An examination of local similarity theory in the stably stratified boundary layer

1987 ◽  
Vol 38 (1-2) ◽  
pp. 63-71 ◽  
Author(s):  
Zbigniew Sorbjan
Keyword(s):  
Boundary Layer ◽  
Similarity Theory ◽  
Local Similarity ◽  
Local Similarity Theory

scholarly journals The Critical Richardson Number and Limits of Applicability of Local Similarity Theory in the Stable Boundary Layer

2012 ◽  
Vol 147 (1) ◽  
pp. 51-82 ◽  
Author(s):  
Andrey A. Grachev ◽  
Edgar L Andreas ◽  
Christopher W. Fairall ◽  
Peter S. Guest ◽  
P. Ola G. Persson
Keyword(s):  
Boundary Layer ◽  
Stable Boundary Layer ◽  
Richardson Number ◽  
Similarity Theory ◽  
Local Similarity ◽  
Stable Boundary ◽  
Critical Richardson Number ◽  
Local Similarity Theory

Evaluation of local similarity theory in the wintertime nocturnal boundary layer over heterogeneous surface

2016 ◽  
Vol 228-229 ◽  
pp. 164-179 ◽  
Author(s):  
Karmen Babić ◽  
Mathias W. Rotach ◽  
Zvjezdana B. Klaić
Keyword(s):  
Boundary Layer ◽  
Similarity Theory ◽  
Nocturnal Boundary Layer ◽  
Heterogeneous Surface ◽  
Local Similarity ◽  
Local Similarity Theory

Local similarity theory of convective turbulent layer using ‘spectral’ Prandtl mixing length and second moment of vertical velocity

2021 ◽  
Author(s):  
Alexander Vulfson ◽  
Petr Nikolaev
Keyword(s):  
Vertical Velocity ◽  
Similarity Theory ◽  
Turbulence Theory ◽  
Local Similarity ◽  
Mixing Length ◽  
Convective Boundary ◽  
Turbulent Layer ◽  
Second Moment ◽  
Basic Parameters ◽  
Local Similarity Theory

AbstractApproximations of the turbulent moments of the atmospheric convective boundary layer are constructed based on a variant of the local similarity theory. As the basic parameters of this theory, the second moment of vertical velocity and the ‘spectral’ Prandtl mixing length are used. This specific choice of the basic parameters allows us to consider the coefficient of turbulent transfer and the dissipation of kinetic energy of the Prandtl turbulence theory as the forms of the local similarity. Therefore, the obtained approximations of the turbulent moments should be considered as natural complementation to the semi-empirical turbulence theory. Moreover, within the atmospheric surface layer, the approximations of the new local similarity theory are identical to the relations of the Monin-Obukhov similarity theory (MOST). Therefore, the proposed approximations should be considered as a direct generalization of the MOST under free convection conditions. The new approximations are compared with the relations of the known local similarity theories. The advantages and limitations of the new theory are discussed. The comparison of the approximations of the new local similarity theory with the field and laboratory experimental data indicates the high effectiveness of the proposed approach.

scholarly journals The Cessation of Continuous Turbulence as Precursor of the Very Stable Nocturnal Boundary Layer

2012 ◽  
Vol 69 (11) ◽  
pp. 3097-3115 ◽  
Author(s):  
B. J. H. Van de Wiel ◽  
A. F. Moene ◽  
H. J. J. Jonker
Keyword(s):  
Boundary Layer ◽  
Time Scale ◽  
Nocturnal Boundary Layer ◽  
Surface Heat ◽  
Heat Extraction ◽  
Local Similarity ◽  
Temporary Reduction ◽  
Turbulent Friction ◽  
Near Surface ◽  
Flow Acceleration

Abstract The mechanism behind the collapse of turbulence in the evening as a precursor to the onset of the very stable boundary layer is investigated. To this end a cooled, pressure-driven flow is investigated by means of a local similarity model. Simulations reveal a temporary collapse of turbulence whenever the surface heat extraction, expressed in its nondimensional form h/L, exceeds a critical value. As any temporary reduction of turbulent friction is followed by flow acceleration, the long-term state is unconditionally turbulent. In contrast, the temporary cessation of turbulence, which may actually last for several hours in the nocturnal boundary layer, can be understood from the fact that the time scale for boundary layer diffusion is much smaller than the time scale for flow acceleration. This limits the available momentum that can be used for downward heat transport. In case the surface heat extraction exceeds the so-called maximum sustainable heat flux (MSHF), the near-surface inversion rapidly increases. Finally, turbulent activity is largely suppressed by the intense density stratification that supports the emergence of a different, calmer boundary layer regime.

Evaluation of Boundary Layer Similarity Theory for Stable Conditions in CASES-99

2007 ◽  
Vol 135 (10) ◽  
pp. 3474-3483 ◽  
Author(s):  
Kyung-Ja Ha ◽  
Yu-Kyung Hyun ◽  
Hyun-Mi Oh ◽  
Kyung-Eak Kim ◽  
Larry Mahrt
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Similarity Theory ◽  
Unknown Origin ◽  
Strong Stability ◽  
Surface Exchange ◽  
Stability Functions ◽  
Stable Conditions ◽  
Mean Wind Speed ◽  
Strong Winds

Abstract The Monin–Obukhov similarity theory and a generalized formulation of the mixing length for the stable boundary layer are evaluated using the Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99) data. The large-scale wind forcing is classified into weak, intermediate, and strong winds. Although the stability parameter, z/L, is inversely dependent on the mean wind speed, the speed of the large-scale flow includes independent influences on the flux–gradient relationship. The dimensionless mean wind shear is found to obey existing stability functions when z/L is less than unity, particularly for the strong and intermediate wind classes. For weak mean winds and/or strong stability (z/L > 1), this similarity theory breaks down. Deviations from similarity theory are examined in terms of intermittency. A case study of a weak-wind night indicates important modulation of the turbulence flux by mesoscale motions of unknown origin.

Similarity Theory, Intermittency and Turbulences in the Stable Boundary Layer

2005 ◽  
pp. 618-624
Author(s):  
Kyungm Ja Ha ◽  
Kyung Eak Kim ◽  
Yu Kyung Hyun ◽  
Eun Hee Jeon ◽  
Larry Mahrt
Keyword(s):  
Boundary Layer ◽  
Stable Boundary Layer ◽  
Similarity Theory ◽  
Stable Boundary

scholarly journals A New Value of the von Kármán Constant: Implications and Implementation

2009 ◽  
Vol 48 (5) ◽  
pp. 923-944 ◽  
Author(s):  
Edgar L. Andreas
Keyword(s):  
Boundary Layer ◽  
Similarity Theory ◽  
Stable Stratification ◽  
Transfer Coefficients ◽  
Obukhov Length ◽  
Von Karman ◽  
Roughness Lengths ◽  
Experimental Values ◽  
Definition Of ◽  
Von Kármán

Abstract The von Kármán constant k occurs throughout the mathematics that describe the atmospheric boundary layer. In particular, because k was originally included in the definition of the Obukhov length, its value has both explicit and implicit effects on the functions of Monin–Obukhov similarity theory. Although credible experimental evidence has appeared sporadically that the von Kármán constant is different than the canonical value of 0.40, the mathematics of boundary layer meteorology still retain k = 0.40—probably because the task of revising all of this math to implement a new value of k is so daunting. This study therefore outlines how to make these revisions in the nondimensional flux–gradient relations; in variance, covariance, and dissipation functions; and in structure parameters of Monin–Obukhov similarity theory. It also demonstrates how measured values of the drag coefficient (CD), the transfer coefficients for sensible (CH) and latent (CE) heat, and the roughness lengths for wind speed (z0), temperature (zT), and humidity (zQ) must be modified for a new value of the von Kármán constant. For the range of credible experimental values for k, 0.35–0.436, revised values of CD, CH, CE, z0, zT, and zQ could be quite different from values obtained assuming k = 0.40, especially if the original measurements were made in stable stratification. However, for the value of k recommended here, 0.39, no revisions to the transfer coefficients and roughness lengths should be necessary. Henceforth, use the original measured values of transfer coefficients and roughness lengths but do use similarity functions modified to reflect k = 0.39.

Local similarity relationships in a horizontally inhomogeneous boundary layer

1990 ◽  
Vol 52 (1-2) ◽  
pp. 17-40 ◽  
Author(s):  
Yaping Shao ◽  
J�rg M. Hacker
Keyword(s):  
Boundary Layer ◽  
Local Similarity ◽  
Similarity Relationships ◽  
Horizontally Inhomogeneous

Non-Darcian Boundary Layer Flow and Forced Convective Heat Transfer Over a Flat Plate in a Fluid-Saturated Porous Medium

1990 ◽  
Vol 112 (1) ◽  
pp. 157-162 ◽  
Author(s):  
A. Nakayama ◽  
T. Kokudai ◽  
H. Koyama
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Flat Plate ◽  
Similarity Solution ◽  
Temperature Fields ◽  
Solid Boundary ◽  
Local Similarity ◽  
Viscous Term ◽  
Inertia Term

The local similarity solution procedure was successfully adopted to investigate non-Darcian flow and heat transfer through a boundary layer developed over a horizontal flat plate in a highly porous medium. The full boundary layer equations, which consider the effects of convective inertia, solid boundary, and porous inertia in addition to the Darcy flow resistance, were solved using novel transformed variables deduced from a scale analysis. The results from this local similarity solution are found to be in good agreement with those obtained from a finite difference method. The effects of the convective inertia term, boundary viscous term, and porous inertia term on the velocity and temperature fields were examined in detail. Furthermore, useful asymptotic expressions for the local Nusselt number were derived in consideration of possible physical limiting conditions.

Boundary Layer Analysis of Exothermic and Endothermic Kind of Chemical Reaction in the Flow of Non-Darcian Unsteady Micropolar Fluid along an Infinite Vertical Surface

2017 ◽  
Vol 28 ◽  
pp. 90-101 ◽  
Author(s):  
O.K. Koriko ◽  
A.J. Omowaye ◽  
Isaac Lare Animasaun ◽  
Idris O. Babatunde
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Micropolar Fluid ◽  
Local Heat Transfer ◽  
Flow Region ◽  
Local Similarity ◽  
Suction Parameter ◽  
Boundary Layer Analysis ◽  
Layer Analysis

The problem of unsteady non – Newtonian flow past a vertical porous surface in the presence of thermal radiation is investigated. Using the theory of boundary layer analysis, the flow of micropolar fluid in the presence of exothermic and endothermic kind of chemical reaction is considered. It is assumed that the relationship between the flow rate and the pressure drop as the fluid flows over a porous medium is non – linear. Using local similarity transformation, the governing partial differential equations of the physical model are reduced to ordinary differential equations. The corresponding boundary value problem is solved numerically using shooting method along with Runge-Kutta Gill method together with quadratic interpolation. It is found that increase in micro-rotation parameter increases the velocity while the micro- rotation decreases across the flow region. Maximum micro-rotation of tiny particles is guaranteed at higher values of suction parameter. Local heat transfer rate decreases with an increase in exothermic /endothermic parameter.

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