scholarly journals Similarity Theory in the Surface Layer of Large-Eddy Simulations of the Wind-, Wave-, and Buoyancy-Forced Southern Ocean

2019 ◽  
Vol 49 (8) ◽  
pp. 2165-2187 ◽  
Author(s):  
William G. Large ◽  
Edward G. Patton ◽  
Alice K. DuVivier ◽  
Peter P. Sullivan ◽  
Leonel Romero
Keyword(s):  
Surface Layer ◽  
Southern Ocean ◽  
Wind Wave ◽  
Similarity Theory ◽  
Large Eddy Simulations ◽  
Stokes Drift ◽  
Total Production ◽  
Similarity Functions ◽  
Wide Range ◽  
Large Eddy

AbstractMonin–Obukhov similarity theory is applied to the surface layer of large-eddy simulations (LES) of deep Southern Ocean boundary layers. Observations from the Southern Ocean Flux Station provide a wide range of wind, buoyancy, and wave (Stokes drift) forcing. Two No-Stokes LES are used to determine the extent of the ocean surface layer and to adapt the nondimensional momentum and buoyancy gradients, as functions of the stability parameter. Stokes-forced LES are used to modify this parameter for wave effects, then to formulate dependencies of Stokes similarity functions on a Stokes parameter ξ. To account for wind-wave misalignment, the dimensional analysis is extended with two independent variables, namely, the production of turbulent kinetic energy in the surface layer due to Stokes shear and the total production, so that their ratio gives ξ. Stokes forcing is shown to reduce vertical shear more than stratification, and to enhance viscosity and diffusivity by factors up to 5.8 and 4.0, respectively, such that the Prandtl number can exceed unity. A practical parameterization is developed for ξ in terms of the meteorological forcing plus a Stokes drift profile, so that the Stokes and stability similarity functions can be combined to give turbulent velocity scales. These scales for both viscosity and diffusivity are evaluated against the LES, and the correlations are nearly 0.97. The benefit of calculating Stokes drift profiles from directional wave spectra is demonstrated by similarly evaluating three alternatives.

scholarly journals Monin–Obukhov Similarity Functions for the Structure Parameters of Temperature and Humidity in the Unstable Surface Layer: Results from High-Resolution Large-Eddy Simulations

2014 ◽  
Vol 71 (2) ◽  
pp. 716-733 ◽  
Author(s):  
Björn Maronga
Keyword(s):  
Surface Layer ◽  
Free Convection ◽  
Measurement Data ◽  
Surface Fluxes ◽  
Large Eddy Simulations ◽  
Structure Parameters ◽  
Similarity Functions ◽  
Dry Air ◽  
Large Eddy ◽  
Temperature And Humidity

Abstract Large-eddy simulations (LESs) of free-convective to near-neutral boundary layers are used to investigate the surface-layer turbulence. The article focuses on the Monin–Obukhov similarity theory (MOST) relationships that relate the structure parameters of temperature and humidity to the surface fluxes of sensible and latent heat, respectively. Moreover, the applicability of local free convection (LFC) similarity scaling is studied. The LES data suggest that the MOST function for is universal. It is shown to be within the range of the functions proposed from measurement data. It is found that follows MOST if entrainment of dry air from the free atmosphere is sufficiently small. In this case the similarity functions for and are identical. If entrainment is significant, dissimilarity between the transport of sensible heat and moisture is observed and no longer follows MOST. In the free-convection limit the LFC similarity functions should collapse to universal constants. The LES data suggest values around 2.7, which is in agreement with the value proposed in the literature. As for MOST, the LFC similarity constant for becomes nonuniversal if entrainment of dry air is significant. It is shown that LFC scaling is applicable even if shear production of turbulence is moderately high.

scholarly journals On the Formulation and Universality of Monin–Obukhov Similarity Functions for Mean Gradients and Standard Deviations in the Unstable Surface Layer: Results from Surface-Layer-Resolving Large-Eddy Simulations

2017 ◽  
Vol 74 (4) ◽  
pp. 989-1010 ◽  
Author(s):  
Björn Maronga ◽  
Joachim Reuder
Keyword(s):  
Surface Layer ◽  
Standard Deviation ◽  
Large Eddy Simulations ◽  
Specific Humidity ◽  
Horizontal Wind ◽  
Convective Conditions ◽  
Similarity Functions ◽  
Large Eddy ◽  
The Mean ◽  
Standard Deviations

Abstract Surface-layer-resolving large-eddy simulations (LESs) of free-convective to near-neutral boundary layers are used to study Monin–Obukhov similarity theory (MOST) functions. The LES dataset, previously used for the analysis of MOST relationships for structure parameters, is extended for the mean vertical gradients and standard deviations of potential temperature, specific humidity, and wind. Also, local-free-convection (LFC) similarity is studied. The LES data suggest that the MOST functions for mean gradients are universal and unique. The data for the mean gradient of the horizontal wind display significant scatter, while the gradients of temperature and humidity vary considerably less. The LES results suggest that this scatter is mostly related to a transition from MOST to LFC scaling when approaching free-convective conditions and that it is associated with a change of the slope of the similarity functions toward the expected value from LFC scaling. Overall, the data show slightly, but consistent, steeper slopes of the similarity functions than suggested in literature. The MOST functions for standard deviations appear to be unique and universal when the entrainment from the free atmosphere into the boundary layer is sufficiently small. If entrainment becomes significant, however, we find that the standard deviation of humidity no longer follows MOST. Under free-convective conditions, the similarity functions should reduce to universal constants (LFC scaling). This is supported by the LES data, showing only little scatter, but displaying a systematic height dependence of these constants. Like for MOST, the LFC similarity constant for the standard deviation of specific humidity becomes nonuniversal when the entrainment of dry air reaches significant levels.

Disruption of the bottom log layer in large-eddy simulations of full-depth Langmuir circulation

2012 ◽  
Vol 699 ◽  
pp. 79-93 ◽  
Author(s):  
A. E. Tejada-Martínez ◽  
C. E. Grosch ◽  
N. Sinha ◽  
C. Akan ◽  
G. Martinat
Keyword(s):  
Gravity Waves ◽  
Large Eddy Simulations ◽  
Stokes Drift ◽  
Navier Stokes ◽  
Wake Region ◽  
Langmuir Circulation ◽  
Mean Velocity ◽  
Wave Forcing ◽  
Large Eddy ◽  
Shear Current

AbstractWe report on disruption of the log layer in the resolved bottom boundary layer in large-eddy simulations (LES) of full-depth Langmuir circulation (LC) in a wind-driven shear current in neutrally-stratified shallow water. LC consists of parallel counter-rotating vortices that are aligned roughly in the direction of the wind and are generated by the interaction of the wind-driven shear with the Stokes drift velocity induced by surface gravity waves. The disruption is analysed in terms of mean velocity, budgets of turbulent kinetic energy (TKE) and budgets of TKE components. For example, in terms of mean velocity, the mixing due to LC induces a large wake region eroding the classical log-law profile within the range $90\lt { x}_{3}^{+ } \lt 200$. The dependence of this disruption on wind and wave forcing conditions is investigated. Results indicate that the amount of disruption is primarily determined by the wavelength of the surface waves generating LC. These results have important implications for turbulence parameterizations for Reynolds-averaged Navier–Stokes simulations of the coastal ocean.

scholarly journals A Closer Look at Boundary Layer Inversion in Large-Eddy Simulations and Bulk Models: Buoyancy-Driven Case

2015 ◽  
Vol 72 (2) ◽  
pp. 728-749 ◽  
Author(s):  
Pierre Gentine ◽  
Gilles Bellon ◽  
Chiel C. van Heerwaarden
Keyword(s):  
Boundary Layer ◽  
Convective Boundary Layer ◽  
Weather Prediction ◽  
Inversion Layer ◽  
Large Eddy Simulations ◽  
Buoyancy Flux ◽  
Convective Boundary ◽  
Strong Inversion ◽  
Wide Range ◽  
Large Eddy

Abstract The inversion layer (IL) of a clear-sky, buoyancy-driven convective boundary layer is investigated using large-eddy simulations covering a wide range of convective Richardson numbers. A new model of the IL is suggested and tested. The model performs better than previous first-order models of the entrainment and provides physical insights into the main controls of the mixed-layer and IL growths. A consistent prognostic equation of the IL growth is derived, with explicit dependence on the position of the minimum buoyancy flux, convective Richardson number, and relative stratification across the inversion G. The IL model expresses the interrelationship between the position and magnitude of the minimum buoyancy flux and inversion-layer depth. These relationships emphasize why zero-order jump models of the convective boundary layer perform well under a strong inversion and show that these models miss the additional parameter G to fully characterize the entrainment process under a weak inversion. Additionally, the position of the minimum buoyancy flux within the new IL model is shown to be a key component of convective boundary layer entrainment. The new IL model is sufficiently simple to be used in numerical weather prediction or general circulation models as a way to resolve the IL in a low-vertical-resolution model.

The Use of Large-Eddy Simulations in Lagrangian Particle Dispersion Models

2004 ◽  
Vol 61 (23) ◽  
pp. 2877-2887 ◽  
Author(s):  
Jeffrey C. Weil ◽  
Peter P. Sullivan ◽  
Chin-Hoh Moeng
Keyword(s):  
Boundary Layer ◽  
Surface Layer ◽  
Dispersion Model ◽  
Particle Dispersion ◽  
Large Eddy Simulations ◽  
Surface Source ◽  
Mean Velocity ◽  
Convective Boundary ◽  
Large Eddy ◽  
Better Than

Abstract A Lagrangian dispersion model driven by velocity fields from large-eddy simulations (LESs) is presented for passive particle dispersion in the planetary boundary layer (PBL). In this combined LES–Lagrangian stochastic model (LSM), the total velocity is divided into resolved or filtered and unresolved or subfilter-scale (SFS) velocities. The random SFS velocity is modeled using an adaptation of Thomson's LSM in which the ensemble-mean velocity and velocity variances are replaced by the resolved velocity and SFS variances, respectively. The random SFS velocity forcing has an amplitude determined by the SFS fraction of the total turbulent kinetic energy (TKE); the fraction is about 0.15 in the bulk of the simulated convective boundary layer (CBL) used here and reaches values as large as 0.31 and 0.37 in the surface layer and entrainment layer, respectively. For the proposed LES–LSM, the modeled crosswind-integrated concentration (CWIC) fields are in good agreement with the 1) surface-layer similarity (SLS) theory for a surface source in the CBL and 2) convection tank measurements of the CWIC for an elevated release in the CBL surface layer. The second comparison includes the modeled evolution of the vertical profile shape with downstream distance, which shows the attainment of an elevated CWIC maximum and a vertically well-mixed CWIC far downstream, in agreement with the tank data. For the proposed model, the agreement with the tank data and SLS theory is better than that obtained with an earlier model in which the SFS fraction of the TKE is assumed to be 1, and significantly better than a model that neglects the SFS velocities altogether.

Resolving urban canopy flows: Scales, turbulence and boundary conditions in obstacle-resolving numerical models

2021 ◽  
Author(s):  
Benedikt Seitzer ◽  
Bernd Leitl ◽  
Frank Harms
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Atmospheric Boundary Layer ◽  
Similarity Theory ◽  
Urban Canopy ◽  
Large Eddy Simulations ◽  
Roughness Sublayer ◽  
Boundary Layer Meteorol ◽  
Large Eddy ◽  
Near Wall

<p>Large-eddy simulations are increasingly used for studying the atmospheric boundary layer. With increasing computational resources even obstacle-resolving Large-eddy simulations became possible and will be used in urban climate studies more frequently. In these applications, grid sizes are in the order of a few meters. Whereas major urban structures can be resolved in general, details like aerodynamically rough surface structures can not be resolved explicitly. Based on the original fields of application, boundary conditions in Large-eddy simulations were initially formulated for surfaces of homogeneous roughness and for wall-distances much larger than the roughness sublayer height (Hultmark et al., 2013). The height of the roughness sublayer depends on the size of small-scale obstacles present on the surface exposed to the flow (Raupach et al., 1991). Typically, boundary conditions are evaluated between the surface and the first grid level. Thus, grid resolution in obstacle-resolved Large-Eddy simulations should also be a question of scales and therefore has to be chosen carefully (Basu and Lacser, 2017; Maronga et al., 2020). <br />In several wind tunnel experiments presented here, we measured the near-wall influence of differently scaled and shaped objects on a flow and its turbulence characteristics. Experimental setups were replicated numerically using the PALM model (Maronga et al. 2019). In a first, more generic experiment, the flow over horizontally homogeneous surfaces of different roughness was investigated. In a second experiment, the spatial separation of the turbulence scales was investigated in a more complex flow case. These experiments lead to considerations on model grid sizes in urban type Large-eddy simulations. The limitations of interpreting simulation results within the urban canopy layer are highlighted. There is an urgent need to reconsider how near-wall results of urban large-eddy simulations are generated and interpreted in the context of practical applications like flow and transport modelling in urban canopies. <br /><br /><em><strong>References</strong></em><br /><em>Basu, S. and Lacser, A. (2017). A Cautionary Note on the Use of Monin–Obukhov Similarity Theory in Very High-Resolution Large-Eddy Simulations. Boundary-Layer Meteorol, 163(2):351–355.</em></p> <p><em>Hultmark, M., Calaf, M., and Parlange, M. B. (2013). A new wall shearstress model for atmospheric boundary layer simulations. J Atmos Sci,70(11):3460–3470.</em></p> <p><em>Maronga, B., et al. (2020). Overview of the PALM model system 6.0. Geosci Model Dev Discussions, 06(June):1–63.</em></p> <p><em>Maronga, B., Knigge, C., and Raasch, S. (2020). An Improved Surface Boundary Condition for Large-Eddy Simulations Based on Monin–Obukhov Similarity Theory: Evaluation and Consequences forGrid Convergence in Neutral and Stable Conditions. Boundary-Layer Meteorol, 174(2):297–325.</em></p> <p><em>Raupach, M. R., Antonia, R. A., and Rajagopalan, S. (1991). Rough-wall turbulent boundary layers. Appl Mech Rev, 44(1):1–25</em></p>

scholarly journals Large-Eddy Simulations and Damped-Oscillator Models of the Unsteady Ekman Boundary Layer*

2015 ◽  
Vol 73 (1) ◽  
pp. 25-40 ◽  
Author(s):  
Mostafa Momen ◽  
Elie Bou-Zeid
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulations ◽  
Reduced Model ◽  
Gradient Force ◽  
Pressure Gradient Force ◽  
Ekman Boundary Layer ◽  
Wide Range ◽  
Large Eddy ◽  
Mass Spring ◽  
Damped Oscillator

Abstract The Ekman boundary layer (EBL) is a central problem in geophysical fluid dynamics that emerges when the pressure gradient force, the Coriolis force, and the frictional force interact in a flow. The unsteady version of the problem, which occurs when these forces are not in equilibrium, is solvable analytically only for a limited set of forcing variability regimes, and the resulting solutions are intricate and not always easy to interpret. In this paper, large-eddy simulations (LESs) of neutral atmospheric EBLs are conducted under various unsteady forcings to reveal the range of physical characteristics of the flow. Subsequently, it is demonstrated that the dynamics of the unsteady EBL can be reduced to a second-order ordinary differential equation that is very similar to the dynamical equation of a damped oscillator, such as a mass–spring–damper system. The validation of the proposed reduced model is performed by comparing its analytical solutions to LES results, revealing very good agreement. The reduced model can be solved for a wide range of variable forcing conditions, and this feature is exploited in the paper to elucidate the physical origin of the inertia (mass), energy storage (spring), and energy dissipation (damper) attributes of Ekman flows.

scholarly journals Large-Eddy Simulation of Langmuir Turbulence in Pure Wind Seas

2008 ◽  
Vol 38 (7) ◽  
pp. 1542-1562 ◽  
Author(s):  
Ramsey R. Harcourt ◽  
Eric A. D’Asaro
Keyword(s):  
Surface Layer ◽  
Surface Wave ◽  
Mixed Layer ◽  
Wave Spectrum ◽  
Vertical Component ◽  
Phase Speed ◽  
Relative Magnitude ◽  
Stokes Drift ◽  
Wave Age ◽  
Large Eddy

Abstract The scaling of turbulent kinetic energy (TKE) and its vertical component (VKE) in the upper ocean boundary layer, forced by realistic wind stress and surface waves including the effects of Langmuir circulations, is investigated using large-eddy simulations (LESs). The interaction of waves and turbulence is modeled by the Craik–Leibovich vortex force. Horizontally uniform surface stress τ0 and Stokes drift profiles uS(z) are specified from the 10-m wind speed U10 and the surface wave age CP/U10, where CP is the spectral peak phase speed, using an empirical surface wave spectra and an associated wave age–dependent neutral drag coefficient CD. Wave-breaking effects are not otherwise included. Mixed layer depths HML vary from 30 to 120 m, with 0.6 ≤ CP/U10 ≤ 1.2 and 8 m s−1 < U10 < 70 m s−1, thereby addressing most possible oceanic conditions where TKE production is dominated by wind and wave forcing. The mixed layer–averaged “bulk” VKE 〈w2〉/u*2 is equally sensitive to the nondimensional Stokes e-folding depth D*S/HML and to the turbulent Langmuir number Lat = u*/US, where u* = |τ0|/ρw in water density ρw and US = |uS|z=0. Use of a D*S scale-equivalent monochromatic wave does not accurately reproduce the results using a full-surface wave spectrum with the same e-folding depth. The bulk VKE for both monochromatic and broadband spectra is accurately predicted using a surface layer (SL) Langmuir number LaSL = u*/〈uS〉SL, where 〈uS〉SL is the average Stokes drift in a surface layer 0 > z > − 0.2HML relative to that near the bottom of the mixed layer. In the wave-dominated limit LaSL → 0, turbulent vertical velocity scales as wrms ∼ u*La−2/3SL. The mean profile (z) of VKE is characterized by a subsurface peak, the depth of which increases with D*S/HML to a maximum near 0.22HML as its relative magnitude /〈w2〉 decreases. Modestly accurate scalings for these variations are presented. The magnitude of the crosswind velocity convergence scales differently from VKE. These results predict that for pure wind seas and HML ≅ 50 m, 〈w2〉/u*2 varies from less than 1 for young waves at U10 = 10 m s−1 to about 2 for mature seas at winds greater than U10 = 30 m s−1. Preliminary comparisons with Lagrangian float data account for invariance in 〈w2〉/u*2 measurements as resulting from an inverse relationship between U10 and CP/U10 in observed regimes.

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