Analysis of Dual Nature of Heat Flux Predicted by Monin‐Obukhov Similarity Theory: An Impact of Empirical Forms of Stability Correction Functions

Abstract

The behavior of sensible heat flux H with stability parameter ζ in the stable atmospheric surface layer is analyzed within the framework of Monin‐Obukhov similarity theory (MOST). Using MOST equations, H is expressed as a function of ζ and wind shear ∂U/∂z. A systematic mathematical analysis is carried out to analyze the behavior of H with ζ utilizing the linear as well as various nonlinear empirical functional forms of the similarity functions. In case of linear form, for a given value of H, two different values of ζ along with the “downward heat flux maximum” with a unique critical point are found to occur. However, for the other selected empirical similarity functions, more than two values of ζ having the same magnitude of H may occur suggesting the existence of multiple critical points. Further, the observational variation of H with ζ is analyzed using data from three different sites. Data suggest the existence of two different stability regimes for the same magnitude of heat flux. However, the data do not support the existence of multiple values of ζ for the same magnitude of H, as predicted by MOST with the other selected empirical forms of similarity functions. This suggests that the phenomenon of existence of downward heat flux maximum, as predicted by MOST equations, depends on the functional form of the similarity functions, and it appears to break down for some selected empirical forms of similarity functions under very stable conditions.

On stability correction functions over the Indian region under stable conditions

“…These gradients are obtained by fitting the following second‐order polynomials through a 1 hr profile similar to Grachev et al . () and Srivastava and Sharan (): where U ( z ) and θ v ( z ), respectively, are the wind speed and temperature at measurement level z . The hourly averaged wind and temperature observations obtained at 1, 2, 4, 8, 16 and 32 m heights are used to evaluate the unknown co‐efficients a i s and b i s using a classical least‐squares approach; the hourly wind and temperature gradients are then estimated.…”

“…(Equation 11) are a m = 2.67 and b m = 0.27, and the curve obtained with these modified co‐efficients shows good agreement with the observational data (Figure b). However, the functional form of φ m with these co‐efficients does not satisfy the condition proposed by Srivastava and Sharan (), which is required for a consistent relationship between heat flux and stability parameter within the framework of the MOST. This is associated with the fact that φ m ’s are observed to increase with ζ at a very slow rate.…”

“…This section describes the data set and estimates the turbulence quantities in parallel to that of Sharan and Srivastava (2016) and Srivastava and Sharan (2019). Data from a fast-response sensor (CSAT3 Sonic anemometer) installed at 10 m height at the Birla Institute of Technology Mesra in Ranchi (23.412 N,85.440 E), India, with an average elevation 609 masl (http://odis.…”

“…The slow measurements (1 Hz) of multilevel wind and temperature observations are used to evaluate the vertical wind and temperature gradients (Equations 1 and 2). These gradients are obtained by fitting the following second-order polynomials through a 1 hr profile similar to Grachev et al (2005) and Srivastava and Sharan (2019):…”

“…Sharan and Kumar () have pointed out the unphysical non‐monotonic nature of drag co‐efficient in the stable boundary layer predicted by various nonlinear stability‐correction functions and deduced a limit of applicability of these empirical functions in a theoretical framework. Recently, Srivastava and Sharan () have pointed out the inconsistency of the various functional forms of φ m in the light of the occurrence of unusual second maxima in the heat flux and stability relationship, which originates from a too quick levelling off of the function φ m . They argued that the functional forms of φ m should be revised to make the secondary peak appearing in the heat flux and stability relationship less pronounced.…”