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The universal velocity log law first proposed by von K\'arm\'an in the near-wall region of turbulent shear flows is one of the cornerstones of turbulence theory. When buoyancy effects are important, the universal velocity log law is…

Fluid Dynamics · Physics 2022-09-16 Yu Cheng , Andrey Grachev , Chiel van Heerwaarden

We develop innovative analytical expressions for the mean wind and potential temperature flux profiles in convective boundary layers (CBLs). CBLs are frequently observed during daytime as the Earth's surface is warmed by solar radiation.…

Fluid Dynamics · Physics 2023-08-07 Luoqin Liu , Srinidhi N. Gadde , Richard J. A. M. Stevens

The Monin-Obukhov Similarity Theory (MOST) is a cornerstone of atmospheric science for describing turbulence in stable boundary layers. Extending MOST to stably stratified turbulent channel flows, however, is non-trivial due to confinement…

Fluid Dynamics · Physics 2026-01-14 Sanath Kotturshettar , Pedro Costa , Rene Pecnik

Monin-Obukhov similarity theory (MOST) stands at the center of understanding of atmospheric surface-layer turbulence. Based on the hypothesis that a single length scale determined by surface fluxes governs the turbulent exchange of…

Atmospheric and Oceanic Physics · Physics 2023-04-05 Ivana Stiperski , Marc Calaf

For nearly a century the universal logarithmic behaviour of the mean velocity profile in a parallel flow was a mainstay of turbulent fluid mechanics and its teaching. Yet many experiments and numerical simulations are not fit exceedingly…

Fluid Dynamics · Physics 2017-06-07 Paolo Luchini

Since the introduction of the logarithmic law of the wall more than 80 years ago, the equation for the mean velocity profile in turbulent boundary layers has been widely applied to model near-surface processes and parameterise surface drag.…

Fluid Dynamics · Physics 2020-02-07 Michael Heisel , Charitha M. de Silva , Nicholas Hutchins , Ivan Marusic , Michele Guala

The higher-order mean velocity profile in the convective atmospheric boundary layer (CBL) is derived using the method of matched asymptotic expansions. The universal expansion coefficients are obtained using field measurement data. The…

Fluid Dynamics · Physics 2026-02-17 Chenning Tong , Davoud Pourabdollah , Kirill Barskov , Mengjie Ding

The classical scaling theory of turbulent parallel flow provides a framework for the description of the mean velocity profile through two functions of one variable, traditionally named law of the wall and law of the wake, and a universal…

Fluid Dynamics · Physics 2018-05-09 Paolo Luchini

Two-dimensional simulations of Rayleigh-B\'enard convection at $Ra = 5\times10^{10}$ show that vertical logarithmic mean temperature profiles can be observed in regions of the boundary layer where thermal plumes are emitted. The profile is…

The Monin--Obukhov similarity theory-based wind speed and potential temperature profiles are inherently coupled to each other. We have developed hybrid approaches to disentangle them, and as a direct consequence, the estimation of Obukhov…

Atmospheric and Oceanic Physics · Physics 2018-09-10 Sukanta Basu

Conventionally neutral atmospheric boundary layers (CNBLs), which are characterized with zero surface potential temperature flux and capped by an inversion of potential temperature, are frequently encountered in nature. Therefore,…

Atmospheric and Oceanic Physics · Physics 2022-07-06 Luoqin Liu , Srinidhi N. Gadde , Richard J. A. M. Stevens

Monin--Obukhov Similarity Theory (MOST), which underpins nearly all bulk estimates of surface fluxes in the atmospheric surface layer, assumes monotonic wind profiles and vertically uniform momentum and heat fluxes. Here, we show that…

Monin Obukhov Similarity Theory (MOST) has long served as the basis for parameterizations of turbulence exchange between the surface and the atmospheric boundary layer in models for weather and climate prediction. Decades of research,…

Atmospheric and Oceanic Physics · Physics 2025-07-17 Tyler Waterman , Ivana Stiperski , Nathaniel Chaney , Marc Calaf

The logarithmic law of mean temperature profile has been observed in different regions in Rayleigh-B\'enard turbulence. However, how thermal plumes correlate to the log law of temperature and how the velocity profile changes with pressure…

Fluid Dynamics · Physics 2019-10-08 Hong-Yue Zou , Wen-Feng Zhou , Xi Chen , Yun Bao , Jun Chen , Zhen-Su She

The logarithmic mean-velocity profile is a key experimental and theoretical result in wall-bounded turbulence. Similarly, here we show that the topographic surface emerging between parallel zero-elevation boundaries presents an intermediate…

Turbulence remains an unsolved multidisciplinary science problem. As one of the most well-known examples in turbulent flows, knowledge of the logarithmic mean velocity profile (MVP), so called the log law of the wall, plays an important…

Fluid Dynamics · Physics 2017-08-22 Chien-chia Liu

In supersonic and hypersonic flows, the near-wall density variation due to wall cooling poses a challenge for accurately predicting the near-wall velocity and temperature profiles using classical eddy viscosity turbulence models.…

Fluid Dynamics · Physics 2025-08-19 Zifei Yin

A generalized logarithmic law for high-order moments of passive scalars is proposed for turbulent boundary layers. This law is analogous to the generalized log law that has been proposed for high-order moments of the turbulent longitudinal…

Fluid Dynamics · Physics 2022-12-12 Kelly Y. Huang , Matt K. Fu , Clayton P. Byers , Andrew D. Bragg , Gabriel G. Katul

A new mixed scaling parameter $Z=z/\sqrt{Lh}$ is proposed for similarity in the stable atmospheric surface layer, where $z$ is the height, $L$ is the Obukhov length, and $h$ is the boundary layer depth. Compared to the parameter $\zeta =…

Atmospheric and Oceanic Physics · Physics 2023-09-01 Michael Heisel , Marcelo Chamecki

Heat and momentum transfer in wall-bounded turbulent flow, coupled with the effects of wall-roughness, is one of the outstanding questions in turbulence research. In the standard Rayleigh-B\'enard problem for natural thermal convection, it…

Fluid Dynamics · Physics 2019-07-05 Michael MacDonald , Nicholas Hutchins , Detlef Lohse , Daniel Chung
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