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Direct numerical simulation of stratified flow past a sphere at a subcritical Reynolds number of 3700 and moderate Froude number

Published online by Cambridge University Press:  02 August 2017

Anikesh Pal ,
Sutanu Sarkar Open the ORCID record for Sutanu Sarkar [Opens in a new window] ,
Antonio Posa  and
Elias Balaras Open the ORCID record for Elias Balaras [Opens in a new window]
Anikesh Pal
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, CA 92093, USA
Sutanu Sarkar*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, CA 92093, USA
Antonio Posa
Affiliation:
Department of Mechanical and Aerospace Engineering, The George Washington University, Washington DC 20052, USA
Elias Balaras
Affiliation:
Department of Mechanical and Aerospace Engineering, The George Washington University, Washington DC 20052, USA
*
†Email address for correspondence: ssarkar@ucsd.edu
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Abstract

Direct numerical simulation of flow past a sphere in a stratified fluid is carried out at a subcritical Reynolds number of 3700 and $Fr=U_{\infty }/ND=1,2$ and 3 to understand the dynamics of moderately stratified flows with $Fr=O(1)$. Here, $U_{\infty }$ is the free stream velocity, $N$ is the background buoyancy frequency and $D$ is the sphere diameter. The unstratified flow past the sphere consists of a separated shear layer that transitions to turbulence, a recirculation zone and a wake with a mean centreline deficit velocity, $U_{0}$, that decreases with downstream distance as a power law. With increasing stratification, the separated shear layer plunges inward vertically and its roll up is inhibited, the recirculation zone is shortened and the mean wake decays at a slower rate of $U_{0}\propto (x_{1}/D)^{-0.25}$ in the non-equilibrium (NEQ) region. The transition from the near wake where $U_{0}$ has a decay rate similar to the unstratified case to the NEQ regime occurs as an oscillatory modulation by a steady lee wave pattern with a period of $t=2\unicode[STIX]{x03C0}/N$ that leads to accelerated $U_{0}$ between $Nt=\unicode[STIX]{x03C0}$ and approximately $Nt=2\unicode[STIX]{x03C0}$. Far downstream, the wake is dominated by coherent horizontal motions. The acceleration of $U_{0}$ by the lee wave and the lower turbulence production in the NEQ regime, thereby less loss to turbulence, prolongs the lifetime of the wake relative to its unstratified counterpart. The intensity, temporal spectra and structure of turbulent fluctuations in the wake are assessed. Buoyancy induces significant anisotropy among the velocity components and between their vertical and horizontal profiles. Consequently, the near wake ($x_{1}/D<10$) exhibits significant differences in turbulence profiles relative to its unstratified counterpart. Spectra of vertical velocity show a discrete peak in the near wake that is maintained further downstream. The turbulent kinetic energy (TKE) balance is computed and contributions from pressure transport and buoyancy are found to become increasingly important as stratification increases. The findings of this investigation will be helpful in designing accurate initial conditions for the temporally evolving model of stratified wakes.

JFM classification

Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulence simulation Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 826 , 10 September 2017 , pp. 5 - 31
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Copyright
© 2017 Cambridge University Press 

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