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Statistics of surface renewal of passive scalars in free-surface turbulence

Published online by Cambridge University Press:  03 May 2011

ALIREZA KERMANI ,
HAMID R. KHAKPOUR ,
LIAN SHEN  and
TAKERU IGUSA
ALIREZA KERMANI
Affiliation:
Department of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
HAMID R. KHAKPOUR
Affiliation:
Department of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
LIAN SHEN*
Affiliation:
Department of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Center for Environmental and Applied Fluid Mechanics, Johns Hopkins University, Baltimore, MD 21218, USA
TAKERU IGUSA
Affiliation:
Department of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: lianshen@jhu.edu
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Abstract

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We perform direct numerical simulation to study the transport of gas and heat as passive scalars in free-surface turbulence. Our analysis focuses on the surface age of surface fluid particles, i.e. the time elapsed since the last surface renewal they experienced. Using Lagrangian tracing of fluid particles combined with heat diffusion analysis, we are able to directly quantify surface age to illustrate scalar characteristics at different stages of interfacial transfer. Results show that at the early stage of surface renewal, vertical advection associated with upwellings greatly enhances surface gas flux; random surface renewal model does not apply at this stage when most of the interfacial gas transfer occurs. After a fluid particle leaves the upwelling region, it may enter a nearby downwelling region immediately, where the gas flux is sharply reduced but the variation in surface temperature is small; alternatively, the fluid particle may travel along the surface for some time before it is absorbed by a downwelling, where the surface temperature has changed significantly due to long duration of diffusion and the gas flux is also reduced. To gain further insight into the relationships between surface velocity and scalar quantities, we perform a statistical analysis of upwellings using clustering and nonlinear regression. With this analysis, we are able to provide qualitative and quantitative descriptions of the skewed probability density functions associated with the surface divergence, temperature and gas flux that support our physics-based investigation of surface renewal and surface age.

JFM classification

Waves/Free-surface Flows: Channel flow Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 379 - 416
Copyright
Copyright © Cambridge University Press 2011. The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution-NonCommercial-ShareAlike licence <http://creativecommons.org/licenses/by-nc-sa/2.5/>. The written permission of Cambridge University Press must be obtained for commercial re-use.

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