The evolution of homogeneous turbulence in a density-stratified medium. 3. Analysis of the near region

  • V. A. Babenko
Article
Received:
  • 21 Downloads

Abstract

Development of a turbulent perturbation in a homogeneous flow moving within a medium that is linearly density-stratified across the direction of flow motion is described. The initial region of the evolution of turbulence with a large turbulent Reynolds numberR λ is considered.

Keywords

Internal Wave Initial Region Algebraic Relation Turbulent Reynolds Number Stratify Turbulence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notation

τ*

dimensional time

U

flow rate

M

size of the lattice cell

τ = τ*U/M

dimensionless time

E* = (ū12 + ū22 + ūs3/2)

doubled kinetic energy of turbulence

E = E*/U2

dimensionless kinetic energy

R22 = ū22/U2

vertical component of the tensor of velocity pulsations

ερ

dissipation rate of density pulsations

εu

dissipation rate of velocity pulsations

Tu = (E*U)/(εuM)

time scale of velocity field

\(T_\rho = (\overline \rho ^{\text{2}} U)/(\varepsilon _\rho M)\)

time scale of densityfield

\(R = T_u /T_\rho ;Q = ( - \overline {u_{\text{2}} } \overline \rho )/(UMd\overline \rho /dx_{\text{2}} )\)

dimensionless turbulent transverse mass flow

Φ = ρ2/Mdρ/dx22

squared velocity pulsations

σ

molecular Prandtl number

ε = Fr2

small parameter

Fr=NBVM/U

Froude number

NBV = ((g/ρ)(dρ/dx2))1/2

Brunt-Väisälä number

\(R_\lambda = (5ET_u RE)^{1/{\text{2}}} \)

turbulent Reynolds number

Re =UM/v

Reynolds number;\(\tilde \tau = \varepsilon ^{1/{\text{2}}} \tau ;t = \varepsilon T_\rho ;e = \sqrt \varepsilon \)

This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. A. Kolovandin, Advances in Heat Transfer, 21, 185–234 (1991).CrossRefGoogle Scholar
  2. 2.
    B. A. Kolavandin, V. V. Bondarchuk, C. Meola, and G. De Felice, Int. J. Heat Mass Transfer, 36, No. 7, 1953–1968 (1993).CrossRefGoogle Scholar
  3. 3.
    V. A. Babenko, Inzh.-Fiz. Zh., 70, No. 1, 30–39 (1997).Google Scholar
  4. 4.
    V. A. Babenko, Inzh.-Fiz. Zh., 70, No. 2, 268–278 (1997).Google Scholar
  5. 5.
    D. W. Dunn and W. H. Reid, Heat Transfer in Isotropic Turbulence During Final Period of Decay, NASA Technical Note, No.4186 (1958).Google Scholar
  6. 6.
    E. C. Itsweire, K. N. Helland, and C. W. van Atta, J. Fluid Mech., 162, 299–338 (1986).CrossRefGoogle Scholar
  7. 7.
    M. D. Van-Dijk, Perturbation Methods [Russian translation], Moscow (1962).Google Scholar
  8. 8.
    T. P. Sommer, R. W. C. So, and J. Zhang, in: Proc. of Int. Conf. on Turbulent Heat Transfer, San Diego (1996).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • V. A. Babenko
    • 1
  1. 1.Academic Scientific ComplexA. V. Luikov Heat and Mass Transfer Institute of the Academy of Sciences of BelarusMinsk

Personalised recommendations