Some problems and issues in geophysical turbulence

Velocity fluctuations in the large scales of the atmosphere's meso-scale ha ve turbulent characteristics of random fluctuations and a scale-size distri bution near k(-5/3) (Gage, 1979. J. Atmos. Sci. 36, 1950-1954; Lilly, 1983. J. Atmos. Sci. 40, 749-761; Lilly et al., 1998. Theoret. Comput. Fluid Dyn . 11, 139-153). Explanations of this motion field have ranged from inverse cascading quasi-geostrophic (i.e, quasi-two-dimensional) turbulence, to gra vity waves (VanZandt, 1982. Ceophys. Res. Lett. 9, 575-578). We describe ef forts to relate observational spectra to various theories ranging from quas i-geostrophic turbulence to gravity waves. We note that at the larger scale s quasi-geostrophic theory may suffice, but at smaller scales, a quasi-geos trophic explanation becomes untenable because the importance of rotation be comes progressively weaker as scales of the flow becomes smaller (the Rossb y number approaches unity). We then discuss numerical simulations designed to discriminate between alternative explanations of the flow. Several simul ations are reviewed, starting with those of Herring and Metais (1989. J. Fl uid Mech. 202, 97-115), and finally those described by Lilly et al. (1998. Theoret. Comput. Fluid Dyn. 11, 139-153). (C) 1999 The Japan Society of Flu id Mechanics and Elsevier Science B.V. All rights reserved.