Getting to know turbulence - Turbulence in the Atmosphere - page 53

2.17 Derive Eq. (2.72) from the Navier-Stokes equation. Then show that it can
be rewritten as Eq. (2.74) .
2.18 Sketch a sequence of stochastic functions of time having decreasing integral
scale τ . Use it to explain why Eq. (2.36) says that the required averaging
time approaches zero as τ does.
References
Bradshaw, P., and Y. M. Koh, 1981: A note on Poisson's equation for pressure in a
turbulent flow. Phys. Fluids , 24 , 777.
Coleman, G. N., J. H. Ferziger, and P. R. Spalart, 1990: A numerical study of the turbulent
Ekman layer. J. Fluid Mech. , 213 , 313-348.
Holmes, P., J. L. Lumley, and G. Berkooz, 1996: Turbulence, Coherent Structures,
Dynamical Systems and Symmetry. Cambridge University Press.
Kolmogorov, A. N., 1941: The local structure of turbulence in incompressible viscous
fluid for very large Reynolds numbers. Doklady ANSSSR , 30 , 301-305.
LeMone, M. A., 1973: The structure and dynamics of horizontal roll vortices in the
planetary boundary layer. J. Atmos. Sci. , 30 , 1077-1091.
Lenschow, D. H., V. Patel, and A. Isbell, 1988: Measurements of fine-scale structure at the
top of marine stratocumulus. Preprint Volume, Eighth Symposium on Turbulence and
Diffusion of the American Meteorological Society , pp. 29-32.
Liu, J. T. C., 1988: Contributions to the understanding of large-scale coherent structures in
developing free turbulent shear flows. Adv. Appl. Mech. , 26 , 183-309.
Lumley, J. L., and H. A. Panofsky, 1964: The Structure of Atmospheric Turbulence .New
York: Interscience.
Monin, A. S., and A. M. Yaglom, 1971: Statistical Fluid Mechanics , Part 1. Cambridge,
MA: MIT Press.
Morrison, I., S. Businger, F. Marks, P. Dodge, and J. A. Businger, 2005: An observational
case for the prevalence of roll vortices in the hurricane boundary layer. J. Atmos. Sci. ,
62 , 2662-2673.
Reynolds, O., 1895: On the dynamical theory of incompressible viscous fluids and the
determination of the criterion. Philos. Trans. R. Soc. London, Ser. A , 186 , 123-164.
Tavoularis, S., and S. Corrsin, 1981: Experiments in nearly homogeneous turbulent shear
flow with a uniform mean temperature gradient. J. Fluid Mech. , 104 , 311-347.
Taylor, G. I., 1935: Statistical theory of turbulence. Parts I -IV. Proc. R. Soc. A151 ,
421-478.
Tennekes, H., and J. L. Lumley, 1972: A First Course in Turbulence . Cambridge, MA:
MIT Press.
Townsend, A. A., 1956: The Structure of Turbulent Shear Flow. Cambridge University
Press.
Van Dyke, M., 1982: An Album of Fluid Motion . Stanford: Parabolic Press.
Willis, G. E., and J. W. Deardorff, 1974: A laboratory model of the unstable planetary
boundary layer. J. Atmos. Sci. , 31 , 1297-1307.