Nonlinear development of the ekman layer structures
DOI:
https://doi.org/10.7242/1999-6691/2017.10.2.17Keywords:
atmospheric boundary layer, nonlinear mode, numerical simulation, helicity, instability, asymmetryAbstract
The nonlinear modes of coherent structure development in the Atmospheric boundary layer are investigated. Two-scale model of Atmospheric boundary layer is used in the calculation. The velocity field splits into large-scale profile of horizontal wind velocity and three-scale velocity field. The former depends only on the vertical coordinate. The latter is connected with roll circulation and is subject to the vertical coordinate and the coordinate perpendicular to the roll direction. The influence of turbulence is parameterized by turbulent viscosity. The modification of wind profile by rolls is taken into account. Depending on the Reynolds number, different types of the hydrodynamic instabilities specific to the Atmospheric boundary layer occurred. This appears at the relative orientation of the arising geostrophic wind and roll circulation, and also at the scales and space periods of the structures. As the Reynolds number grows, the mean energy and helicity increase. Within the range of the Reynolds number between 200÷300 the dependence is close to linear, which points to the possibility of utilizing weakly nonlinear theory methods, where perturbation amplitudes increase as Re1/2. The rise of the roll asymmetry followed by remarkable growing of the extreme amplitude of a longitudinal velocity component in the direction opposite to geostrophic wind compared to the amplitudes along the lines of geostrophic wind is detected. Increase of the positive component of helicity by contrast to the negative ones is observed simultaneously. A qualitative comparison between the modeling findings and the measured characteristics of the coherent structures observed in the Atmospheric boundary layer is carried out. In July 2007, these structures were measured by acoustic sounding methods in Kalmykia, where asymmetry in the distribution of longitudinal velocity component was observed as well. An apparent pattern of roll circulation begins to reproduce in the mesoscale atmospheric model RAMS under grid size about 500 meters. Reasonably good correspondence between simulation findings and observable vortex with centers lying about 1200÷1300 meters high is received. The values of turbulent viscosity and effective Reynolds number are typical for unstable stratification conditions.
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Granberg I.G., Kramar V.F., Kuznecov R.D., Chetiani O.G., Kallistratova M.A., Kulickov S.N., Artamonova M.S., Kuznecov D.D., Perepelkin V.G., Perepelkin D.B., Pogarskij F.A. Issledovanie prostranstvennoj struktury atmosfernogo pogranicnogo sloa set’u doplerovskih sodarov // Izvestia RAN. FAO. - 2009. - T. 45, No 5. - C. 579-587. DOI
2. Etling D., Brown R.A. Roll vortices in the planetary boundary layer: A review // Bound.-Lay. Meteorol. - 1993. - Vol. 65, no. 3. - P. 215-248. DOI
3. Foster R. Signature of large aspect ratio roll vortices in synthetic aperture radar images of tropical cyclones // Oceanography. - 2013. - Vol. 26, no. 2. - P. 58-67. DOI
4. Chou S.-H., Atlas D. Satellite estimates of ocean-air heat fluxes during cold air outbreaks // Mon. Weather Rev. - 1982. - Vol. 110, no. 10. - P. 1434-1450. DOI
5. Hein P.F., Brown R.A. Observations of longitudinal roll vortices during arctic cold air outbreaks over open water // Bound.-Lay. Meteorol. - 1988. - Vol. 45, no. 1. - P. 177-199. DOI
6. Brummer B. Roll and cell convection in wintertime arctic cold-air outbreaks // J. Atmos. Sci. - 1999. - Vol. 56, no. 15. - P. 2613-2636. DOI
7. Wurman J., Winslow J. Intense sub-kilometer-scale boundary layer rolls observed in hurricane fran // Science. - 1998. - Vol. 280, no. 5363. - P. 555-557. DOI
8. Morrison H., Curry J.A., Khvorostyanov V.I. A New double-moment microphysics parameterization for application in cloud and climate models. Part I: Description // J. Atmos. Sci. - 2005. - Vol. 62, no. 6. - P. 1665-1677. DOI
9. Foster R.C. Why rolls are prevalent in the hurricane boundary layer // J. Atmos. Sci. - 2005. - Vol. 62, no. 8. - P. 2647-2661. DOI
10. Ginis I., Khain A. P., Morozovsky E. Effects of large eddies on the structure of the marine boundary layer under strong wind conditions // J. Atmos. Sci. - 2004. - Vol. 72, no. 9. - P. 3049-3063. DOI
11. Gao K., Ginis I. On the equilibrium-state roll vortices and their effects in the hurricane boundary layer // J. Atmos. Sci. - 2016. - Vol. 73, no. 3. - P. 1205-1222. DOI
12. Chou S.H., Ferguson M.P. Heat fluxes and roll circulations over the western Gulf Stream during an intense cold-air outbreak // Bound.-Lay. Meteorol. - 1991. - Vol. 55, no. 3. - P. 255-281. DOI
13. Braun R.A. Analiticeskie metody modelirovania planetarnogo pogranicnogo sloa. - L.: Gidrometeoizdat, 1976. - 150 s.
14. Lilly D.K. On the stability of Ekman boundary flow // J. Atmos. Sci. - 1966. - Vol. 23. - P. 481-494. DOI
15. Ordanovic A.E., Paskovskaa U.V. Vlianie termiceskoj stratifikacii na ustojcivost’ ekmanovskogo tecenia // MZG. - 1998. - No 3. - S. 71-76. DOI
16. Kaylor R., Faller A.J. Instability of the stratified Ekman boundary layer and the generation of internal waves // J. Atmos. Sci. - 1972. - Vol. 29, no. 3. - P. 497-509. DOI
17. Weckwerth T.M., Wilson J.W., Wakimoto R.M., Crook N.A. Horizontal convective rolls: Determining the environmental conditions supporting their existence and characteristics // Mon. Weather Rev. - 1997. - Vol. 125, no. 4. - P. 505-526. DOI
18. Mihajlova L.A., Ordanovic A.E. Modelirovanie dvuhmernyh uporadocennyh vihrej v pogranicnom sloe atmosfery // Meteorologia i gidrologia. - 1988. - No 11. - S. 29-42.
19. Brown R.A. Longitudinal instabilities and secondary flows in the planetary boundary layer: A review // Rev. Geophys. - 1980. - Vol. 18, no. 3. - P. 683-697. DOI
20. Stensrud D.J., Shirer H.N. Development of boundary layer rolls from dynamic instabilities // J. Atmos. Sci. - 1988 - Vol. 45, no. 6. - P. 1007-1019. DOI
21. Dubos T., Barthlott C., Drobinski P. Emergence and secondary instability of Ekman layer rolls // J. Atmos. Sci. - 2008. - Vol. 65, no. 7. - P. 2326-2342. DOI
22. Gavrilov K.A., Morvan D., Accary G., Lubimov D.V., Meradji S., Bessonov O.A. Cislennoe modelirovanie kogerentnyh struktur pri rasprostranenii primesi v atmosfernom pogranicnom sloe nad lesnym pologom // Vycisl. meh. splos. sred. - 2010. - T. 3, No 2. - S. 34-45.23. DOI
23. Svarc K.G., Svarc U.A., Sklaev V.A. Dvumernaa model’ mezomasstabnyh processov v niznem sloe atmosfery s ucetom neodnorodnosti temperatury i vlaznosti vozduha // Vycisl. meh. splos. sred. - 2015. - T. 8, No 1. - S. 5-15. DOI
24. Etling D. Some aspect of helicity in atmospheric flows // Beitr. Phys. Atmosph. - 1985. - Vol. 58, no. 1. - P. 88-100.
25. Kurganskij M.V. O svazi mezdu spiral’nost’u i potencial’nym vihrem v szimaemoj vrasausejsa zidkosti // Izvestia AN SSSR. FAO. - 1989. - T. 25, No 12. - S. 1326-1329.
26. Hide R. Superhelicity, helicity and potential vorticity // Geophys. Astro. Fluid. - 1989. - Vol. 48, no. 1-3. - P. 69-79. DOI
27. Chetiani O.G. O spiral’noj strukture ekmanovskogo pogranicnogo sloa // Izvestia RAN. FAO. - 2001. - T. 37, No 5. - S. 614-620.
28. Koprov B.M., Koprov V.M., Ponomarev V.M., Chetiani O.G. Izmerenie turbulentnoj spiral’nosti i ee spektra v pogranicnom sloe atmosfery // DAN. - 2005. - T. 403, No 5. - S. 627-630. DOI
29. Koprov B.M., Koprov V.M., Kurganskij M.V., Chetiani O.G. Spiral’nost’ i potencial’nyj vihr’ v prizemnoj turbulentnosti // Izvestia RAN. FAO. - 2015. - T. 51, No 6. - S. 637-647. DOI
30. Deusebio E., Lindborg E. Helicity in the Ekman boundary layer // J. Fluid Mech. - 2014. - Vol. 755. - P. 654-671. DOI
31. Coleman G.N., Ferziger J.H., Spalart P.R. A numerical study of the turbulent Ekman layer // J. Fluid Mech. - 1990. - Vol. 213. - P. 313-348. DOI
32. Coleman G.N., Ferziger J.H., Spalart P.R. A numerical study of the convective boundary layer // Bound.-Lay. Meteorol. - 1994. - Vol. 70, no. 3. - P. 247-272. DOI
33. Deardorff J. W. Numerical investigation of neutral and unstable planetary boundary layers // J. Atmos. Sci. - 1972. - Vol. 29, no. 1. - P. 91-115. DOI
34. Foster R.C. An analytic model for planetary boundary roll vortices / PhD Thesis. - WA, Seattle: University of Washington, 1996. - 196 p.
35. Mason P., Thomson D. Large-eddy simulations of the neutral-static-stability planetary boundary layer // Q. J. Roy. Meteor. Soc. - 1987. - Vol. 113, no. 476. - P. 413-443.36. DOI
36. Lin C.-L., McWilliams J., Moeng C.-H., Sullivan P. Coherent structures and dynamics in a neutrally stratified planetary boundary layer flow // Phys. Fluids. - 1996. - Vol. 8, no. 10. - P. 2626-2639. DOI
37. Drobinski P., Carlotti P., Redelsperger J.-L., Masson V., Banta R.M., Newsom R.K. Numerical and experimental investigation of the neutral atmospheric surface layer // J. Atmos. Sci. - 2007. - Vol. 64. - P. 137-156. DOI
38. Ponomarev V.M., Chetiani O.G., Sestakova L.V. Nelinejnaa dinamika krupnomasstabnyh vihrevyh struktur v turbulentnom ekmanovskom sloe // MZG. - 2007. - No 4. - S. 72-82. DOI
39. Ponomarev V.M., Chetiani O.G., Sestakova L.V. Cislennoe modelirovanie razvitoj gorizontal’noj cirkulacii v atmosfernom pogranicnom sloe // Vycisl. meh. splos. sred. - 2009. - T. 2, No 1. - S. 68-80. DOI
40. Ponomarev V.M., Chetiani O.G. Poluempiriceskaa model’ pogranicnogo sloa atmosfery s parametrizaciej vliania turbulentnoj spiral’nosti // Izvestia RAN. FAO. - 2005. - T. 41, No 4. - S. 464-479.
41. Rouc P. Vycislitel’naa gidrodinamika. - M.: Mir, 1980. - 618 s.
42. Samarskij A.A., Gulin A.V. Cislennye metody. - M.: Nauka, 1989. - 432 s.
43. Tom A., Ejplt K., Templa D. Cislovye rascety polej v tehnike i fizike. - M.: Energia, 1964. - 208 s.
44. Kraichnan R.H. Helical turbulence and absolute equilibrium // J. Fluid Mech. - 1973. - Vol. 59, no. 4. - P. 745-752. DOI
45. Kalasnik M.V., Hapaev A.A., Chetiani O.G. O ciklon-anticiklonnoj asimmetrii v ustojcivosti vrasausihsa sdvigovyh tecenij // MZG. - 2016. - No 2. - S. 44-55. DOI
46. Hoffmann N., Busse F.H., Chen W.L. Transitions to complex flows in the Ekman-Couette layer // J. Fluid Mech. - 1998. - Vol. 366. - P. 311-331. DOI
47. Hoffmann N.P., Busse F.H. Isolated solitary vortex solutions for the Ekman Couette layer // Eur. J. Mech. B-Fluid. - 2000. - Vol. 19, no. 3. - P. 391-402. DOI
48. Mourad P.D., Brown R.A. Multiscale large eddy states in weakly stratified planetary boundary layers // J. Atmos. Sci. - 1990. - Vol. 47, no. 4. - P. 414-438. DOI
49. Corke T.C., Knasiak K.F. Stationary travelling cross-flow mode interactions on a rotating disk // J. Fluid Mech. - 1998. - Vol. 355. - P. 285-315. DOI
50. Cotton W.R., Pielke Sr. R.A., Walko R.L., Liston G.E., Tremback C.J., Jiang H., McAnelly R.L., Harrington J.Y., Nicholls M.E., Carrio G.G., McFadden J.P. RAMS 2001: Current status and future directions // Meteorol. Atmos. Phys. - 2003. - Vol. 82, no. 1. - P. 5-29. DOI
51. Blackadar A.K. The vertical distribution of wind and turbulent exchange in a neutral atmosphere // J. Geophys. Res. - 1962. - Vol. 67, no. 8. - P. 3095-3102. DOI
52. Vazaeva N.V., Chetiani O.G., Kuznecov R.D., Kallistratova M.A., Kramar V.F., Lulukin V.S., Kuznecov D.D. Ocenka spiral’nosti v atmosfernom pogranicnom sloe po dannym akusticeskogo zondirovania // Izvestia RAN. FAO. - 2017. - T. 53, No 2. - S. 200-214. DOI
53. Etling D. The Stability of the Ekman boundary layer flow as influenced by the thermal stratification // Beitr. Phys. Atmosph. - 1971. - Vol. 44. - P. 168-186.
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