Fluid Mech. 14, 189–212.Google Scholar
Lu, R. & Turco, R. P. 1994 Air pollutant transport in a coastal environment. Part 1: 2-D simulations of sea breeze and mountain effects. J. Atmos. Sci. 51, 2285–2308.Google Scholar
Mason, P. J. 1987 Diurnal variations in flow over a succession of ridges and valleys. Q. J. R. Meteorol. Soc. 113, 1117–1140.CrossRefGoogle Scholar
Mason, P. J. & King, J. C. 1985 Measurements and predictions of flow and turbulence over an isolated hill of moderate slope. Q. J. R. Meteorol. Soc. 111, 617–640.Google Scholar
Moreira, G. A. A., dos Santos, A. A. C., do Nascimento, C. A. M. & Valle, R. M. 2012 Numerical study of the neutral atmospheric boundary layer over complex terrain. Boundary-Layer Meteorol. 143, 393–407.CrossRefGoogle Scholar
Papanicolaou, P. N. & List, E. J. 1988 Investigations of round vertical turbulent buoyant jets. J. Fluid Mech. 195, 341–391.Google Scholar
Pardyjak, E. R., Fernando, H. J. S., Hunt, J. C. R., Grachev, A. A. & Anderson, J. 2009 A case study of the development of nocturnal slope flows in a wide open valley and associated air quality implications. Meteorol. Z. 18 (1), 85–100.Google Scholar
Politovich, M. K., Goodrich, R. K., Morse, C. S., Yates, A., Barron, R. & Cohn, S. A. 2011 The Juneau terrain-induced turbulence alert system. Bull. Am. Meteorol. Soc. 92 (March), 299–313.Google Scholar
Princevac, M. & Fernando, H. J. S. 2007 A criterion for the generation of turbulent anabatic flows. Phys. Fluids 19, 105102.Google Scholar
Princevac, M. & Fernando, H. J. S. 2008 Morning break-up of cold pools in complex terrain. J. Fluid Mech. 616, 99–109.Google Scholar
Queney, P. 1948 The problem of air flow over mountains: a summary of theoretical studies. Bull. Am. Meteorol. Soc. 29, 16–26.Google Scholar
Raupach, M. R. & Finnigan, J. J. 1997 The influence of topography on meteorological variables and surface-atmosphere interactions. J. Hydrol. 190, 182–213.Google Scholar
Raymond, D. J. 1972 Calculation of airflow over an arbitrary ridge including diabatic heating and cooling. J. Atmos. Sci. 29, 837–843.2.0.CO;2>CrossRefGoogle Scholar
Reisner, J. M. & Smolarkiewicz, P. K. 1994 Thermally forced low Froude number flow past three-dimensional obstacles. J. Atmos. Sci. 51, 117–133.2.0.CO;2>CrossRefGoogle Scholar
Reuten, C., Steyn, D. G. & Allen, S. E. 2007 Water tank studies of atmospheric boundary layer structure and air pollution transport in upslope flow systems. J. Geophys. Res. 112, D11114.Google Scholar
Reuten, C., Steyn, D. G., Strawbridge, K. B. & Bovis, P. 2005 Observations of the relation between upslope flows and the convective boundary layer in steep terrain. Boundary-Layer Meteorol. 116, 37–61.Google Scholar
Rouse, H., Yih, C. S. & Humphreys, H. W. 1952 Gravitational convection from a boundary source. Tellus 4, 201–210.Google Scholar
Schumann, U. 1989 Large-eddy simulation of the up-slope boundary layer. Q. J. R. Meteorol. Soc. 116, 637–670.CrossRefGoogle Scholar
Scorer, R. S. 1997 Dynamics of Meteorology and Climate. Wiley.Google Scholar
Serafin, S. & Zardi, D. 2010a Structure of the atmospheric boundary layer in the vicinity of a developing upslope flow system: a numerical model study. J. Atmos. Sci. 67, 1171–1185.Google Scholar
Serafin, S. & Zardi, D. 2010b Daytime heat transfer processes related to slope flows and turbulent convection in an idealized mountain valley. J. Atmos. Sci. 67, 3739–3756.Google Scholar
Smith, R. B. & Lin, Y. L. 1982 The addition of heat to a stratified airstream with application to the dynamics of orographic rain. Q. J. R. Meteorol. Soc. 108, 353–378.Google Scholar
Taylor, P. A. & Teunissen, H. W. 1987 The Askervein Hill project: overview and background data. Boundary-Layer Meteorol. 39, 15–39.Google Scholar
Tian, W. & Parker, D. J. 2003 A modeling study and scaling analysis of orographic effects on boundary layer shallow convection. J. Atmos. Sci. 60, 1981–1991.2.0.CO;2>CrossRefGoogle Scholar
Whiteman, C. D. 2000 Mountain Meteorology: Fundamentals and Applications. Oxford University Press.Google Scholar
Wood, N. 1995 The onset of separation in neutral, turbulent flow over hills. Boundary-Layer Meteorol. 76, 137–164.CrossRefGoogle Scholar
Xu, D., Ayotte, K. W. & Taylor, P. A. 1994 Development of a non-linear mixed spectral finite difference model for turbulent boundary-layer flow over topography. Boundary-Layer Meteorol. 70, 341–367.CrossRefGoogle Scholar