Skip to main content
    • Aa
    • Aa

Kinetic energy transport in Rayleigh–Bénard convection

  • K. Petschel (a1), S. Stellmach (a1), M. Wilczek (a2), J. Lülff (a3) and U. Hansen (a1)...

The kinetic energy balance in Rayleigh–Bénard convection is investigated by means of direct numerical simulations for the Prandtl number range $0.01\leqslant \mathit{Pr}\leqslant 150$ and for fixed Rayleigh number $\mathit{Ra}=5\times 10^{6}$ . The kinetic energy balance is divided into a dissipation, a production and a flux term. We discuss the profiles of all the terms and find that the different contributions to the energy balance can be spatially separated into regions where kinetic energy is produced and where kinetic energy is dissipated. By analysing the Prandtl number dependence of the kinetic energy balance, we show that the height dependence of the mean viscous dissipation is closely related to the flux of kinetic energy. We show that the flux of kinetic energy can be divided into four additive contributions, each representing a different elementary physical process (advection, buoyancy, normal viscous stresses and viscous shear stresses). The behaviour of these individual flux contributions is found to be surprisingly rich and exhibits a pronounced Prandtl number dependence. Different flux contributions dominate the kinetic energy transport at different depths, such that a comprehensive discussion requires a decomposition of the domain into a considerable number of sublayers. On a less detailed level, our results reveal that advective kinetic energy fluxes play a key role in balancing the near-wall dissipation at low Prandtl number, whereas normal viscous stresses are particularly important at high Prandtl number. Finally, our work reveals that classical velocity boundary layers are deeply connected to the kinetic energy transport, but fail to correctly represent regions of enhanced viscous dissipation.

Corresponding author
Email address for correspondence:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

G. Ahlers , S. Grossmann  & D. Lohse 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81 (2), 503537.

M. Breuer , S. Wessling , J. Schmalzl  & U. Hansen 2004 Effect of inertia in Rayleigh–Bénard convection. Phys. Rev. E 69 (2), 026302.

B. Castaing , G. Gunaratne , F. Heslot , L. Kadanoff , A. Libchaber , S. Thomae , X.-Z. Wu , S. Zaleski  & G. Zanetti 1989 Scaling of hard thermal turbulence in Rayleigh–Bénard convection. J. Fluid Mech. 204, 130.

F. Chillà  & J. Schumacher 2012 New perspectives in turbulent Rayleigh–Bénard convection. Euro. Phys. J. E 35 (7), 125.

J. W. Deardorff  & G. E. Willis 1967 Investigation of turbulent thermal convection between horizontal plates. J. Fluid Mech. 28 (04), 675704.

S. Grossmann  & D. Lohse 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 2756.

G. Grötzbach 1983 Spatial resolution requirements for direct numerical simulation of the Rayleigh–Bénard convection. J. Comput. Phys. 49 (2), 241264.

R. M. Kerr 2001 Energy budget in Rayleigh–Bénard convection. Phys. Rev. Lett. 87 (24), 244502.

R. M. Kerr  & J. R. Herring 2000 Prandtl number dependence of Nusselt number in direct numerical simulations. J. Fluid Mech. 419, 325344.

S. Lam , X.-D. Shang , S.-Q. Zhou  & K.-Q. Xia 2002 Prandtl number dependence of the viscous boundary layer and the Reynolds numbers in Rayleigh–Bénard convection. Phys. Rev. E 65 (6), 066306.

L. Li , N. Shi , R. du Puits , C. Resagk , J. Schumacher  & A. Thess 2012 Boundary layer analysis in turbulent Rayleigh–Bénard convection in air: experiment versus simulation. Phys. Rev. E 86 (2), 026315.

K. Petschel , S. Stellmach , M. Wilczek , J. Lülff  & U. Hansen 2013 Dissipation layers in Rayleigh–Bénard convection: a unifying view. Phys. Rev. Lett. 110 (11), 114502.

J. D. Scheel , E. Kim  & K. R. White 2012 Thermal and viscous boundary layers in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 711, 281305.

J. D. Scheel  & J. Schumacher 2014 Local boundary layer scales in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 758, 344373.

H. Schlichting  & K. Gersten 2000 Boundary-Layer Theory, 8th edn.Springer.

N. Shi , M. S. Emran  & J. Schumacher 2012 Boundary layer structure in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 706, 533.

O. Shishkina , R. J. A. M. Stevens , S. Grossmann  & D. Lohse 2010 Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution. New J. Phys. 12 (7), 075022.

S. Stellmach  & U. Hansen 2008 An efficient spectral method for the simulation of dynamos in Cartesian geometry and its implementation on massively parallel computers. Geochem. Geophys. Geosyst. 9 (5), Q05003.

A. Tilgner , A. Belmonte  & A. Libchaber 1993 Temperature and velocity profiles of turbulent convection in water. Phys. Rev. E 47 (4), R2253R2256.

S. Wagner , O. Shishkina  & C. Wagner 2012 Boundary layers and wind in cylindrical Rayleigh–Bénard cells. J. Fluid Mech. 697, 336366.

J. M. Wallace 2009 Twenty years of experimental and direct numerical simulation access to the velocity gradient tensor: what have we learned about turbulence? Phys. Fluids 21 (2), 021301.

Q. Zhou  & K.-Q. Xia 2010 Measured instantaneous viscous boundary layer in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 104 (10), 104301.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 1
Total number of PDF views: 50 *
Loading metrics...

Abstract views

Total abstract views: 130 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th September 2017. This data will be updated every 24 hours.