Abstract
One-dimensional spectra in uniformly sheared, nearly homogeneous, turbulent flows with various magnitudes of mean shear and mean streamline curvature are presented and analyzed. These spectra confirm our previous observations (Holloway and Tavoularis, 1992) that curvature affects the partition of the kinetic energy among its three components and, especially, the covariance of the streamwise and transverse velocity fluctuations. It is also evident from these spectra, particularly form the coherence, that the energy containing eddies are most strongly affected by curvature, while the fine structure is affected indirectly, probably through changes in the input to the energy cascade. For relatively mild curvature, the coherence of large-scale motions diminished in cases where the mean velocity increased away from the center of curvature and increased in cases where the mean velocity decreased away from the center of curvature. For “strong” curvature in the same direction as the mean shear, the sign of the coherence of large eddies was reversed and momentum was transported up the gradient of mean velocity and away from the center of curvature. For certain combinations of mean shear and curvature, the coherence of large scales was opposite to that of the small scales.
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Abbreviations
- Cuv (k1):
-
the coherence function
- Dsn :
-
mean strain rate
- Fuu(k1), Fvv (k1), Fww(k1), Fuv(k1):
-
streamwise, one-dimensional spectra of the velocity fluctuations and the shear stress
- K1 :
-
streamwise component of the wavenumber vector
- Luu :
-
the integral length scale of the streamwise fluctuations
- P:
-
the production rate of turbulence kinetic energy
- Rc :
-
radius of curvature of the tunnel centerline
- Re :
-
real part of a complex function
- RL :
-
turbulence Reynolds number based on the integral length scale
- Rλ :
-
turbulence Reynolds number based on the Taylor microscale
- s, n, z:
-
streamwise, transverse and spanwise coordinates 384 A.G.L. Holloway and S. Tavoularis
- S:
-
curvature paramter (= (UU/R,)/(dU/dn))
- U, V, W:
-
streamwise, transverse and spanwise mean velocity components
- u, v, w:
-
streamwise, transverse and spanwise velocity fluctuations
- Uc :
-
streamwise mean velocity component on the tunnel centerline
- є:
-
the rate of viscous dissipation of the turbulence kinetic energy
- η:
-
Kolmogorov microscale
- θ:
-
turning angle
- λu :
-
streamwise Taylor microscale
- ν:
-
kinematic viscosity
- τ:
-
dimensionless time
- τ0 :
-
dimensionless time at the entrance to the curved section
- v:
-
Kolmogorov velocity
- Ωz :
-
mean rotation rate
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© 1993 Springer-Verlag Berlin Heidelberg
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Holloway, A.G.L., Tavoularis, S. (1993). Scaling and Structure of Turbulent Eddies in Curved Sheared Flows. In: Durst, F., Friedrich, R., Launder, B.E., Schmidt, F.W., Schumann, U., Whitelaw, J.H. (eds) Turbulent Shear Flows 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77674-8_26
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DOI: https://doi.org/10.1007/978-3-642-77674-8_26
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