The physics of orographic gravity wave drag

Frontiers in Physics

Volumn 2, Issue , 2014, Pages 1-24

  Teixeira, Miguel A C ^a  

^a UNIVERSITY OF READING   (United Kingdom)

Author keywords

Coriolis force; Drag; Momentum flux; Mountain waves; Non hydrostatic effects; Nonlinearity; Stratification; Wind shear

Indexed keywords

BOUNDARY LAYERS; GRAVITY WAVES; HYDRAULICS; MOMENTUM; RADIATION EFFECTS; SHEAR FLOW;

ADIABATIC CONDITIONS; GRAVITY WAVE DRAG; MOMENTUM FLUX; MOUNTAIN WAVE; NON-HYDROSTATIC; NON-HYDROSTATIC EFFECT; NONLINEARITY; OROGRAPHIC GRAVITY WAVES; STRATIFICATION; WIND SHEARS;

DRAG;

EID: 84948763283     PISSN: None     EISSN: 2296424X     Source Type: Journal    
DOI: 10.3389/fphy.2014.00043     Document Type: Article

References (166)

1. Gill AE. Atmosphere-Ocean Dynamics. London: Academic Press (1982).
2. Lin YL. Mesoscale Dynamics. Cambridge: Cambridge University Press (2007). doi: 10.1017/CBO9780511619649
3. Eliassen A, Palm E. On the transfer of energy in stationary mountain waves. Geofys Publ. (1960) 22:1-23.
4. Broad AS. Linear theory of momentum fluxes in 3-D flows with turning of the mean wind with height. Q J R Meteor Soc. (1995) 121:1891-1902. doi: 10.1002/qj.49712152806
5. Clark TL, Miller MJ. Pressure drag and momentum fluxes due to the Alps. II: representation in large-scale atmospheric models. Q J R Meteor Soc. (1991) 117:527-52. doi: 10.1002/qj.49711749906
6. Nappo CJ. An Introduction to Atmospheric Gravity Waves - 2nd Edn. London: Academic Press (2012).
7. Wallace JM, Tibaldi S, Simmons AJ. Reduction of systematic forecast errors in the ECMWF model through the introduction of an envelope orography. Q J R Meteor Soc. (1983) 109:683-717. doi: 10.1002/qj.49710946202
8. Tibaldi S. Envelope orography and maintenance of the quasi-stationary circulation in the ECMWF global models. Adv Geophys. (1986) 29:339-74. doi: 10.1016/S0065-2687(08)60045-X
9. Palmer TN, Shutts GJ, Swinbank R. Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parametrization. Q J R Meteor Soc. (1986)112:1001-39. doi: 10.1002/qj.49711247406
10. Chouinard C, Béland M, McFarlane N. A simple gravity wave drag parametrization for use in medium-range weather forecast models. Atmos-Ocean (1986) 24:91-110. doi: 10.1080/07055900.1986.9649242
11. McFarlane NA. The effect of orographically excited gravity-wave drag on the general circulation of the lower stratosphere and troposphere. J Atmos Sci. (1987) 44:1775-1800. doi: 10.1175/1520-0469(1987)044<1775:TEOOEG>2.0.CO;2
12. Baines PG, Palmer TN. Rationale for a New Physically Based Parametrization of Sub-Grid Scale Orographic Effects. European Centre for Medium-Range Weather Forecasts (1990).
13. Kim YJ, Arakawa A. Improvement of orographic gravity wave parameterization using a mesoscale gravity wave model. J Atmos Sci. (1995) 52:1875-902. doi: 10.1175/1520-0469(1995)052<1875:IOOGWP>2.0.CO;2
14. Sarin VB, Forichon M, Treut HL. Parameterization and influence of the orographic gravity-wave drag in the LMD-GCM. Math Comput Modelling (1996) 24:71-84. doi: 10.1016/0895-7177(96)00108-2
15. Lott F, Miller MJ. A new subgrid-scale orographic drag parametrization: its formulation and testing. Q J R Meteor Soc. (1997) 123:101-27. doi: 10.1002/qj.49712353704
16. Gregory D, Shutts GJ, Mitchell JR. A new gravity-wave-drag scheme incorporating anisotropic orography and low-level wave breaking. Impact upon the climate of the UK Meteorological Office Unified Model. Q J R Meteor Soc. (1998) 124:463-93. doi: 10.1002/qj.49712454606
17. Webster S, Brown AR, Cameron DR, Jones CP. Improvements to the representation of orography in the Met Office Unified Model. Q J Roy Meteor Soc. (2003) 129:1989-2010. doi: 10.1256/qj.02.133
18. Kim YJ, Doyle JD. Extension of an orographic-drag parametrization scheme to incorporate orographic anisotropy and flow blocking. Q J R Meteor Soc. (2005) 131:1893-921. doi: 10.1256/qj.04.160
19. Garner ST. A topographic drag closure built on an analytical base flux. J Atmos Sci. (2005) 62:2302-15. doi: 10.1175/JAS3496.1
20. Solomon S. Stratospheric ozone depletion: a review of concepts and history. Rev Geophys. (1999) 37:275-316. doi: 10.1029/1999RG900008
21. Okamoto K, Sato K, Akiyoshi H. A study on the formation and trend of the Brewer-Dobson circulation. J Geophys Res. (2011) 116:D10117. doi: 10.1029/2010JD014953
22. Peixoto JP, Oort AH. The Physics of Climate. New York, NY: Springer-Verlag (1992).
23. Egger J, Weickmann K, Hoinka KP. Angular momentum in the global atmospheric circulation. Rev Geophys. (2007) 45:RG4007. doi: 10.1029/2006RG000213
24. Wolf WL, Smith RB. Length-of-day changes and mountain torque during El Niño. J Atmos Sci. (1987) 44:3656-60. doi: 10.1175/1520-0469(1987)044<3656:LODCAM>2.0.CO;2
25. del Rio RA, Gambis D, Salstein DA. Interannual signals in length of day and atmospheric angular momentum. Ann Geophys. (2000) 18:347-64. doi: 10.1007/s005850050894
26. Madden RA, Speth P. Estimates of Atmospheric Angular momentum, friction, and mountain torques during 1987-1988. J Atmos Sci. (1995) 52:3681-94. doi: 10.1175/1520-0469(1995)052<3681:EOAAMF>2.0.CO;2
27. Huang HP, Sardeshmukh P, Weickmann K. The balance of global anglular momentum in a long-term atmospheric data set. J Geophys Res. (1999) 104:2031-40. doi: 10.1029/1998JD200068
28. Egger J, Hoinka KP. The annual cycle of the axial angular momentum of the atmosphere. J Clim. (2005)18:757-771. doi: 10.1175/JCLI-3290.1
29. Hafner TA, Smith RB. Pressure drag on the European Alps in relation to synoptic events. J Atmos Sci. (1985)42:562-75. doi: 10.1175/1520-0469(1985)042<0562:PDOTEA>2.0.CO;2
30. Davies HC, Pichler H. Mountain meteorology and ALPEX. Meteor Atmos Phys. (1990) 43:3-4. doi: 10.1007/BF01028104
31. Bougeault P, Benech B, Bessemoulin P, Carissimo B, Clar AJ, Pelon J, et al. PYREX: a summary of findings. Bull Am Meteor Soc. (1997) 78:637-50. doi: 10.1175/1520-0477(1997)078<0637:PASOF>2.0.CO;2
32. Rotunno R, Houze RA. Lessons on orographic precipitation from the mesoscale alpine programme. Q J R Meteor Soc. (2007) 133:811-30. doi: 10.1002/qj.67
33. Smith RB, Doyle JD, Jiang QF, Smith SA. Alpine gravity waves: lessons from MAP regarding mountain wave generation and breaking. Q J R Meteor Soc. (2007) 133:917-36. doi: 10.1002/qj.103
34. Grubišić V, Doyle JD, Kuettner J, Mobbs S, Smith RB, Whiteman CD, et al. The terrain-induced rotor experiment: a field campaign overview including observational highlights. Bull Am Meteor Soc. (2008) 89:1513-33. doi: 10.1175/2008BAMS2487.1
35. Doyle JD, Grubišić V, Brown WOJ, Wekker SFJD, Dornbrack A, Jiang QF, et al. Observations and numerical simulations of subrotor vortices during T-REX. J Atmos Sci. (2009) 66:1229-1249. doi: 10.1175/2008JAS2933.1
36. Miranda PMA, Ferreira JJ, Thorpe AJ. Gravity-wave drag produced by Madeira. Q J R Meteor Soc. (1999)125:1341-57. doi: 10.1002/qj.1999.49712555612
37. Vosper SB, Mobbs SD. Lee waves over the English lake district. Q J R Meteor Soc. (1996) 122:1283-1305. doi: 10.1002/qj.49712253404
38. Queney P. The problem of air flow over mountains: a summary of theoretical studies. Bull Am Meteor Soc. (1948) 29:16-26.
39. Smith RB. The influence of mountains on the atmosphere. Adv Geophys. (1979) 21:87-230. doi: 10.1016/S0065-2687(08)60262-9
40. Baines PG. Upstream blocking and airflow over mountains. Ann Rev Fluid Mech. (1987) 19:75-97. doi: 10.1146/annurev.fl.19.010187.000451
41. Smith RB. Hydrostatic airflow over mountains. Adv Geophys. (1989) 31:1-41. doi: 10.1016/S0065-2687(08)60052-7
42. Durran DR. Mountain waves and downslope winds. In: Blumen W, editor. Atmospheric Processes over Complex Terrain. American Meteorological Society (1990). p. 59-81.
43. Wurtele MG, Sharman RD, Datta A. Atmospheric lee waves. Ann Rev Fluid Mech. (1996) 28:429-76. doi: 10.1146/annurev.fl.28.010196.002241
44. Durran DR. Lee waves and mountain waves. In: Holton J, Curry J, Pyle J, editors. Encyclopedia of the Atmospheric Sciences. Academic Press (2003). p. 1161-69. doi: 10.1016/B0-12-227090-8/00202-5
45. Smith RB. Stratified flow over topography. In: Grimshaw R, editor. Environmental Stratified Flows. Kluwer Academic Publishers (2003). p. 119-159. doi: 10.1007/0-306-48024-7-5
46. Kim YJ, Eckermann SD, Chun HY. An overview of the past, present and future of gravity-wave drag parametrization for numerical climate and weather prediction models - Survey article. Atmos-Ocean (2003)41:65-98. doi: 10.3137/ao.410105
47. Kim YJ, Hogan TF. Response of a global atmospheric forecast model to various drag parametrizations. Tellus A(2004) 56:472-84. doi: 10.1111/j.1600-0870.2004.00087.x
48. Lott F, Millet C. The representation of gravity waves in atmospheric general circulation models (CGMs). In: Pinchon AL, Blanc E, Hauchecorne A, editors. Infrasound Monitoring for Atmospheric Studies. Springer (2009). p. 685-699.
49. Smith RB, Doyle JD, Brown AR, Webster S. Sensitivity of resolved mountain drag to model resolution for MAP case-studies. Q J R Meteor Soc. (2006) 132:1467-87. doi: 10.1256/qj.05.67
50. Teixeira MAC, Miranda PMA, Valente MA. An analytical model of mountain wave drag for wind profiles with shear and curvature. J Atmos Sci. (2004) 61:1040-54. doi: 10.1175/1520-0469(2004)061<1040:AAMOMW>2.0.CO;2
51. Phillips DS. Analytical surface pressure and drag for linear hydrostatic flow over three-dimensional elliptical mountains. J Atmos Sci. (1984) 41:1073-84. doi: 10.1175/1520-0469(1984)041<1073:ASPADF>2.0.CO;2
52. Smith RB. Further development of a theory of lee cyclogenesis. J Atmos Sci. (1986) 43:1582-602. doi: 10.1175/1520-0469(1986)043<1582:FDOATO>2.0.CO;2
53. Smith RB. Linear theory of stratified flow past an isolated mountain in isosteric coordinates. J Atmos Sci. (1988) 45:3889-96. doi: 10.1175/1520-0469(1988)045<3889:LTOSFP>2.0.CO;2
54. Hines CO. A modeling of atmospheric gravity waves and wave drag generated by isotropic and anisotropic terrain. J Atmos Sci. (1988) 45:309-322. doi: 10.1175/1520-0469(1988)045<0309:AMOAGW>2.0.CO;2
55. Scinocca JF, McFarlane NA. The parametrization of drag induced by stratified flow over anisotropic orography. Q J R Meteor Soc. (2000) 126:2353-93. doi: 10.1002/qj.49712656802
56. Bauer MH, Mayr GJ, Vergeiner I, Pichler H. Strongly nonlinear flow over and around a three-dimensional mountain as a function of the horizontal aspect ratio. J Atmos Sci. (2000) 57:3971-3991. doi: 10.1175/1520-0469(2001)058<3971:SNFOAA>2.0.CO;2
57. Wells H, Vosper SB, Ross AN, Brown AR, Webster S. Wind direction effects on orographic drag. Q J R Meteor Soc. (2008) 134:689-701. doi: 10.1002/qj.247
58. Epifanio CC, Durran DR. Three-dimensional effects in high-drag-state flows over long ridges. J Atmos Sci. (2001) 58:1051-65. doi: 10.1175/1520-0469(2001)058<1051:TDEIHD>2.0.CO;2
59. Blumen W, McGregor CD. Wave drag by three-dimensional mountain lee-waves in nonplanar shear flow. Tellus(1976) 4:287-98. doi: 10.1111/j.2153-3490.1976.tb00678.x
60. Grisogono B. Dissipation of wave drag in the atmospheric boundary layer. J Atmos Sci. (1994) 51:1237-43. doi: 10.1175/1520-0469(1994)051<1237:DOWDIT>2.0.CO;2
61. Bender CM, Orszag SA. Advanced Mathematical Methods for Scientists and Engineers. New York, NY: Springer (1999). doi: 10.1007/978-1-4757-3069-2
62. Grubišić V, Smolarkiewicz PK. The effect of critical levels on 3D orographic flows: linear regime. J Atmos Sci. (1997) 54:1943-60. doi: 10.1175/1520-0469(1997)054<1943:TEOCLO>2.0.CO;2
63. Wang TA, Lin YL. Effects of shear and sharp gradients in static stability on two-dimensional flow over an isolated mountain ridge. Meteor Atmos Phys. (2000) 75:69-99. doi: 10.1007/s007030070017
64. Miranda PMA. Gravity Waves and Wave Drag in Flow Past Three-Dimensional Isolated Mountains. PhD dissertation, University of Reading (1991).
65. Valente MA. Effects of Directional Wind Shear on Orographic Gravity Wave Drag. PhD dissertation, University of Reading (2000).
66. Teixeira MAC, Miranda PMA. The effect of wind shear and curvature on the gravity wave drag produced by a ridge. J Atmos Sci. (2004) 61:2638-43. doi: 10.1175/JAS3282.1
67. Teixeira MAC, Miranda PMA. A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains. Q J R Meteor Soc. (2006) 132:2439-58. doi: 10.1256/qj.05.220
68. Miranda PMA, Martins JPA, Teixeira MAC. Assessing wind profile effects on the global atmospheric torque. Q J R Meteor Soc. (2009) 135:807-14. doi: 10.1002/qj.393
69. Tang JY, Tang J, Wang Y. Analytical investigation on 3D non-Boussinesq mountain wave drag for wind profiles with vertical variations. Appl Math Mech. (2007) 28:317-25. doi: 10.1007/s10483-007-0305-z
70. Booker JR, Bretherton FP. The critical layer for internal gravity waves in a shear flow. J Fluid Mech. (1967)27:513-39. doi: 10.1017/S0022112067000515
71. Breeding RJ. A non-linear investigation of critical levels for internal atmospheric gravity waves. J Fluid Mech. (1971) 50:545-63. doi: 10.1017/S0022112071002751
72. Fritts DC, Geller MA. Viscous stabilization of gravity wave critical level flows. J Atmos Sci. (1976) 33:2276-84. doi: 10.1175/1520-0469(1976)033<2276:VSOGWC>2.0.CO;2
73. Clark TL, Peltier WR. Critical level reflection and the resonant growth of nonlinear mountain waves. J Atmos Sci. (1984) 41:3122-34. doi: 10.1175/1520-0469(1984)041<3122:CLRATR>2.0.CO;2
74. Scinocca JF, Peltier WR. On the Richardson number dependence of nonlinear critical-layer flow over localized topography. J Atmos Sci. (1991) 48:1560-72. doi: 10.1175/1520-0469(1991)048<1560:OTRNDO>2.0.CO;2
75. Lindzen RS, Tung KK. Banded convective activity and ducted gravity waves. Mon Wea Rev. (1976) 104:1602-17. doi: 10.1175/1520-0493(1976)104<1602:BCAADG>2.0.CO;2
76. Wang TA, Lin YL. Wave ducting in a stratified shear flow over two-dimensional mountains. Part I: general linear criteria. J Atmos Sci. (1999) 56:412-36. doi: 10.1175/1520-0469(1999)056<0412:WDIASS>2.0.CO;2
77. Wang TA, Lin YL. Wave ducting in a stratified shear flow over a two-dimensional mountain. Part II: implications for the development of high-drag states for severe downslope windstorms. J Atmos Sci. (1999)56:437-52. doi: 10.1175/1520-0469(1999)056<0437:WDIASS>2.0.CO;2
78. Lott F. The reflection of a stationary gravity wave by a viscous boundary layer. J Atmos Sci. (2007) 64:3363-71. doi: 10.1175/JAS4020.1
79. Grimshaw R. Internal gravity waves: critical layer absorption in a rotating fluid. J Fluid Mech. (1975) 70:287-304. doi: 10.1017/S0022112075002030
80. Shutts G. Gravity-wave drag parametrization over complex terrain: the effect of critical-level absorption in directional wind-shear. Q J R Meteor Soc. (1995) 121:1005-21. doi: 10.1002/qj.49712152504
81. Shutts GJ, Gadian A. Numerical simulations of orographic gravity waves in flows which back with height. Q J R Meteor Soc. (1999) 125:2743-65. doi: 10.1002/qj.49712555920
82. Shutts GJ. Stationary gravity-wave structure in flows with directional wind shear. Q J R Meteor Soc. (1998)124:1421-42.
83. Broad AS. Do orographic gravity waves break in flows with uniform wind direction turning with height. Q J R Meteor Soc. (1999) 125:1695-714. doi: 10.1002/qj.49712555711
84. Doyle JD, Jiang QF. Observations and numerical simulations of mountain waves in the presence of directional wind shear. Q J R Meteor Soc. (2006) 132:1877-905. doi: 10.1256/qj.05.140
85. Teixeira MAC, Miranda PMA. On the momentum fluxes associated with mountain waves in directionally sheared flows. J Atmos Sci. (2009) 66:3419-33. doi: 10.1175/2009JAS3065.1
86. Xu X, Wang Y, Xue M. Momentum flux and flux divergence of gravity waves in directional shear flows over three-dimensional mountains. J Atmos Sci. (2012) 69:3733-44. doi: 10.1175/JAS-D-12-044.1
87. Xu X, Xue M, Wang Y. Gravity wave momentum flux in directional shear flows over three-dimensional mountains: linear and nonlinear numerical solutions as compared to linear analytical solutions. J Geophys Res. (2013) 118:7670-81. doi: 10.1002/jgrd.50471
88. Teixeira MAC, Yu CL. The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains. Eur J Mech B Fluids (2014). 47:16-31. doi: 10.1016/j.euromechflu.2014.02.004
89. Lilly DK. A severe downslope windstorm and aircraft turbulence event induced by a mountain wave. J Atmos Sci. (1978) 35:59-77. doi: 10.1175/1520-0469(1978)035<0059:ASDWAA>2.0.CO;2
90. Peltier WR, Clark TL. The evolution and stability of finite-amplitude mountain waves. Part II: surface wave drag and severe downslope windstorms. J Atmos Sci. (1979) 36:1498-1529. doi: 10.1175/1520-0469(1979)036<1498:TEASOF>2.0.CO;2
91. Smith RB. On severe downslope winds. J Atmos Sci. (1985) 42:2597-603. doi: 10.1175/1520-0469(1985)042<2597:OSDW>2.0.CO;2
92. Bacmeister JT, Pierrehumbert RT. On high-drag states of nonlinear stratified flow over an obstacle. J Atmos Sci. (1988) 45:63-80. doi: 10.1175/1520-0469(1988)045<0063:OHDSON>2.0.CO;2
93. Durran DR. Another look at downslope windstorms. Part I: the development of analogous to supercritical flow in an infinitely deep, continuously stratified fluid. J Atmos Sci. (1986) 43:2527-43. doi: 10.1175/1520-0469(1986)043<2527:ALADWP>2.0.CO;2
94. Leutbecher M. Surface pressure drag for hydrostatic two-layer flow over axisymmetric mountains. J Atmos Sci. (2001) 58:797-807. doi: 10.1175/1520-0469(2001)058<0797:SPDFHT>2.0.CO;2
95. Durran DR. Two-layer solutions to Long's equation for vertically propagating mountain waves: how good is linear theory? Q J R Meteor Soc. (1992) 118:415-33. doi: 10.1002/qj.49711850502
96. Teixeira MAC, Miranda PMA, Argaín JL, Valente MA. Resonant gravity-wave drag enhancement in linear stratified flow over mountains. Q J R Meteor Soc. (2005) 131:1795-814. doi: 10.1256/qj.04.154
97. Miranda PMA, Valente MA. Critical level resonance in three-dimensional flow past isolated mountains. J Atmos Sci. (1997) 54:1574-88. doi: 10.1175/1520-0469(1997)054<1574:CLRITD>2.0.CO;2
98. Teixeira MAC, Miranda PMA. Linear criteria for gravity-wave breaking in resonant stratified flow over a ridge. Q J R Meteor Soc. (2005) 131:1815-20. doi: 10.1256/qj.04.155
99. Wells H, Vosper SB. The accuracy of linear theory for predicting mountain-wave drag: implications for parametrization schemes.
100. Teixeira MAC, Miranda PMA, Argaín JL. Mountain waves in two-layer sheared flows: critical level effects, wave reflection and drag enhancement. J Atmos Sci. (2008) 65:1912-26. doi: 10.1175/2007JAS2577.1
101. Teixeira MAC, Argaín JL, Miranda PMA. The importance of friction in mountain wave drag amplification by Scorer parameter resonance. Q J R Meteor Soc. (2012) 138:1325-37. doi: 10.1002/qj.1874
102. Wurtele MG, Sharman RD, Keller TL. Analysis and simulations of a troposphere-stratosphere gravity wave model. Part I. J Atmos Sci. (1987) 44:3269-81. doi: 10.1175/1520-0469(1987)044<3269:AASOAT>2.0.CO;2
103. Keller TL. Implications of the hydrostatic assumption on atmospheric gravity waves. J Atmos Sci. (1994)51:1915-29. doi: 10.1175/1520-0469(1994)051<1915:IOTHAO>2.0.CO;2
104. Sharman RD, Wurtele MG. Three-dimensional structure of forced gravity waves and lee waves. J Atmos Sci. (2004) 61:664-81. doi: 10.1175/1520-0469(2004)061<0664:TSOFGW>2.0.CO;2
105. Lott F. Linear mountain drag and averaged pseudo-momentum flux profiles in the presence of trapped-lee waves. Tellus A (1998) 50:12-25. doi: 10.1034/j.1600-0870.1998.00002.x
106. Broad AS. Momentum flux due to trapped lee waves forced by mountains. Q J R Meteor Soc. (2002)128:2167-73. doi: 10.1256/003590002320603593
107. Bretherton FP. Momentum transport by gravity waves. Q J R Meteor Soc. (1969) 95:213-43. doi: 10.1002/qj.49709540402
108. Smith RB. The generation of lee waves by the Blue Ridge. J Atmos Sci. (1976) 33:507-19. doi: 10.1175/1520-0469(1976)033<0507:TGOLWB>2.0.CO;2
109. Tutiś V. Trapped lee waves: a special analytical solution. Meteor Atmos Phys. (1992) 50:189-95. doi: 10.1007/BF01026016
110. Scorer RS. Theory of waves in the lee of mountains. Q J R Meteor Soc. (1949) 75:41-56. doi: 10.1002/qj.49707532308
111. Teixeira MAC, Argaín JL, Miranda PMA. Drag produced by trapped lee waves and propagating mountain and propagating mountain waves in a two-layer atmosphere. Q J R Meteor Soc. (2013) 139:964-81. doi: 10.1002/qj.2008
112. Teixeira MAC, Argaín JL, Miranda PMA. Orographic drag associated with lee waves trapped at an inversion. J Atmos Sci. (2013) 70:2930-47. doi: 10.1175/JAS-D-12-0350.1
113. Vosper SB. Inversion effects on mountain lee waves. Q J R Meteor Soc. (2004) 130:1723-48. doi: 10.1256/qj.03.63
114. Vosper S. Gravity-wave drag on two mountains. Q J R Meteor Soc. (1996) 22:993-9. doi: 10.1002/qj.49712253211
115. Grisogono B, Pryor SC, Keislar RE. Mountain wave drag over double bell-shaped orography. Q J R Meteor Soc. (1993) 119:199-206.
116. Grubišić V, Stiperski I. Lee-wave resonances over double bell-shaped obstacles. J Atmos Sci. (2009)66:1205-28. doi: 10.1175/2008JAS2885.1
117. Stiperski I, Grubišić V. Trapped lee wave interference in presence of surface friction. J Atmos Sci. (2011)68:918-36. doi: 10.1175/2010JAS3495.1
118. Doyle JD, Durran DR. The dynamics of mountain-wave-induced rotors. J Atmos Sci. (2002) 59:186-201. doi: 10.1175/1520-0469(2002)059<0186:TDOMWI>2.0.CO;2
119. Inverarity GW, Shutts GJ. A general, linearized vertical structure equation for the vertical velocity: properties, scalings and special cases. Q J R Meteor Soc. (2000) 126:2709-24. doi: 10.1002/qj.49712656906
120. Jones WL. Propagation of internal gravity waves in fluids with shear flow and rotation. J Fluid Mech. (1967)30:439-48. doi: 10.1017/S0022112067001521
121. Eliassen A. On mesoscale mountain waves on the rotating Earth. Geofys Publ. (1968) 27:1-15.
122. Wurtele MG, Datta A, Sharman RD. The propagation of gravity-inertia waves and lee waves under a critical level. J Atmos Sci. (1996) 53:1505-23. doi: 10.1175/1520-0469(1996)053<1505:TPOGWA>2.0.CO;2
123. Wurtele MG, Datta A, Sharman RD. The propagation of a gravity-inertia wave in a positively sheared flow. J Atmos Sci. (2000) 57:3703-15. doi: 10.1175/1520-0469(2000)057<3703:TPOAGI>2.0.CO;2
124. Shutts G. A linear model of back-sheared flow over an isolated hill in the presence of rotation. J Atmos Sci. (2001) 58:3293-311. doi: 10.1175/1520-0469(2001)058<3293:ALMOBS>2.0.CO;2
125. Smith RB. The influence of the Earth's rotation on mountain wave drag. J Atmos Sci. (1979) 36:177-80. doi: 10.1175/1520-0469(1979)036<0177:TIOTER>2.0.CO;2
126. Miranda PMA, James IN. Non-linear three dimensional effects on the wave drag: splitting flow and breaking waves. Q J R Meteor Soc. (1992) 118:1057-81. doi: 10.1002/qj.49711850803
127. Teixeira MAC, Miranda PMA, Cardoso RM. Asymptotic gravity wave drag expressions for non-hydrostatic rotating flow over a ridge. Q J R Meteor Soc. (2008) 134:271-6. doi: 10.1002/qj.196
128. Ólafsson H, Bougeault P. The effect of rotation and surface friction on orographic drag. J Atmos Sci. (1997)54:193-210. doi: 10.1175/1520-0469(1997)054<0193:TEORAS>2.0.CO;2
129. Ólafsson H. The impact of flow regimes on asymmetry of orographic drag at moderate and low Rossby numbers. Tellus A (2000) 54:365-79. doi: 10.1034/j.1600-0870.2000.00765.x
130. Petersen GN, Kristjansson JE, Ólafsson H. The effect of upstream wind direction on atmospheric flow in the vicinity of a large mountain. Q J R Meteor Soc. (2005) 131:1113-28. doi: 10.1256/qj.04.01
131. Doyle JD, Shapiro MA, Jiang Q, Bartels D. Large-amplitude mountain wave breaking over Greenland. J Atmos Sci. (2005) 62:3106-26. doi: 10.1175/JAS3528.1
132. Martin A, Lott F. Synoptic responses to mountain gravity waves encountering directional critical levels. J Atmos Sci. (2007) 64:828-48. doi: 10.1175/JAS3873.1
133. Janowitz GS. The barotropic Rossby wave drag due to an isolated topography. J Atmos Sci. (1977) 34:802-5. doi: 10.1175/1520-0469(1977)034<0802:TBRWDD>2.0.CO;2
134. McCartney MS. Inertial Taylor columns on a beta plane. J Fluid Mech. (1975) 68:71-95. doi: 10.1017/S0022112075000699
135. Bannon PR. Rotating barotropic flow over finite isolated topography. J Fluid Mech. (1980) 101:281-306. doi: 10.1017/S0022112080001668
136. Thompson L, Flierl GR. Barotropic flow over finite isolated topography: steady solutions on the beta-plane and the initial value problem. J Fluid Mech. (1993) 250:553-86. doi: 10.1017/S0022112093001569
137. Teixeira MAC, Grisogono B. Internal wave drag in stratified flow over mountains on a beta plane. Q J R Meteor Soc. (2008) 134:11-19. doi: 10.1002/qj.188
138. Long RR. Some aspects of the flow of stratified fluids, a theoretical investigation. Tellus (1953) 5:42-58. doi: 10.1111/j.2153-3490.1953.tb01035.x
139. Huppert HE, Miles JW. Lee waves in a stratified flow. Part 3. Semi-elliptical obstacle. J Fluid Mech. (1969)35:481-96. doi: 10.1017/S0022112069001236
140. Miles JW, Huppert HE. Lee waves in a stratified flow. Part 4. Perturbation approximation. J Fluid Mech. (1969)35:497-525. doi: 10.1017/S0022112069001248
141. Lilly DK, Klemp JB. The effects of terrain shape on nonlinear hydrostatic mountain waves. J Fluid Mech. (1979) 95:241-61. doi: 10.1017/S0022112079001452
142. Miller PP, Durran DR. On the sensitivity of downslope windstorms to the asymmetry of the mountain profile. J Atmos Sci. (1991) 48:1457-73. doi: 10.1175/1520-0469(1991)048<1457:OTSODW>2.0.CO;2
143. Clark TL, Peltier WR. On the evolution and stability of finite-amplitude mountain waves. J Atmos Sci. (1977)34:1715-30. doi: 10.1175/1520-0469(1977)034<1715:OTEASO>2.0.CO;2
144. Stein J. Investigation of the regime diagram of hydrostatic flow over a mountain with a primitive equation model. Part I: Two-dimensional flows. Mon Wea Rev. (1992) 120:2962-76. doi: 10.1175/1520-0493(1992)120<2962:IOTRDO>2.0.CO;2
145. Garner ST. Permanent and transient upstream effects in nonlinear stratified flow over a ridge. J Atmos Sci. (1995) 52:227-46. doi: 10.1175/1520-0469(1995)052<0227:PATUEI>2.0.CO;2
146. Durran DR. Do breaking mountain waves decelerate the local mean flow? J Atmos Sci. (1995) 52:4010-32. doi: 10.1175/1520-0469(1995)052<4010:DBMWDT>2.0.CO;2
147. Mayr GJ, Gohm A. 2D airflow over a double bell-shaped mountain. Meteor Atmos Phys. (2000) 72, 13-27. doi: 10.1007/s007030050002
148. Smolarkiewicz PK, Rotunno R. Low Froude number flow past three-dimensional obstacles. Part II: upwind flow reversal zone. J Atmos Sci. (1990) 47:1498-1511. doi: 10.1175/1520-0469(1990)047<1498:LFNFPT>2.0.CO;2
149. Smith RB. Mountain-induced stagnation points in hydrostatic flow. Tellus A (1989) 41:270-4. doi: 10.1111/j.1600-0870.1989.tb00381.x
150. Ólafsson H, Bougeault P. Nonlinear flow past an elliptic mountain ridge. J Atmos Sci. (1996) 53:2465-89. doi: 10.1175/1520-0469(1996)053<2465:NFPAEM>2.0.CO;2
151. Vosper SB, Castro IP, Snyder WH, Mobbs SD. Experimental studies of strongly stratified flow past three-dimensional orography. J Fluid Mech. (1999) 390:223-49. doi: 10.1017/S0022112099005133
152. Eckermann S, Lindeman J, Broutman D, Ma J, Boybeyi Z. Momentum fluxes of gravity waves generated by variable Froude number flow over three-dimensional obstacles. J Atmos Sci. (2010) 67:2260-78. doi: 10.1175/2010JAS3375.1
153. Lindzen RS. Supersaturation of vertically propagating internal gravity waves. J Atmos Sci. (1988) 45:705-11. doi: 10.1175/1520-0469(1988)045<0705:SOVPIG>2.0.CO;2
154. Kim J, Mahrt L. Momentum transport by gravity waves. J Atmos Sci. (1992) 49:735-48. doi: 10.1175/1520-0469(1992)049<0735:MTBGW>2.0.CO;2
155. Richard E, Mascart P, Nickerson E. The role of surface friction in downslope windstorms. J Appl Meteor. (1989) 28:241-51. doi: 10.1175/1520-0450(1989)028<0241:TROSFI>2.0.CO;2
156. Jiang Q, Smith RB, Doyle JD. Impact of the atmospheric boundary layer on mountain waves. J Atmos Sci. (2008) 65:592-608. doi: 10.1175/2007JAS2376.1
157. Peng MS, Thompson WT. Some aspects of the effect of surface friction on flows over mountains. Q J R Meteor Soc. (2003) 129:2527-57. doi: 10.1256/qj.02.06
158. Belcher SE, Wood N. Form and wave drag due to stably stratified turbulent flow over low ridges. Q J R Meteor Soc. (1996) 122:863-902. doi: 10.1002/qj.49712253205
159. Athanassiadou M. Wave and form drag: their relation in the linear gravity wave regime. Tellus A (2003)55:173-80. doi: 10.1034/j.1600-0870.2003.00016.x
160. Hunt JC, Leibovich S, Richards KJ. Turbulent shear flows over low hills. Q J R Meteor Soc. (1988) 114:1435-70. doi: 10.1002/qj.49711448405
161. Vosper SB, Brown AR. The effect of small-scale hills on orographic drag. Q J R Meteor Soc. (2007) 133:1345-52. doi: 10.1002/qj.101
162. Steeneveld GJ, Holtslag AAM, Nappo CJ, de Wiel BJHV, Mahrt L. Exploring the possible role of small-scale terrain drag on stable boundary layers over land. J Appl Meteor Climatol. (2008) 47:2518-30. doi: 10.1175/2008JAMC1816.1
163. Nappo CJ, Chimonas G. Wave exchange between the ground surface and a boundary-layer critical level. J Atmos Sci. (1992) 49:1075-91. doi: 10.1175/1520-0469(1992)049<1075:WEBTGS>2.0.CO;2
164. Jiang Q, Doyle JD, Smith RB. Interaction between trapped waves and boundary layers. J Atmos Sci. (2006)63:617-33. doi: 10.1175/JAS3640.1
165. Smith RB. Interacting mountain waves and boundary layers. J Atmos Sci. (2007) 64:594-607. doi: 10.1175/JAS3836.1
166. Jiang Q, Doyle JD. On the diurnal variation of mountain waves. J Atmos Sci. (2008) 65:1360-77. doi: 10.1175/2007JAS2460.1