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Growth and spectra of gravity–capillary waves in countercurrent air/water turbulent flow

Published online by Cambridge University Press:  15 July 2015

Francesco Zonta ,
Alfredo Soldati  and
Miguel Onorato
Francesco Zonta*
Affiliation:
Department of Physics, University of Torino, Via Pietro Giuria 1, 10125 Torino, Italy Department of Electrical, Management and Mechanical Engineering, University of Udine, Via delle Scienze 208, 33100 Udine, Italy
Alfredo Soldati
Affiliation:
Department of Electrical, Management and Mechanical Engineering, University of Udine, Via delle Scienze 208, 33100 Udine, Italy Department of Fluid Mechanics, CISM, 33100 Udine, Italy
Miguel Onorato
Affiliation:
Department of Physics, University of Torino, Via Pietro Giuria 1, 10125 Torino, Italy
*
†Email address for correspondence: [email protected]
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Abstract

Using direct numerical simulation of the Navier–Stokes equations, we analyse the dynamics of the interface between air and water when the two phases are driven by opposite pressure gradients (countercurrent configuration). The Reynolds number ($\mathit{Re}_{{\it\tau}}$), the Weber number ($\mathit{We}$) and the Froude number ($\mathit{Fr}$) fully describe the physical problem. We examine the problem of the transient growth of interface waves for different combinations of physical parameters. Keeping $\mathit{Re}_{{\it\tau}}$ constant and varying $\mathit{We}$ and $\mathit{Fr}$, we show that, in the initial stages of the wave generation process, the amplitude of the interface elevation ${\it\eta}$ grows in time as ${\it\eta}\propto t^{2/5}$. The wavenumber spectra, $E(k_{x})$, of the surface elevation in the capillary range are in good agreement with the predictions of wave turbulence theory. Finally, the wave-induced modification of the average wind and current velocity profiles is addressed.

JFM classification

Waves/Free-surface Flows: Capillary waves Multiphase and Particle-laden Flows: Gas/liquid flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 777 , 25 August 2015 , pp. 245 - 259
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Copyright
© 2015 Cambridge University Press 

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