Abstract
We performed a numerical simulation of penetrative convection of an inversion-topped weakly stratified atmospheric boundary layer over urban terrain with a strong localized source of heat and moisture. With some simplifications, the case mimics the real environment of the Krasnoyarsk region in Russia where the non-freezing river Yenisei acts as a thermal and humidity source during winter, generating an undulating fog pattern along the river accompanied with scattered ‘steam devils’. An idealized full diurnal cycle was simulated using an unsteady Reynolds-averaged Navier–Stokes (RANS) three-equation algebraic flux model and the novel buoyancy-accounting functions for treating the ground boundary conditions. The results show a significant effect of the river on the net temperature and moisture distribution. The localized heat and moisture source leads to strong horizontal convection and marked non-uniformity of humidity concentration in the air. An interplay of several distinct large-scale vortex systems leads to a wavy pattern of moisture plumes over the river. The simulations deal with rare natural phenomena and show the capability of the RANS turbulence closure to capture the main features of flow and scalar fields on an affordable, relatively coarse, computational grid.
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Notes
The approach here followed was earlier labelled as “T-RANS” (transient, time-resolved RANS, Kenjereš and Hanjalić 1999) to indicate its triple-decomposition framework and resolving the large-scale, deterministic motion. It can also be interpreted as very-large eddy simulations in which the constitutive relations play the role of the “subscale” model in the spirit of LES, but not related to the grid-cell size.
References
André JC, De Moor G, Lacarrére P, Therry G, du Vachat R (1978) Modelling the 24-hour evolution of the mean and turbulent structures of the planetary boundary layer. J Atmos Sci 35:1861–1883
Andrén A, Moeng Ch-H (1994) Single-point closures in a neutrally stratified boundary layer. J Atmos Sci 50(20):3366–3379
Antonelli M, Rotunno R (2007) Large-eddy simulation of the onset of the sea breeze. J Atmos Sci 64:4445–4457
Baroud ChN, Plapp BB, Swinney HL, She Zh-S (2003) Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows. Phys Fluids 15(8):2091–2104
Brown RA (1980) Longitudinal instabilities and secondary flows in planetary boundary layers: a review. Rev Geophys Space Phys 18:683–697
Celani A, Musacchio S, Vincenzi D (2010) Turbulence in more than two and less than three dimensions. Phys Rev Lett 104(18):184506. doi:10.1103/PhysRevLett.104.184506
Chen G, Zhu X, Sha W, Iwasaki T, Seko H, Saito K et al (2015) Toward improved forecasts of sea-breeze horizontal convective rolls at super high resolutions. Part I: configuration and verification of a Down-Scaling Simulation System (DS3). Mon Weather Rev 143(5):1849–1872
Deardorff JW, Willis GE, Lilly DK (1969) Laboratory investigation of non-steady penetrative convection. J Fluid Mech 35(1):7–31
Dupont J-C, Haeffelin M, Protat A, Bouniol D, Boyouk N, Morille Y (2012) Stratus-fog formation and dissipation: a 6-day case study. Boundary-Layer Meteorol 143:207–225
Forthofer JM, Goodrick SL (2011) Review of vortices in wildland fire. J Combust 2011:984363. doi:10.1155/2011/984363
Gayen B, Griffiths RW, Hughes GO, Saenz JA (2012) Energetics of horizontal convection, JFM Rapids. J Fluid Mech 716:R10
Giridharan R, Kolokotroni M (2009) Urban heat island characteristics in London during winter. Solar Energy 83(9):1668–1682
Haines DA, Smith MC (1987) Three types of horizontal vortices observed in wildland mass and crown fires. J Clim Appl Meteorol 26:1624–1637
Hanjalić K (2006) One-point closure models for buoyancy-driven turbulent flows. Annu Rev Fluid Mech 34:321–47
Hanjalić K, Hrebtov M (2016) Ground boundary conditions for thermal convection over horizontal surfaces at high rayleigh numbers. Boundary-Layer Meteorol 160:41–61
Hanjalić K, Musemić R (1997) Modelling the dynamics of double-diffusive scalar fields at various stability conditions. Int J Heat Fluid Flow 18(4):360–367
Hathway EA, Sharples S (2012) The interaction of rivers and urban from in mitigating the urban heat island effect: a UK case study. Build Environ 58:14–22
Hunt JC, Morrison JF (2000) Eddy structure in turbulent boundary layers. Eur J Mech B Fluid 19(5):673–694
Ito J, Nino H (2013) Formation mechanism of dust devil-like vortices in idealised convective mixed layers. J Atmos Sci 70:1174–1156
Kenjereš S, Hanjalić K (1999) Transient analysis of Rayleigh–Bénard convection with a RANS model. Int J Heat Fluid Flow 27:329–340
Kenjereš S, Hanjalić K (2002) Combined effects of terrain orography and thermal stratification on pollutant dispersion in a town valley: a T-RANS simulations. J Turbul 3:1–26
Kenjereš S, Hanjalić K (2006) LES, T-RANS and hybrid simulations of thermal convection at high Ra number. Int J Heat Fluid Flow 27:800–810
Kenjereš S, Hanjalić K (2009) Tackling complex turbulent flows with transient RANS. Fluid Dyn Res 41:012201. doi:10.1088/0169-5983/41/1/012201
Khlebopros RG, Taseyko YD, Ivanova SV, Mikhailuta SV (2012) Krasnoyarsk. The ecological studies. Siberian Federal University Press, 130 pp (in Russian)
Kuettner JP, Hildebrand PA, Clark TL (1987) Convection waves: observations of gravity wave systems over convectively active boundary layers. Q J Roy Meteorol Soc 113:445–467
Lappa M (2009) Thermal convection: patterns, evolution and stability. Wiley, New York, 690 pp
Liu AQ, Moore GWK, Tsuboki K, Renfrew IA (2004) A high-resolution simulation of convective roll clouds during a cold-air outbreak. Geophys Res Lett 31(3):L03101. doi:10.1029/2003GL018530
Lyons WA, Pease SR (1972) ‘Steam Devils’ over Lake Michigan during a January arctic outbreak. Mon Weather Rev 100(3):235–237
Mellor GL, Yamada T (1974) A hierarchy of turbulence closure models for planetary boundary layers. J Atmos Sci 31:1791–1806
Mikhailuta SV, Taseyko OV, Zakharov YV (2011) Pollutant dispersion dynamics in urban environment. Lambert Academic Publishing, Germany, 136 pp (in Russian)
Nakanishi M, Shibuya R, Ito J, Niino H (2014) Large-eddy simulation of a residual layer: low-level jet, convective rolls and Kelvin–Helmholtz Instability. J Atmos Sci 71:4473–4491
Navarro MC, Herrero H (2011) Effects of thermal gradients on the intensity of vortices generated in a cylindrical annulus. Chaos 21(4):043132
Park SB, Baik JJ (2014) Large-eddy simulations of convective boundary layers over flat and urban-like surfaces. J Atmos Sci 71:1880–1892
Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge, 771 pp
Pope SB (2004) Ten questions concerning the large-eddy simulation of turbulent flows. New J Phys 6(35):1–24
Raasch S, Franke T (2011) Structure and formation of dust devil-like vortices in the atmospheric boundary layer: a high-resolution numerical study. J Geophys Res 116:D16120. doi:10.1029/2011JD016010
Sarris IE, Lekakis I, Vlachos NS (2004) Natural convection in rectangular tanks heated locally from below. Int J Heat Mass Transf 47(14):3549–3563
Scagliarini A, Gylfason Á, Toschi F (2014) Heat flux scaling in turbulent Rayleigh–Be’nard convection with an imposed longitudinal wind. Phys Rev E 89:043012
Sha W, Kawamura T, Ueda H (1991) A numerical study on sea/land breezes as a gravity current: Kelvin–Helmholtz billows and inland penetration of the sea-breeze front. J Atmos Sci 48(14):1649–1665
Shapiro A, Fedorovich E (2007) Katabatic flow along a differentially cooled sloping surface. J Fluid Mech 571:149–175
Simpson JE (1994) Sea breeze and local winds. Cambridge University Press, Cambridge, 234 pp
Slotnick J, Khodadoust A, Alonso J, Darmofal D, Gropp W, Lurie E, Mavriplis D (2014) CFD vision 2030 study: a path to revolutionary computational aerosciences. NASA/CR–2014-218178
Weber JE (1978) On the stability of thermally driven shear flow heated from below. J Fluid Mech 87(1):65–84
Wyngaard JC (1992) Atmospheric turbulence. Annu Rev Fluid Mech 24:205–234
Yamada T, Mellor GL (1975) A simulation of the Wangara atmospheric boundary layer data. J Atmos Sci 32:2309–2329
Young GS, Kristovich DA, Hjelmfelt MR, Foster RC (2002) Supplement to rolls, streets, waves, and more. Bull Am Meteorol Soc 83(7):1001–1001
Yu CH, Chang MY, Lin TF (1997) Structures of moving transverse and mixed rolls in mixed convection of air in a horizontal plane channel. Int J Heat Mass Transfer 40(2):333–346
Zurn-Birkhimer S, Agee EM, Sorbjan Z (2005) Convective structures in a cold air outbreak over Lake Michigan during Lake-ICE. J Atmos Sci 62(7, part 2):2414–2432
Acknowledgements
This work was supported by Russian Science Foundation (Grant 114-29-00203). The authors thank Dr. Saša Kenjereš from TU Delft, Nl, for invaluable help and advice to MH in mastering the BuoyFlow CFD code.
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Appendix: Turbulence Model and Ground Boundary Conditions
Appendix: Turbulence Model and Ground Boundary Conditions
The equation set 1–3 is closed by solving the transport equations for the scalar quantities
where
with \(\phi \) standing for a scalar (k, \(\varepsilon \), \(\overline{\theta ^{2}} )\), \(\sigma _{\phi } \) for the corresponding turbulent Prandtl-Schmidt number, and the coefficients in the \(\varepsilon \) equation take the common values \(C_{\varepsilon 1} =1.44\) and \(C_{\varepsilon 2} =1.92\).
The model (with inclusion of the molecular terms and the appropriate low-Re-number modifications) was shown earlier to reproduce well the Rayleigh–Bénard convection with integration up to the walls using an adequately refined/clustered grid in the wall-normal direction (Kenjereš and Hanjalić 2006). In the present work we employed modified ground (“wall”) functions approach suitable for high Ra buoyancy-dominated flows, (Hanjalić and Hrebtov 2016), which provide boundary conditions for all mean and turbulence variables at the ground-adjacent grid nodes, well outside the molecular layer.
For the vapour concentration H one can use the same approach as for the temperature by specifying the vapour surface flux \(\dot{m}_s^{\prime \prime } =D_s^{{ eff}} \left( {H_P -H_s } \right) /z_P\), where \(D_s^{{ eff}} \) is the effective wall mass diffusivity. However in view of humidity being treated as a passive scalar, we assume that the absolute humidity (vapour concentration) at the ground-nearest grid node can be considered as equal to that at the water surface corresponding to the saturation pressure, for which we employed the following approximation (World Meteorological Organization)
where
is the saturation pressure, resulting in the value of absolute humidity at point P
The model and the ground functions were re-tested in Rayleigh–Bénard convection and in the penetrative convection of a mixed layer heated from below (Deardorff et al. 1969) using one-dimensional \((1 \times 1 \times N_{z})\) and three-dimensional (\(60 \times 60 \times N_{z}\) and \(10 \times 10 \times N_{z)}\) fine and coarse grids, the former with \(N_{z} =100\) and the latter with \(N_{z} = 20\) uniformly spaced grid nodes in the vertical direction (the latter chosen deliberately to be extremely coarse), both showing very good agreement with the reference DNS/LES and experimental data. The tests show that the model and the applied ground functions are capable of predicting adequately the mean temperature and the vertical turbulent heat-flux evolution, as well as other properties, on very coarse meshes even in the limit of zero convection, when the second moments are provided solely by the model without any resolved contribution (Hanjalić and Hrebtov 2016).
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Hrebtov, M., Hanjalić, K. Numerical Study of Winter Diurnal Convection Over the City of Krasnoyarsk: Effects of Non-freezing River, Undulating Fog and Steam Devils. Boundary-Layer Meteorol 163, 469–495 (2017). https://doi.org/10.1007/s10546-016-0231-0
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DOI: https://doi.org/10.1007/s10546-016-0231-0