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\begin{document}

\title{Analysis of Effects of Meander Curvature in Thermally Stratified
Turbulent Open-channel Flow}



\author[1]{Duy Nguyen}%
\author[2]{Michael Kirkpatrick}%
\author[1]{Nicholas Williamson}%
\author[1]{Steven Armfield}%
\author[3]{Wenxian Lin}%
\affil[1]{University of Sydney}%
\affil[2]{The University of Sydney}%
\affil[3]{James Cook University}%


\vspace{-1em}



  
  \date{May 24, 2024}


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\selectlanguage{english}
\begin{abstract}
Thermal stratification can lead to the damping of turbulence, which
reduces the mixing of solutes in a fluid body, and in turn, affects river
health. A series of Direct Numerical Simulation (DNS) solutions sweeping
through a range of four different channel radius of curvature is obtained
to investigate the effect of curvature on stratification in meandering
thermally stratified turbulent open channel flow. This range of radius of
curvature will cover a range of the curvature parameter 0.2 \textless{}
\selectlanguage{greek}γ \selectlanguage{english}\textless{}1.5, which is typical of rivers in the sharp to mild
curvature range. Here \selectlanguage{greek}γ \selectlanguage{english}= C\_f\^{}-\{1\} (H/R\_\{min\} is a dominant
control parameter with respect to velocity redistribution in curved
open-channel flow, where C\_f is the Chezy friction coefficient, R\_\{min\}
the minimum radius of curvature, which occurs at the meander apex, H the
meander height. An internal heat source models radiative heating from
above following an exponential Beer's law profile, which varies with
height due to progressive absorption. Based on the DNS results, the
present paper addresses two issues. Firstly, the influence of changing
curvature on the complex tri-cellular pattern of the secondary flow is
investigated, including the distribution of turbulent stresses.
Secondly, the effect of changing curvature on the degree of stratification
is analysed. Stratification can be characterised by the friction
Richardson number Ri\_\selectlanguage{greek}τ \selectlanguage{english}= (\selectlanguage{greek}β\selectlanguage{english}gH\selectlanguage{greek}ΔΦ\selectlanguage{english})/u\^{}2\_\selectlanguage{greek}τ, \selectlanguage{english}and the bulk Richardson
number Ri\_b = (\selectlanguage{greek}β\selectlanguage{english}gH\selectlanguage{greek}ΔΦ\selectlanguage{english})/u\^{}2\_\{bulk\}. Here \selectlanguage{greek}ΔΦ \selectlanguage{english}is the difference
between the mean temperature at the top and bottom of the channel, u\_\selectlanguage{greek}τ
\selectlanguage{english}the mean friction velocity on the solid surfaces bounding the channel,
u\_\{bulk\} the domain averaged streamwise velocity, \selectlanguage{greek}β \selectlanguage{english}the volumetric
coefficient of expansion and g gravity. Stratification can also be viewed
in terms of the transfer of energy from mean flow kinetic energy to
potential energy via buoyancy fluxes. We study the effect of curvature on
stratification by investigating its effect on the friction and bulk
Richardson numbers, the global available, background, total potential
energy, and the domain averaged kinetic energy. It is found that with
the increase of curvature, Ri\_\selectlanguage{greek}τ \selectlanguage{english}and Ri\_\{bulk\} decrease, while
available potential energy increases due to increased overturning of the
flow, indicating that increasing curvature leads to a decrease in the
level of stratification.%
\end{abstract}%



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