scholarly journals The Influence of Stratification and Nonlocal Turbulent Production on Estuarine Turbulence: An Assessment of Turbulence Closure with Field Observations

2011 ◽  
Vol 41 (1) ◽  
pp. 166-185 ◽  
Author(s):  
Malcolm E. Scully ◽  
W. Rocky Geyer ◽  
John H. Trowbridge
Keyword(s):  
Richardson Number ◽  
Turbulence Closure ◽  
Length Scale ◽  
Field Observations ◽  
Turbulent Length Scale ◽  
Stability Functions ◽  
Gradient Richardson Number ◽  
Simple Scaling ◽  
The Impact ◽  
Distance To The Boundary

Abstract Field observations of turbulent kinetic energy (TKE), dissipation rate ɛ, and turbulent length scale demonstrate the impact of both density stratification and nonlocal turbulent production on turbulent momentum flux. The data were collected in a highly stratified salt wedge estuary using the Mobile Array for Sensing Turbulence (MAST). Estimates of the dominant length scale of turbulent motions obtained from the vertical velocity spectra provide field confirmation of the theoretical limitation imposed by either the distance to the boundary or the Ozmidov scale, whichever is smaller. Under boundary-limited conditions, anisotropy generally increases with increasing shear and decreased distance to the boundary. Under Ozmidov-limited conditions, anisotropy increases rapidly when the gradient Richardson number exceeds 0.25. Both boundary-limited and Ozmidov-limited conditions demonstrate significant deviations from a local production–dissipation balance that are largely consistent with simple scaling relationships for the vertical divergence in TKE flux. Both the impact of stratification and deviation from equilibrium turbulence observed in the data are largely consistent with commonly used turbulence closure models that employ “nonequilibrium” stability functions. The data compare most favorably with the nonequilibrium version of the L. H. Kantha and C. A. Clayson stability functions. Not only is this approach more consistent with the observed critical gradient Richardson number of 0.25, but it also accounts for the large deviations from equilibrium turbulence in a manner consistent with the observations.

Modeling of pollution from the wastewater discharge of the city of Limassol

1995 ◽  
Vol 32 (9-10) ◽  
pp. 197-204
Author(s):  
G. C. Christodoulou ◽  
I. Ioakeim ◽  
K. Ioannou
Keyword(s):  
Field Observations ◽  
Wastewater Discharge ◽  
Dispersion Models ◽  
Preliminary Assessment ◽  
Westerly Winds ◽  
Dimensional Finite Element ◽  
The Impact ◽  
The City ◽  
Oceanographic Conditions ◽  
Continuous Loading

The paper presents a numerical modeling study aimed at a preliminary assessment of the impact of the planned sea outfall of the city of Limassol, Cyprus, on the waters of Akrotiri bay. First the local meteorological and oceanographic conditions as well as the loading characteristics are briefly reviewed. Two-dimensional finite element hydrodynamic and dispersion models are subsequently applied to the study area. The results of the former show an eastbound flow pattern under the prevailing westerly winds, in general agreement with available field observations. The spread of BOD and N under continuous loading is then examined for eastward as well as for westward flow as an indicator for the extent of pollution to be expected. The computed concentrations are generally low and confined to the shallower parts of the bay.

scholarly journals Turbulence Characteristics Across a Range of Idealized Urban Canopy Geometries

2021 ◽  
Author(s):  
Lewis P. Blunn ◽  
Omduth Coceal ◽  
Negin Nazarian ◽  
Janet F. Barlow ◽  
Robert S. Plant ◽  
...  
Keyword(s):  
Momentum Flux ◽  
Mixing Layer ◽  
Urban Canopy ◽  
Turbulence Closure ◽  
Length Scale ◽  
Good Representation ◽  
Mixing Length ◽  
Turbulence Characteristics ◽  
First Order ◽  
Turbulent Momentum

AbstractGood representation of turbulence in urban canopy models is necessary for accurate prediction of momentum and scalar distribution in and above urban canopies. To develop and improve turbulence closure schemes for one-dimensional multi-layer urban canopy models, turbulence characteristics are investigated here by analyzing existing large-eddy simulation and direct numerical simulation data. A range of geometries and flow regimes are analyzed that span packing densities of 0.0625 to 0.44, different building array configurations (cubes and cuboids, aligned and staggered arrays, and variable building height), and different incident wind directions ($$0^\circ $$ 0 ∘ and $$45^\circ $$ 45 ∘ with regards to the building face). Momentum mixing-length profiles share similar characteristics across the range of geometries, making a first-order momentum mixing-length turbulence closure a promising approach. In vegetation canopies turbulence is dominated by mixing-layer eddies of a scale determined by the canopy-top shear length scale. No relationship was found between the depth-averaged momentum mixing length within the canopy and the canopy-top shear length scale in the present study. By careful specification of the intrinsic averaging operator in the canopy, an often-overlooked term that accounts for changes in plan area density with height is included in a first-order momentum mixing-length turbulence closure model. For an array of variable-height buildings, its omission leads to velocity overestimation of up to $$17\%$$ 17 % . Additionally, we observe that the von Kármán coefficient varies between 0.20 and 0.51 across simulations, which is the first time such a range of values has been documented. When driving flow is oblique to the building faces, the ratio of dispersive to turbulent momentum flux is larger than unity in the lower half of the canopy, and wake production becomes significant compared to shear production of turbulent momentum flux. It is probable that dispersive momentum fluxes are more significant than previously thought in real urban settings, where the wind direction is almost always oblique.

scholarly journals The impact of atmospheric stability and wind shear on vertical cloud overlap over the Tibetan Plateau

2018 ◽  
Vol 18 (10) ◽  
pp. 7329-7343 ◽  
Author(s):  
Jiming Li ◽  
Qiaoyi Lv ◽  
Bida Jian ◽  
Min Zhang ◽  
Chuanfeng Zhao ◽  
...  
Keyword(s):  
Tibetan Plateau ◽  
Wind Shear ◽  
Cloud Cover ◽  
Atmospheric Stability ◽  
Length Scale ◽  
The Tibetan Plateau ◽  
Total Cloud Cover ◽  
Atmospheric Models ◽  
The Impact ◽  
Overlap Parameter

Abstract. Studies have shown that changes in cloud cover are responsible for the rapid climate warming over the Tibetan Plateau (TP) in the past 3 decades. To simulate the total cloud cover, atmospheric models have to reasonably represent the characteristics of vertical overlap between cloud layers. Until now, however, this subject has received little attention due to the limited availability of observations, especially over the TP. Based on the above information, the main aim of this study is to examine the properties of cloud overlaps over the TP region and to build an empirical relationship between cloud overlap properties and large-scale atmospheric dynamics using 4 years (2007–2010) of data from the CloudSat cloud product and collocated ERA-Interim reanalysis data. To do this, the cloud overlap parameter α, which is an inverse exponential function of the cloud layer separation D and decorrelation length scale L, is calculated using CloudSat and is discussed. The parameters α and L are both widely used to characterize the transition from the maximum to random overlap assumption with increasing layer separations. For those non-adjacent layers without clear sky between them (that is, contiguous cloud layers), it is found that the overlap parameter α is sensitive to the unique thermodynamic and dynamic environment over the TP, i.e., the unstable atmospheric stratification and corresponding weak wind shear, which leads to maximum overlap (that is, greater α values). This finding agrees well with the previous studies. Finally, we parameterize the decorrelation length scale L as a function of the wind shear and atmospheric stability based on a multiple linear regression. Compared with previous parameterizations, this new scheme can improve the simulation of total cloud cover over the TP when the separations between cloud layers are greater than 1 km. This study thus suggests that the effects of both wind shear and atmospheric stability on cloud overlap should be taken into account in the parameterization of decorrelation length scale L in order to further improve the calculation of the radiative budget and the prediction of climate change over the TP in the atmospheric models.

Novel Perturbation Analysis for a Widely Applicable Curvature Law of the Wall

1999 ◽  
Author(s):  
Namhyo Kim ◽  
David L. Rhode
Keyword(s):  
Perturbation Analysis ◽  
Richardson Number ◽  
Perturbation Technique ◽  
Solution Approach ◽  
Law Of The Wall ◽  
Streamline Curvature ◽  
Curvature Effects ◽  
Gradient Richardson Number ◽  
Closed Form Analytical Solution ◽  
First Time

Abstract A streamline curvature law of the wall is analytically derived to include very strong curved-channel wall curvature effects through a novel perturbation analysis. The new law allows improved analysis of such flows, and it provides the basis for improved wall function boundary conditions for their computation (CFD) over a wider range of y+, even for very strong curvature cases. The unique derivation is based on the Boussinesq eddy viscosity and curvature-corrected mixing length concepts, which is a linear function of the gradient Richardson number. For the first time, to include more complete curved flow physics, local streamline curvature effects in the gradient Richardson number are kept. To overcome the mathematical difficulty of keeping all of these local streamline curvature terms, a novel perturbation solution approach is successfully developed. This novel perturbation technique allows a closed-form analytical solution to many similar non-linear problems which previously required more complicated techniques. Qualitative and quantitative comparisons with measurements and previous curvature laws of the wall obtained by different approaches reveal that the new law shows improved representation of the wall curvature effects for all of the four test cases.

Les travaux sur la turbulence : les origines, Toucans, Cost-ES0905 et influence de l'entropie

2021 ◽  
pp. 079
Author(s):  
Ivan Bašták Ďurán ◽  
Pascal Marquet
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Richardson Number ◽  
Stable Stratification ◽  
Turbulence Energy ◽  
Third Order ◽  
Length Scales ◽  
Gradient Richardson Number ◽  
Turbulence Length ◽  
Consistent Treatment

Le schéma de turbulence Toucans est utilisé dans la configuration opérationnelle Alaro du modèle Aladin depuis début 2015. Son développement a été initié, guidé et en grande partie conçu par Jean-François Geleyn. Ce développement a commencé avec le prédécesseur du schéma Toucans, le schéma « pseudo-pronostique » en énergie cinétique turbulente, lui-même basé sur l'ancien schéma de turbulence de Louis, mais étendu dans Toucans à un schéma pronostique. Le schéma Toucans a pour objectif de traiter de manière cohérente les fonctions qui dépendent de la stabilité verticale de l'atmosphère, de l'influence de l'humidité et des échelles de longueur de la turbulence (de mélange et de dissipation). De plus, de nouvelles caractéristiques ont été ajoutées : une représentation améliorée pour les stratifications très stables (absence de nombre de Richardson critique), une meilleure représentation de l'anisotropie, un paramétrage unifié de la turbulence et des nuages par l'ajout d'une deuxième énergie turbulente pronostique et la paramétrisation des moments du troisième ordre. The Toucans turbulence scheme is a turbulence scheme that is used in the operational Alaro configuration of the Aladin model since early 2015. Its development was initiated, guided and to a large extend authored by Jean-François Geleyn. The development started with the predecessor of the Toucans scheme, the "pseudo-prognostic" turbulent kinetic energy scheme which itself was built on the "Louis" turbulence scheme, but extended to a prognostic scheme. The Toucans scheme aims for a consistent treatment of stability dependency functions, influence of moisture, and turbulence length scales. Additionally, new features were added to the turbulence scheme: improved representation of turbulence in very stable stratification (absence of critical gradient Richardson number), better representation of anisotropy, unified parameterization of turbulence and clouds via addition of second prognostic turbulence energy, and parameterization of third order moments.

scholarly journals Modulation of Small-Scale Turbulence by Ducted Gravity Waves in the Nocturnal Boundary Layer

2008 ◽  
Vol 65 (4) ◽  
pp. 1414-1427 ◽  
Author(s):  
Y. P. Meillier ◽  
R. G. Frehlich ◽  
R. M. Jones ◽  
B. B. Balsley
Keyword(s):  
Boundary Layer ◽  
Gravity Waves ◽  
Richardson Number ◽  
Potential Temperature ◽  
Nocturnal Boundary Layer ◽  
Small Scale ◽  
Temperature Structure ◽  
Turbulence Measurements ◽  
Gradient Richardson Number ◽  
Scale Turbulence

Abstract Constant altitude measurements of temperature and velocity in the residual layer of the nocturnal boundary layer, collected by the Cooperative Institute for Research in Environmental Sciences (CIRES) Tethered Lifting System (TLS), exhibit fluctuations identified by previous work (Fritts et al.) as the signature of ducted gravity waves. The concurrent high-resolution TLS turbulence measurements (temperature structure constant C2T and turbulent kinetic energy dissipation rate ɛ) reveal the presence of patches of enhanced turbulence activity that are roughly synchronized with the troughs of the temperature and velocity fluctuations. To investigate the potentially dominant role ducted gravity waves might play on the modulation of atmospheric stability and therefore, on turbulence, time series of the wave-modulated gradient Richardson number (Ri) and of the vertical gradient of potential temperature ∂θ/∂z(t) are computed numerically and compared to the TLS small-scale turbulence measurements. The results of this study agree with the predictions of previous theoretical studies (i.e., wave-generated fluctuations of temperature and velocity modulate the gradient Richardson number), resulting in periodic enhancements of turbulence at Ri minima. The patches of turbulence observed in the TLS dataset are subsequently identified as convective instabilities generated locally within the unstable phase of the wave.

Representing Richardson Number Hysteresis in the NWP Boundary Layer

2015 ◽  
Vol 143 (4) ◽  
pp. 1232-1258 ◽  
Author(s):  
Ron McTaggart-Cowan ◽  
Ayrton Zadra
Keyword(s):  
Boundary Layer ◽  
Richardson Number ◽  
Numerical Models ◽  
Rain Event ◽  
Vertical Diffusion ◽  
Predictive Skill ◽  
Turbulence Regime ◽  
Pbl Scheme ◽  
Critical Richardson Number ◽  
The Impact

Abstract Turbulence in the planetary boundary layer (PBL) transports heat, momentum, and moisture in eddies that are not resolvable by current NWP systems. Numerical models typically parameterize this process using vertical diffusion operators whose coefficients depend on the intensity of the expected turbulence. The PBL scheme employed in this study uses a one-and-a-half-order closure based on a predictive equation for the turbulent kinetic energy (TKE). For a stably stratified fluid, the growth and decay of TKE is largely controlled by the dynamic stability of the flow as represented by the Richardson number. Although the existence of a critical Richardson number that uniquely separates turbulent and laminar regimes is predicted by linear theory and perturbation analysis, observational evidence and total energy arguments suggest that its value is highly uncertain. This can be explained in part by the apparent presence of turbulence regime-dependent critical values, a property known as Richardson number hysteresis. In this study, a parameterization of Richardson number hysteresis is proposed. The impact of including this effect is evaluated in systems of increasing complexity: a single-column model, a forecast case study, and a full assimilation cycle. It is shown that accounting for a hysteretic loop in the TKE equation improves guidance for a canonical freezing rain event by reducing the diffusive elimination of the warm nose aloft, thus improving the model’s representation of PBL profiles. Systematic enhancements in predictive skill further suggest that representing Richardson number hysteresis in PBL schemes using higher-order closures has the potential to yield important and physically relevant improvements in guidance quality.

The viscous nonlinear symmetric baroclinic instability of a zonal shear flow

1975 ◽  
Vol 68 (4) ◽  
pp. 757-768 ◽  
Author(s):  
I. C. Walton
Keyword(s):  
Constant Velocity ◽  
Richardson Number ◽  
Baroclinic Instability ◽  
Lower Boundary ◽  
Length Scale ◽  
Ekman Number ◽  
Zonal Current ◽  
Horizontal Length ◽  
The Stability ◽  
Zonal Momentum

The stability of a baroclinic zonal current to symmetric perturbations on a meridionally unboundedf-plane is considered. The lower boundary is at rest but the upper one moves with a constant velocity in keeping with the velocity of the zonal current. Following Stone (1966) a horizontal length scaleO(Ro) is taken, whereRois the Rossby number, with the Richardson numberRi=O(1). Instability sets in when the wavelength isO(E1/3), whereEis the Ekman number based on the distance between the rigid horizontal boundaries, which corresponds to Stone's inviscid value zero, and to McIntyre's (1970) value infinity on a length scaleO(E½).A nonlinear analysis about the point of onset of instability yields the result that for the monotonic mode zonal momentum is convected polewards. The possible implications of this result for the dynamics of Jupiter's atmosphere are discussed.

Gradient Richardson number measurements in a stratified shear layer

1999 ◽  
Vol 30 (1) ◽  
pp. 47-63 ◽  
Author(s):  
I.P.D De Silva ◽  
A Brandt ◽  
L.J Montenegro ◽  
H.J.S Fernando
Keyword(s):  
Shear Layer ◽  
Richardson Number ◽  
Gradient Richardson Number
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