# Large-Eddy Simulation of Very-Large-Scale Motions in the Neutrally Stratified Atmospheric Boundary Layer

- 778 Downloads
- 11 Citations

## Abstract

Large-eddy simulation is used to investigate very-large-scale motions (VLSMs) in the neutrally stratified atmospheric boundary layer at a very high friction Reynolds number, \(Re{_{\tau }} \sim \mathcal {O}(10^{8})\). The vertical height of the computational domain is \(L_{z}=1000\) m, which corresponds to the thickness of the boundary layer. In order to make sure that the largest flow structures are properly resolved, the horizontal domain size is chosen to be \(L_{x}=32\pi L_{z}\) and \(L_{y}=4\pi L_{z}\), which is much larger than the standard domain size, especially in the streamwise direction (i.e., the direction of elongation of the flow structures). It is shown that the contributions to the resolved turbulent kinetic energy and the resolved shear stress from streamwise wavelengths larger than \(10 L_{z}\) are up to 27 and 31 % respectively. Therefore, the large computational domain adopted here is essential for the purpose of investigating VLSMs. The spatially coherent structures associated with VLSMs are characterized through flow visualization and statistical analysis. The instantaneous velocity fields in horizontal planes give evidence of streamwise-elongated flow structures of low-speed fluid with negative fluctuation of the streamwise velocity component, and which are flanked on either side by similarly elongated high-speed structures. The pre-multiplied power spectra and two-point correlations indicate that the scales of these streak-like structures are very large, up to \(20L_{z}\) in the streamwise direction and \(0.6 L_{z}\) in the spanwise direction. These features are similar to those found in the logarithmic and outer regions of laboratory-scale boundary layers by direct numerical simulation and experiments conducted at low to moderate Reynolds numbers. The three-dimensional correlation map and conditional average of the three components of velocity further indicate that the low-speed and high-speed regions possess the same elongated ellipsoid-like structure, which is inclined upward along the streamwise direction, and they are accompanied by counter-rotating roll modes in the cross-section perpendicular to the streamwise direction. These results are in agreement with recent observations in the atmospheric surface layer.

## Keywords

Large-eddy simulation Turbulent boundary layer Coherent structures Very-large-scale motions## Notes

### Acknowledgments

This work was supported by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID s495. The authors also would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.

## References

- Abe H, Kawamura H, Choi H (2004) Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to \( {R}e_{\tau }= 640\). J Fluid Eng-T ASME 126(5):835–843CrossRefGoogle Scholar
- Abkar M, Porté-Agel F (2012) A new boundary condition for large-eddy simulation of boundary-layer flow over surface roughness transitions. J Turbul 13:N23CrossRefGoogle Scholar
- Adrian RJ (2007) Hairpin vortex organization in wall turbulence. Phys Fluids 19(4):041301CrossRefGoogle Scholar
- Albertson JD, Parlange MB (1999) Surface length scales and shear stress: Implications for land–atmosphere interaction over complex terrain. Water Resour Res 35(7):2121–2132CrossRefGoogle Scholar
- Anderson W, Passalacqua P, Porté-Agel F, Meneveau C (2012) Large-eddy simulation of atmospheric boundary-layer flow over fluvial-like landscapes using a dynamic roughness model. Boundary-Layer Meteorol 144(2):263–286CrossRefGoogle Scholar
- Andren A (1994) Large-eddy simulation of a neutrally stratified boundary layer: a comparison of four computer codes. Q J R Meteorol Soc 120(520):1457–1484CrossRefGoogle Scholar
- Ayotte KW, Sullivan PP, Andren A, Doney SC, Holtslag AAM, Large WG, McWilliams JC, Moeng C-H, Otte MJ, Tribbia JJ, Wyngaard JC (1996) An evaluation of neutral and convective planetary boundary-layer parameterizations relative to large eddy simulations. Boundary-Layer Meteorol 79(1–2):131–175CrossRefGoogle Scholar
- Balakumar BJ, Adrian RJ (2007) Large- and very-large-scale motions in channel and boundary-layer flows. Philos Trans R Soc A 365(1852):665–681CrossRefGoogle Scholar
- Basu S, Porté-Agel F (2006) Large-eddy simulation of stably stratified atmospheric boundary layer turbulence: a scale-dependent dynamic modeling approach. J Atmos Sci 63(8):2074–2091CrossRefGoogle Scholar
- Boppe RS, Neu WL (1995) Quasi-coherent structures in the marine atmospheric surface layer. J Geophys Res 100(C10):20635–20648CrossRefGoogle Scholar
- Bou-Zeid E, Meneveau C, Parlange MB (2004) Large-eddy simulation of neutral atmospheric boundary layer flow over heterogeneous surfaces: blending height and effective surface roughness. Water Resour Res 40:W02505Google Scholar
- Bou-Zeid E, Meneveau C, Parlange MB (2005) A scale-dependent lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys Fluids 17(2):025105CrossRefGoogle Scholar
- Cancelli DM, Chamecki M, Dias NL (2014) A large-eddy simulation study of scalar dissimilarity in the convective atmospheric boundary layer. J Atmos Sci 71:3–15CrossRefGoogle Scholar
- Carlotti P (2002) Two-point properties of atmospheric turbulence very close to the ground: comparison of a high resolution LES with theoretical models. Boundary-Layer Meteorol 104(3):381–410CrossRefGoogle Scholar
- Chung D, McKeon BJ (2010) Large-eddy simulation of large-scale structures in long channel flow. J Fluid Mech 661:341–364CrossRefGoogle Scholar
- Coceal O, Dobre A, Thomas TG, Belcher SE (2007) Structure of turbulent flow over regular arrays of cubical roughness. J Fluid Mech 589:375–409CrossRefGoogle Scholar
- Del Álamo JC, Jiménez J (2009) Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J Fluid Mech 640:5–26CrossRefGoogle Scholar
- Del Álamo JC, Jiménez J, Zandonade P, Moser RD (2004) Scaling of the energy spectra of turbulent channels. J Fluid Mech 500:135–144CrossRefGoogle Scholar
- Del Álamo JC, Jiménez J, Zandonade P, Moser RD (2006) Self-similar vortex clusters in the turbulent logarithmic region. J Fluid Mech 561:329–358CrossRefGoogle Scholar
- Dennis DJC, Nickels TB (2008) On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer. J Fluid Mech 614:197–206CrossRefGoogle Scholar
- Dennis DJC, Nickels TB (2011) Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer, Part 2. Long structures. J Fluid Mech 673:218–244CrossRefGoogle Scholar
- Ding F, Palarya S, Lin YL (2001) Large-eddy simulations of the atmospheric boundary layer using a new subgrid-scale model: I. Slightly unstable and neutral cases. Environ Fluid Mech 1(1):29–47CrossRefGoogle Scholar
- Drobinski P, Carlotti P, Newsom RK, Banta RM, Foster RC, Redelsperger JL (2004) The structure of the near-neutral atmospheric surface layer. J Atmos Sci 61(6):699–714CrossRefGoogle Scholar
- Dubos T, Drobinski P, Carlotti P (2008) Turbulence anisotropy carried by streaks in the neutral atmospheric surface layer. J Atmos Sci 65(8):2631–2645CrossRefGoogle Scholar
- Finnigan JJ, Shaw RH, Patton EG (2009) Turbulence structure above a vegetation canopy. J Fluid Mech 637:387–424CrossRefGoogle Scholar
- Foster RC, Vianey F, Drobinski P, Carlotti P (2006) Near-surface coherent structures and the vertical momentum flux in a large-eddy simulation of the neutrally-stratified boundary layer. Boundary-Layer Meteorol 120(2):229–255CrossRefGoogle Scholar
- Ganapathisubramani B, Longmire EK, Marusic I (2003) Characteristics of vortex packets in turbulent boundary layers. J Fluid Mech 478:35–46CrossRefGoogle Scholar
- Ganapathisubramani B, Hutchins N, Monty JP, Chung D, Marusic I (2012) Amplitude and frequency modulation in wall turbulence. J Fluid Mech 712:61–91CrossRefGoogle Scholar
- Guala M, Hommema SE, Adrian RJ (2006) Large-scale and very-large-scale motions in turbulent pipe flow. J Fluid Mech 554:521–542CrossRefGoogle Scholar
- Guala M, Metzger M, McKeon BJ (2011) Interactions within the turbulent boundary layer at high Reynolds number. J Fluid Mech 666:573–604CrossRefGoogle Scholar
- Hambleton WT, Hutchins N, Marusic I (2006) Simultaneous orthogonal-plane particle image velocimetry measurements in a turbulent boundary layer. J Fluid Mech 560:53–64CrossRefGoogle Scholar
- Högström U, Hunt JCR, Smedman AS (2002) Theory and measurements for turbulence spectra and variances in the atmospheric neutral surface layer. Boundary-Layer Meteorol 103(1):101–124CrossRefGoogle Scholar
- Horiguchi M, Hayashi T, Hashiguchi H, Ito Y, Ueda H (2010) Observations of coherent turbulence structures in the near-neutral atmospheric boundary layer. Boundary-Layer Meteorol 136(1):25–44CrossRefGoogle Scholar
- Hoyas S, Jiménez J (2006) Scaling of the velocity fluctuations in turbulent channels up to \({R}e_{\tau }=2003\). Phys Fluids 18(1):011702CrossRefGoogle Scholar
- Hunt JCR, Carlotti P (2001) Statistical structure at the wall of the high Reynolds number turbulent boundary layer. Flow Turbul Combust 66(4):453–475CrossRefGoogle Scholar
- Hunt JCR, Morrison JF (2000) Eddy structure in turbulent boundary layers. Eur J Mech B 19(5):673–694CrossRefGoogle Scholar
- Hutchins N, Marusic I (2007a) Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J Fluid Mech 579:1–28CrossRefGoogle Scholar
- Hutchins N, Marusic I (2007b) Large-scale influences in near-wall turbulence. Philos Trans R Soc A 365(1852):647–664CrossRefGoogle Scholar
- Hutchins N, Hambleton WT, Marusic I (2005) Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers. J Fluid Mech 541:21–54CrossRefGoogle Scholar
- Hutchins N, Chauhan K, Marusic I, Monty J, Klewicki J (2012) Towards reconciling the large-scale structure of turbulent boundary layers in the atmosphere and laboratory. Boundary-Layer Meteorol 145(2):273–306CrossRefGoogle Scholar
- Inagaki A, Kanda M (2010) Organized structure of active turbulence over an array of cubes within the logarithmic layer of atmospheric flow. Boundary-Layer Meteorol 135(2):209–228CrossRefGoogle Scholar
- Khanna S, Brasseur JG (1998) Three-dimensional buoyancy- and shear-induced local structure of the atmospheric boundary layer. J Atmos Sci 55(5):710–743CrossRefGoogle Scholar
- Kim KC, Adrian RJ (1999) Very large-scale motion in the outer layer. Phys Fluids 11(2):417–422CrossRefGoogle Scholar
- Kirkil G, Mirocha J, Bou-Zeid E, Chow F, Kosović B (2012) Implementation and evaluation of dynamic subfilter-scale stress models for large-eddy simulation using WRF. Mon Weather Rev 140(1):266–284CrossRefGoogle Scholar
- Kleissl J, Kumar V, Meneveau C, Parlange MB (2006) Numerical study of dynamic Smagorinsky models in large-eddy simulation of the atmospheric boundary layer: Validation in stable and unstable conditions. Water Resour Res 42:W06D10Google Scholar
- Kumar V, Kleissl J, Meneveau C, Parlange MB (2006) Large-eddy simulation of a diurnal cycle of the atmospheric boundary layer: atmospheric stability and scaling issues. Water Resour Res W06D42:09Google Scholar
- Lee JH, Sung HJ (2011) Very-large-scale motions in a turbulent boundary layer. J Fluid Mech 673:80–120CrossRefGoogle Scholar
- Lee JH, Sung HJ (2013) Comparison of very-large-scale motions of turbulent pipe and boundary layer simulations. Phys Fluids 25(4):045103CrossRefGoogle Scholar
- Lin CL, McWilliams JC, Moeng CH, Sullivan PP (1996) Coherent structures and dynamics in a neutrally stratified planetary boundary layer flow. Phys Fluids 8(10):2626–2639CrossRefGoogle Scholar
- Liu Z, Adrian RJ, Hanratty TJ (2001) Large-scale modes of turbulent channel flow: transport and structure. J Fluid Mech 448:53–80CrossRefGoogle Scholar
- Lu H, Porté-Agel F (2010) A modulated gradient model for large-eddy simulation: application to a neutral atmospheric boundary layer. Phys Fluids 22(1):1–12CrossRefGoogle Scholar
- Ludwig F, Chow F, Street R (2009) Effect of turbulence models and spatial resolution on resolved velocity structure and momentum fluxes in large-eddy simulations of neutral boundary layer flow. J Appl Meteorol Clim 48(6):1161–1180CrossRefGoogle Scholar
- Marusic I, Hutchins N (2008) Study of the log-layer structure in wall turbulence over a very large range of Reynolds number. Flow Turbul Combust 81(1–2):115–130CrossRefGoogle Scholar
- Mathis R, Hutchins N, Marusic I (2009) Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J Fluid Mech 628:311–337CrossRefGoogle Scholar
- Mejia-Alvarez R, Wu Y, Christensen K (2014) Observations of meandering superstructures in the roughness sublayer of a turbulent boundary layer. Int J Heat Fluid Flow 48:43–51CrossRefGoogle Scholar
- Meneveau C, Lund T, Cabot W (1996) A Lagrangian dynamic subgrid-scale model of turbulence. J Fluid Mech 319:353–385CrossRefGoogle Scholar
- Mirocha J, Lundquist J, Kosović B (2010) Implementation of a nonlinear subfilter turbulence stress model for large-eddy simulation in the advanced research WRF model. Mon Weather Rev 138(11):4212–4228CrossRefGoogle Scholar
- Mirocha J, Kirkil G, Bou-Zeid E, Chow F, Kosović B (2013) Transition and equilibration of neutral atmospheric boundary layer flow in one-way nested large-eddy simulations using the weather research and forecasting model. Mon Weather Rev 141(3):918–940CrossRefGoogle Scholar
- Moeng CH, Sullivan PP (1994) A comparison of shear- and buoyancy-driven planetary boundary layer flows. J Atmos Sci 51(7):999–1022CrossRefGoogle Scholar
- Morrison JF (2007) The interaction between inner and outer regions of turbulent wall-bounded flow. Philos Trans R Soc A 365(1852):683–698CrossRefGoogle Scholar
- Newsom R, Calhoun R, Ligon D, Allwine J (2008) Linearly organized turbulence structures observed over a suburban area by dual-doppler lidar. Boundary-Layer Meteorol 127(1):111–130CrossRefGoogle Scholar
- Porté-Agel F (2004) A scale-dependent dynamic model for scalar transport in large-eddy simulations of the atmospheric boundary layer. Boundary-Layer Meteorol 112(1):81–105CrossRefGoogle Scholar
- Porté-Agel F, Meneveau C, Parlange MB (2000) A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J Fluid Mech 415:261–284CrossRefGoogle Scholar
- Priymak VG, Miyazaki T (1994) Long-wave motions in turbulent shear flows. Phys Fluids 6(10):3454–3464CrossRefGoogle Scholar
- Shaw RH, Schumann U (1992) Large-eddy simulation of turbulent flow above and within a forest. Boundary-Layer Meteorol 61(1–2):47–64CrossRefGoogle Scholar
- Stoll R, Porté-Agel F (2006) Dynamic subgrid-scale models for momentum and scalar fluxes in large-eddy simulations of neutrally stratified atmospheric boundary layers over heterogeneous terrain. Water Resour Res 42(1):W01409Google Scholar
- Stoll R, Porté-Agel F (2008) Large-eddy simulation of the stable atmospheric boundary layer using dynamic models with different averaging schemes. Boundary-Layer Meteorol 126(1):1–28CrossRefGoogle Scholar
- Tang ZQ, Jiang N, Schröder A, Geisler R (2012) Tomographic PIV investigation of coherent structures in a turbulent boundary layer flow. Acta Mech Sinica 28(3):572–582CrossRefGoogle Scholar
- Toh S, Itano T (2005) Interaction between a large-scale structure and near-wall structures in channel flow. J Fluid Mech 524:249–262CrossRefGoogle Scholar
- Tomkins CD, Adrian RJ (2003) Spanwise structure and scale growth in turbulent boundary layers. J Fluid Mech 490:37–74CrossRefGoogle Scholar
- Van der Hoven I (1957) Power spectrum of horizontal wind speed in the frequency range from 0.0007 to 900 cycles per hour. J Meteorol 14(2):160–164CrossRefGoogle Scholar
- Wilczak JM, Tillman JE (1980) The 3-dimensional structure of convection in the atmospheric surface layer. J Atmos Sci 37(11):2424–2443CrossRefGoogle Scholar
- Wu X, Baltzer JR, Adrian RJ (2012) Direct numerical simulation of a 30R long turbulent pipe flow at \({R}^{+} = 685\): large-and very large-scale motions. J Fluid Mech 698:235–281CrossRefGoogle Scholar
- Young GS, Kristovich DAR, Hjelmfelt MR, Foster RC (2002) Rolls, streets, waves, and more: a review of quasi-two-dimensional structures in the atmospheric boundary layer. Bull Am Meteorol Soc 83(7):997–1001CrossRefGoogle Scholar