Stably stratified atmospheric boundary layers

Annual Review of Fluid Mechanics

Volumn 46, Issue , 2014, Pages 23-45

  Mahrt, L ^a,b  

^a NORTHWEST RESEARCH ASSOCIATES   (United States)

^b OREGON STATE UNIVERSITY   (United States)

Author keywords

Atmospheric turbulence; Gravity waves; Nocturnal boundary layer; Stratified turbulence; Submeso motions

Indexed keywords

HOMOGENEOUS CONDITIONS; NOCTURNAL BOUNDARY LAYERS; STABLE BOUNDARY LAYER; STRATIFIED TURBULENCE; STRONG STRATIFICATION; SUBMESO MOTIONS; TURBULENCE STRUCTURES; WEAK STRATIFICATION;

ATMOSPHERIC TURBULENCE; GRAVITY WAVES;

ATMOSPHERIC BOUNDARY LAYER;

GRAVITY WAVE; HOMOGENEITY; NOCTURNAL BOUNDARY LAYER; NUMERICAL MODEL; STRATIFIED FLOW; TURBULENCE;

EID: 84891795847     PISSN: 00664189     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev-fluid-010313-141354     Document Type: Article

References (146)

1. Abarbanel H, Holm D, Marsden J, Ratiu T. 1984. Richardson number criterion for the nonlinear stability of three-dimensional stratified flow. Phys. Rev. Lett. 52:2352-55
2. Anderson P. 2003. Fine-scale structure observed in a stable atmospheric boundary layer by Sodar and kiteborne tethersonde. Bound-Layer Meteorol. 107:323-51
3. Anderson P. 2009. Measurement of Prandtl number as a function of Richardson number avoiding selfcorrelation. Bound-Layer Meteorol. 131:345-62
4. Andreas EL, Claffey K, Makshtas A. 2000. Low-level atmospheric jets and inversions over the western Weddell Sea. Bound-Layer Meteorol. 97:459-86
5. Anfossi D, Oetti D, Degrazia G, Boulart A. 2005. An analysis of sonic anemometer observations in low wind speed conditions. Bound-Layer Meteorol. 114:179-203
6. Anquetin A, Guilbaud C, Chollet JP. 1998. The formation and destruction of inversion layers within a deep valley. J. Appl. Meteorol. 37:1547-60
7. Aubinet M, Heinesch B, Yernaux M. 2003. Horizontal and vertical CO2 advection in a sloping forest. Bound Layer Meteorol. 108:397-417
8. Baas P, Steeneveld G, Van De Weil B, Holtslag A. 2006. Exploring self-correlation in the flux-gradient relationships for stably stratified conditions. J. Atmos. Sci. 63:3045-54
9. Bakas NA, Ioannou PJ. 2007. Momentum and energy transport by gravity waves in stochastically driven stratified flows Part I: Radiation of gravity waves from a shear layer. J. Atmos. Sci. 64:1509-29
10. Balsley B, Frehlich R, Jensen ML, Meillier Y. 2003. Extreme gradients in the nocturnal boundary layer: Structure, evolution and potential causes. J. Atmos. Sci. 60:2496-508
11. Balsley B, Frehlich RG, Jensen ML, Meillier Y. 2006. High-resolution in situ profiling through the stable boundary layer: Examination of the SBL top in terms of minimum shear, maximum stratification, and turbulence decrease. J. Atmos. Sci. 63:1291-307
12. Banta R, Pichugina Y, Brewer W. 2006. Turbulent velocity-variance profiles in the stable boundary layer generated by a nocturnal low-level jet. J. Atmos. Sci. 63:2700-19
13. Basu S, Porté-Agel F, Foufoula-Georgiou E, Vinuesa JF, Pahlow M. 2006. Revisiting the local scaling hypothesis in stably stratified atmospheric boundary-layer turbulence: An integration of field and laboratory measurements with large-eddy simulations. Bound-Layer Meteorol. 119:473-500
14. Belüsi'c D, Mahrt L. 2012. Is geometry more universal than physics in atmospheric boundary layer flow?. J. Geophys. Res. 117:D09115
15. Billant P, Chomaz JM. 2000. Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid. J. Fluid Mech. 418:167-88
16. Blumen W. 1984. An observational study of instability and turbulence in nighttime drainage winds. Bound Layer Meteorol. 28:245-69
17. Blumen W, Grossman R, Piper M. 1999. Analysis of heat budget, dissipation and frontogenesis in a shallow density current. Bound-Layer Meteorol. 91:281-306
18. Böhme T, Hauf T, Lehmann V. 2004. Investigation of short-period gravity waves with the Lindenberg 482 MHz tropospheric wind profiler. Q. J. R. Meteorol. Soc. 130:2933-52
19. Bonin T, Chilson P, Zielke B, Fedorovich E. 2013. Observations of the early evening boundary-layer transition using a small unmanned aerial system. Bound-Layer Meteorol. 146:119-32
20. BrownR. 1972.Onthe inflection point instability of a stratifiedEkman boundary layer. J. Atmos. Sci. 29:850-59
21. Burns S, Sun J, Delany A, Semmer S, Oncley S, Horst T. 2003. A field intercomparison technique to improve the relative accuracy of longwave radiation measurements and an evaluation of CASES-99 pyrgeometer data quality. J. Atmos. Ocean. Technol. 20:348-61
22. Busch NE, Vinnichenko NK, Waterman AT Jr, Beard C, Stewart RW, Scotti RS. 1969. Waves and turbulence. Radio Sci. 4:1377-79
23. Caughey S, Readings C. 1975. An observation of waves and turbulence in the earth's boundary layer. Bound Layer Meteorol. 9:279-96
24. Cava D, Giostra U, Siqueira M, Katul G. 2004. Organizedmotion and radiative perturbations in the nocturnal canopy sublayer above an even-Aged pine forest. Bound-Layer Meteorol. 112:129-57
25. Cava D, Katul G. 2009. The effects of thermal stratification on clustering properties of canopy turbulence. Bound-Layer Meteorol. 130:307-25
26. Chemel C, Staquet C, Largeron Y. 1991. Generation of internal gravity waves by a katabatic wind in an idealized alpine valley. Meteorol. Atmos. Phys. 103:187-94
27. Chimonas G. 1994. Jeffrey's drag instability applied to waves in the lower atmosphere: Linear and nonlinear growth rates. J. Atmos. Sci. 51:3758-74
28. Christie DR, Muirhead KJ, Hales AL. 1978. Long nonlinear waves in the lower atmosphere. J. Atmos. Sci. 35:805-25
29. Conangla L, Cuxart J, Soler MR. 2008. Characterisation of the nocturnal boundary layer at a site in northern Spain. Bound-Layer Meteorol. 128:255-76
30. Cuxart J, Morales G, Terradellas E, Yagüe C. 2002. Study of coherent structures and estimation of the pressure transport terms for the nocturnal boundary layer. Bound-Layer Meteorol. 105:305-28
31. DeBaas AF, Driedonks AGM. 1985. Internal gravity waves in a stably-stratified boundary layer. Bound-Layer Meteorol. 31:303-23
32. Derbyshire H. 1995. Stable boundary layers: Observations, models and variability part I: Modelling and measurements. Bound-Layer Meteorol. 74:19-54
33. Derbyshire H. 1995. Stable boundary layers: Observations, models and variability part II: Data analysis and averaging effects. Bound-Layer Meteorol. 75:1-24
34. Doran JC, Horst TW. 1981. Velocity and temperature oscillations in drainage winds. J. Appl. Meteorol. 20:360-64
35. Duynkerke P. 1999. Turbulence, radiation and fog in Dutch stable boundary layers. Bound-Layer Meteorol. 90:447-77
36. Einaudi F, Finnigan JJ. 1993. Wave-Turbulence dynamics in the stably stratified boundary layer. J. Atmos. Sci. 50:1842-64
37. Farrell BF, Ioannou PJ. 2008. The stochastic parametric mechanism for growth of wind-driven surface water waves. J. Phys. Oceanogr. 38:862-79
38. Fernando HJS. 2003. Turbulence patches in a stratified shear flow. Phys. Fluids 15:3164-69
39. Fernando HJS, Weil JC. 2010. Whither the stable boundary layer?. A shift in the research agenda. Bull. Am. Meteorol. Soc. 91:1475-84
40. Finnigan J. 1999. A note on wave-Turbulence interaction and the possibility of scaling the very stable boundary layer. Bound-Layer Meteorol. 90:529-39
41. Finnigan J. 2000. Turbulence in plant canopies. Agric. For. Meteorol. 32:519-71
42. Finnigan J, Einaudi F, Fua D. 1984. The interaction between an internal gravity wave and turbulence in the stably-stratified nocturnal boundary layer. J. Atmos. Sci. 41:2409-36
43. Flores O, Riley J. 2011. Analysis of turbulence collapse in the stably stratified surface layer using direct numerical simulation. Bound-Layer Meteorol. 139:241-59
44. Foster RC, Levy G. 1998. The contribution of organized roll vortices to the surface wind vector in baroclinic conditions. J. Atmos. Sci. 55:1466-72
45. Fritts D, Nappo C, Riggin D, Balsley B, Eichinger W, Newsom R. 2003. Analysis of ducted motions in the stable boundary layer during CASES-99. J. Atmos. Sci. 60:2450-72
46. Gage K. 1971. The effect of stable thermal stratification on the stability of viscous parallel flows. J. FluidMech. 47:1-20
47. Galperin B, Sukoriansky S, Anderson P. 2007.Onthe critical Richardson number in stably stratified turbulence. Atmos. Sci. Lett. 8:65-69
48. Garratt J. 1992. The Atmospheric Boundary Layer. Cambridge, UK: Cambridge Univ. Press
49. Gerz T, Howell JF, Mahrt L. 1994. Vortex stretching and microfronts. Phys. Fluids A 6:1242-51
50. Gibert F, Arnault N, Cuesta J, Plougonven R, Flammant P. 2011. Internal gravity waves convectively forced in the atmospheric residual layer during the morning transition. Q. J. R. Meteorol. Soc. 137:1610-24
51. Gibson C. 1999. Fossil turbulence revisited. J. Mar. Sys. 21:147-67
52. Godoy-Diana R, Chomaz JM, Donnadieu C. 2006. Internal gravity waves in a dipolar wind: A wave-vortex interaction experiment in a stratified fluid. J. Fluid Mech. 548:281-308
53. Grachev A, Andreas E, Fairall C, Guest P, Persson P. 2013. The critical Richardson number and limits of applicability of local similarity theory in the stable boundary layer. Bound-Layer Meteorol. 147:51-82
54. Grachev A, Fairall C, Persson P, Andreas E, Guest P. 2005. Stable boundary-layer scaling regimes: The SHEBA data. Bound-Layer Meteorol. 116:201-35
55. Grisogono B. 1994. A curvature effect on the critical Richardson number. Croat. Meteorol. J. 29:43-46
56. Grisogono B. 2011. The angle of near-surface wind-Turning in weakly stable boundary layers. Q. J. R. Meteorol. Soc. 137:700-8
57. Helmis C. 1996. Some aspects of the variation with time of katabatic flow over a simple slope. Q. J. R. Meteorol. Soc. 122:595-610
58. Hicks B. 1978. Some limitations of dimensional analysis and power laws. Bound-Layer Meteorol. 14:567-69
59. HohreiterV. 2008. Finescale structure and dynamics of an atmospheric temperature interface. Q. J. R. Meteorol. Soc. 65:1701-10
60. Hooke WH, Jones RM. 1986. Dissipative waves excited by gravity wave encounters with the stably stratified planetary boundary layer. J. Atmos. Sci. 43:2048-60
61. Hopfinger EJ. 1987. Turbulence in stratified fluids: A review. J. Geophys. Res. 92:5287-303
62. Howell J, Sun J. 1999. Surface layer fluxes in stable conditions. Bound-Layer Meteorol. 90:495-520
63. Hunt J, Kaimal J, Gaynor J. 1985. Some observations of turbulence structure in stable layers. Q. J. R. Meteorol. Soc. 111:793-815
64. Hunt J, Vassilicos J. 1991. Kolmogorov's contributions to the physical and geometrical understanding of small-scale turbulence and recent developments. Proc. R. Soc. Lond. A 434:183-210
65. Inoue R, Smyth WD. 2009. Efficiency of mixing forced by unsteady shear flow. J. Phys. Oceanogr. 39:1150-66
66. Katul G, Albertson J, Parlange M, Chu CR, Stricker H. 1994. Conditional sampling, bursting and the intermittent structure of sensible heat flux. J. Geophys. Res. 99:22869-76
67. Katul G, Hsieh CI, Bowling D, Clark K, Shurpali N, et al. 1999. Spatial variability of turbulent fluxes in the roughness sublayer of an even-Aged pine forest. Bound-Layer Meteorol. 93:1-28
68. Keuttner J, Hildebrand P, Clark T. 1993. Convection waves: Observations of gravity wave systems over convectively active boundary layers. Q. J. R. Meteorol. Soc. 113:445-67
69. Klipp C, Mahrt L. 2004. Flux-gradient relationship, self-correlation and intermittency in the stable boundary layer. Q. J. R. Meteorol. Soc. 130:2087-104
70. Kristensen L, Jensen N, Peterson EL. 1981. Lateral dispersion of pollutants in a very stable atmosphere: The effect of the meandering. Atmos. Environ. 15:837-44
71. Lee X, Barr A. 1998. Climatology of gravity waves in a forest. Q. J. R. Meteorol. Soc. 124:1403-19
72. Lee X, Neuman H, den Hartog G, Fuentes J, Black T, et al. 1997. Observations of gravity waves in a boreal forest. Bound-Layer Meteorol. 84:383-98
73. Li XS, Gaynor JE, Kaimal JC. 1983. A study of multiple stable layers in the nocturnal lower atmosphere. Bound-Layer Meteorol. 26:157-68
74. Lilly D. 1983. Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci. 40:749-61
75. Liu Z, Thorpe SA, Smyth WD. 2012. Instability and hydraulics of turbulent stratified shear flows. J. Fluid Mech. 695:235-56
76. Lu NP, Neff WD, Kaimal JC. 1983. Wave and turbulence structure in a disturbed nocturnal inversion. Bound-Layer Meteorol. 26:141-55
77. Luhar A, Hurley P, Rayner K. 2009. Modeling near-surface low winds over land under stable conditions: Sensitivity tests, flux-gradient relationships and stability parameters. Bound-Layer Meteorol. 130:249-74
78. Mahrt L. 1989. Intermittency of atmospheric turbulence. J. Atmos. Sci. 46:79-95
79. Mahrt L. 2008. The influence of transient flow distortion on turbulence in stable weak-wind conditions. Bound-Layer Meteorol. 127:1-16
80. Mahrt L. 2010. Common microfronts and other solitary events in the nocturnal boundary layer. Q. J. R. Meteorol. Soc. 136:1712-22
81. Mahrt L, Howell J. 1994. The influence of coherent structures and microfronts on scaling laws using global and local transforms. J. Fluid Mech. 260:247-70
82. Mahrt L, Richardson S, Seaman N, Stauffer D. 2012. Turbulence in the nocturnal boundary layer with light and variable winds. Q. J. R. Meteorol. Soc. 138:1430-39
83. Mahrt L, Thomas C, Richardson S, Seaman N, Stauffer D, Zeeman M. 2013. Non-stationary generation of weak turbulence for very stable and weak-wind conditions. Bound-Layer Meteorol. 147:179-99
84. Mahrt L, Vickers D. 2002. Contrasting vertical structures of nocturnal boundary layers. Bound-LayerMeteorol. 105:351-63
85. Mahrt L, Vickers D. 2006. Extremely weak mixing in stable conditions. Bound-Layer Meteorol. 119:19-39
86. Majda A, Shefter M. 1998. Elementary stratified flows with instability at large Richardson number. J. Fluid Mech. 376:319-50
87. McNaughton KG. 2012. The flow of mechanical energy in convective boundary layers. Bound-LayerMeteorol. 145:145-63
88. McNider R, England D, Friedman M, Shi X. 1995. Predictability of the stable atmospheric boundary layer. J. Atmos. Sci. 52:1602-14
89. Meillier Y, Frehlich RG, Jones RM, Balsley BB. 2008. Modulation of small-scale turbulence by ducted gravity waves in the nocturnal boundary layer. J. Atmos. Sci. 65:1414-27
90. Meunier P, Dizés SL, Leweke T. 2005. Physics of vortex merging. C. R. Phys. 6:431-50
91. Monti PF, Chan W, Princevac M, Kowalewski T, Pardyjak E. 2002. Observations of flow and turbulence in the nocturnal boundary layer over a slope. J. Atmos. Sci. 59:2513-34
92. Mukund V, Singh DK, Ponnulakshmi VK, Subramanian G, Sreenivas KR. 2013. Field and laboratory experiments on aerosol-induced cooling in the nocturnal boundary layer. Q. J. R. Meteorol. Soc. In Press
93. Muschinski A, Frehlich R, Balsley B. 2004. Small-scale and large-scale intermittency in the nocturnal boundary layer and the residual layer. J. Fluid Mech. 515:319-51
94. Nakamura R, Mahrt L. 2005. A study of intermittent turbulence with CASES-99 towermeasurements. Bound Layer Meteorol. 114:367-87
95. Nappo CJ. 1991. Sporadic breakdown of stability in the PBL over simple and complex terrain. Bound-Layer Meteorol. 54:69-87
96. Nappo CJ. 2012. An Introduction to Atmospheric Gravity Waves. New York: Academic. 359 pp. 2nd e.d.
97. Nappo CJ, Miller DR, Hiscox AL. 2008. Wave-modified flux and plume dispersion in the stable boundary layer. Bound-Layer Meteorol. 129:211-23
98. Ohya Y, Nakamura R, Uchida T. 2008. Intermittent bursting of turbulence in a stable boundary layer with low-level jet. Bound-Layer Meteorol. 126:249-63
99. Panofsky H, Dutton J. 1984. Atmospheric Turbulence: Models and Methods for Engineering Applications. New York:Wiley
100. Pardyjak E, Monti P, Fernando HJS. 2002. Flux Richardson number measurements in stable atmospheric shear flows. J. Fluid Mech. 449:307-16
101. Porch W, Clements W, Coulter R. 1991. Nighttime valley waves. J. Appl. Meteorol. 30:145-56
102. Pulido M, Chimonas G. 2001. Forest canopy waves: The long-wavelength component. Bound-Layer Meteorol. 100:209-24
103. Rao M, Castracane P, Fua D, Fiocco G. 2004. Observations of atmospheric solitary waves in the urban boundary layer. Bound-Layer Meteorol. 111:85-108
104. Rees J, Anderson P, King J. 1998. Observations of solitary waves in the stable atmospheric boundary layer. Bound-Layer Meteorol. 86:47-61
105. Rees J, Denholm-Price J, King J, Anderson P. 2000. A climatological study of internal gravity waves in the atmospheric boundary layer overlying the Brunt Ice Shelf, Antarctica. J. Atmos. Sci. 57:511-26
106. Reuder J, Jonassen M, Olafsson H. 2012. The Small Unmanned Meteorological Observer SUMO: Recent developments and applications of a micro-UAS for atmospheric boundary layer research. Acta Geophys. 60:1454-73
107. Riley JJ, Lelong MP. 2000. Fluidmotions in the presence of strong stable stratification. Annu. Rev. FluidMech. 32:613-57
108. Riley JJ, Lindborg E. 2008. Stratified turbulence: A possible interpretation of some geophysical turbulence measurements. J. Atmos. Sci. 65:2416-24
109. Smedman AS. 1988. Observations of a multi-level turbulence structure in a very stable atmospheric boundary layer. Bound-Layer Meteorol. 44:231-53
110. Smedman AS, Tjernstrõm H, Högstrõm U. 1993. Analysis of the turbulence structure of a marine low-level jet. Bound-Layer Meteorol. 66:105-26
111. Smith RB. 2007. Interacting mountain waves and boundary layers. J. Atmos. Sci. 64:594-607
112. Smyth W, Moum JN. 2012. Ocean mixing by Kelvin-Helmholtz instability. Oceanography. 25:140-49
113. Sorbjan Z. 1989. Structure of the Atmospheric Boundary Layer. Englewood Cliffs, NJ: Prentice Hall
114. Sorbjan Z. 2010. Gradient-based scales and similarity laws in the stable boundary layer. Q. J. R. Meteorol. Soc. 136:1243-54
115. Stewart RW. 1969. Turbulence and waves in a stratified atmosphere. Radio Sci. 4:1269-78
116. Stull R. 1988. An Introduction to Boundary Layer Meteorology. Dordrecht: Kluwer Acad.
117. Sukorianski S, Dikovskaya N, Galperin B. 2009. Transport of momentum and scalar in turbulent flows with anisotropic dispersive waves. Geophys. Res. Lett. 36:L14609
118. Sukorianski S, Galperin B. 2013. An analytical theory of the buoyancy: Kolmogorov subrange transition in turbulent flows with stable stratification. Philos. Trans. R. Lond. Ser. A 371:20120212
119. Sun J, Burns S, Lenschow D, Banta R, Newsom R, et al. 2002. Intermittent turbulence associated with a density current passage in the stable boundary layer. Bound-Layer Meteorol. 105:199-219
120. Sun J, Lenschow DH, Burns SP, Banta RM, Newsom RK, et al. 2004. Atmospheric disturbances that generate intermittent turbulence in nocturnal boundary layers. Bound-Layer Meteorol. 110:255-79
121. Sun J, Mahrt L, Banta R, Pichugina Y. 2012. Turbulence regimes and turbulence intermittency in the stable boundary layer during CASES-99. J. Atmos. Sci. 69:338-51
122. Tennekes H. 1976. Fourier-Transform ambiguity in turbulence dynamics. J. Atmos. Sci. 32:1660-63
123. Tennekes H, Lumley J. 1972. A First Course in Turbulence. Cambridge, MA: MIT Press
124. Terradellas E, Morales G, Cuxart J, Yagüe C. 2001. Wavelet methods: Application to the study of the stable atmospheric boundary layer. Dyn. Atmos. Oceans 34:225-44
125. Terradellas E, Soler M, Ferreres E, Bravo M. 2005. Analysis of oscillations in the stable boundary layer using wavelet methods. Bound-Layer Meteorol. 114:489-518
126. Thomas C, Kennedy A, Selker J, Moretti A, Schroth M, et al. 2012. High-resolution fibre-optic temperature sensing: A new tool to study the two-dimensional structure of atmospheric surface-layer flow. Bound-Layer Meteorol. 142:177-92
127. Tjernstrõm M, Balsley BB, Svensson G, Nappo C. 2009. The effects of critical layers on residual layer turbulence. J. Atmos. Sci. 66:468-80
128. Tjernstrõm M, Mauritsen T. 2009. Mesoscale variability in the summer Arctic boundary layer. Bound-Layer Meteorol. 130:383-406
129. Udina M, Soler M, Viana S, Yagüe C. 2013. Model simulation of gravity waves triggered by a density current. Q. J. R. Meteorol. Soc. 139:701-14
130. Van deWiel BJH, Moene A, Hartogenesis G, Bruin HD, Holtslag AAM. 2003. Intermittent turbulence in the stable boundary layer over land. Part III: A classification for observations during CASES-99. J. Atmos. Sci. 60:2509-22
131. Van deWiel BJH, Moene AF, Jonker HJJ. 2012. The cessation of continuous turbulence as precursor of the very stable nocturnal boundary layer. J. Atmos. Sci. 69:3097-115
132. Van de Wiel BJH, Moene AF, Jonker HJJ, Baas P, Basu S, et al. 2012. Theminimum wind speed for sustainable wind speed in the nocturnal boundary layer. J. Atmos. Sci. 69:3116-27
133. Van de Wiel BJH, Moene AF, Steeneveld GJ, Baas P, Bosveld FC, Holtslag AAM. 2010. A conceptual view on inertial oscillations and nocturnal low-level jets. J. Atmos. Sci. 67:2679-89
134. Van Gorsel E, Harman IN, Finnigan JJ, Leuning R. 2011. Decoupling of air flow above and in plant canopies and gravity waves affect micrometeorological estimates of net scalar exchange. Agric. For. Meteorol. 151:927-33
135. Vassilicos JC, Hunt J. 1978. Fractal dimensions and spectra of interfaces with application to turbulence. Proc. R. Soc. Lond. A 435:505-34
136. Viana S, Terradellas S, Yagüe C. 2010. Analysis of gravity waves generated at the top of a drainage flow. J. Atmos. Sci. 67:3949-66
137. Viana S, Yagüe C, Maqueda G. 2009. Propagation and effects of a mesoscale gravity wave over a weaklystratified stable boundary layer during SABLES2006 field campaign. Bound-Layer Meteorol. 133:165-88
138. Vickers D, Mahrt L. 2007. Observations of the cross-wind velocity variance in the stable boundary layer. Environ. Fluid Mech. 7:55-71
139. Waite M, Bartello P. 2004. Stratified turbulence dominated by vortical motion. J. Fluid Mech. 517:281-308
140. Weinstock J. 1985.Onthe theory of temperature spectra in a stably stratified fluid. J. Phys.Oceanogr. 15:475-77
141. Winters K, Lombard P, Riley J, D'Asaro E. 1995. Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289:115-28
142. Wyngaard JC. 2010. Turbulence in the Atmosphere. Cambridge, UK: Cambridge Univ. Press
143. Yagüe C, Viana S, Maqueda G, Redondo JM. 2006. Influence of stability on the flux-profile relationships for wind speed, φm, and temperature, φh, for the stable atmospheric boundary layer. Nonlinear Proc. Geophys. 13:185-203
144. Zhang F, Koch S, Davis C, Kaplan M. 2001. Wavelet analysis and the governing dynamics of a large-Amplitude mesoscale gravity-wave event along theEastCoast of theUnited States. Q. J. R. Meteorol. Soc. 127:2209-45
145. Zilitinkevich S, Elperin T, Kleeorin N, Rogachevskii I. 2007. Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows Part I: Steady state homogeneous regimes. Bound-LayerMeteorol. 125:167-91
146. Zilitinkevich S, Mammarella M, Baklanov AA, Joffre SS. 2008. The effect of stratification on the aerodynamic roughness length and displacement height. Bound-Layer Meteorol. 129:179-90