Rossby waves and cascade phenomena
Pleiades Publishing Ltd - 2012
Tóm tắt
Nonlinear triad interactions in the Navier-Stokes equation describing quasi-geostrophic thermal convection in a spherical layer are considered. The analysis provides an insight into the nature of kinetic energy transfer across the spectrum and allows us to assess the degree of nonlocality in the energy transfer. The distinguishing feature of the spherical problem is the emergence of the Rossby waves, which cause nonlocal redistribution of energy in the system. The results of this study are compared with their counterparts for the plane model.
Từ khóa
Tài liệu tham khảo
Brandenburg, A., Astrophysical Magnetic Fields and Nonlinear Dynamo Theory, Phys. Rep., 2005, vol. 417, pp. 1–209.
Busse, F.H., Thermal Instabilities in Rapidly Rotating Systems, J. Fluid Mech., 1970, vol. 44, pp. 441–460.
Busse, F.H., Convective Flows in Rapidly Rotating Spheres and Their Dynamo Action, Phys. Fluids, 2002, vol. 14, no. 4, pp. 1301–1314.
Drobyshevski, E.M. and Yuferev, B.S., Topological Pumping of Magnetic Flux by Three-Dimensional Convection, J. Fluid Mech., 1974, vol. 65, pp. 33–44.
Frisch, U., Turbulence: The Legacy of A.N. Kolmogorov, Cambridge: Cambridge Univ. Press, 1995.
Hejda, P. and Reshetnyak, M., Effects of Anisotropy in the Geostrophic Turbulence, Phys. Earth Planet. Int., 2009, vol. 177, pp. 152–160.
Hejda, P. and Reshetnyak, M., Nonlinearity in Dynamo, Geophys. Astrophys. Fluid Dyn., 2010, vol. 104, no. 6, pp. 25–34.
Jones, C.A. and Roberts, P.H., Convection Driven Dynamos in a Rotating Plane Layer, J. Fluid Mech., 2000, vol. 404, pp. 311–343.
Krause, F. and Rädler, K.-H., Mean Field Magnetohydrodynamics and Dynamo Theory, Berlin: Akademie-Verlag, 1980.
Küppers, G. and Lortz, D., Transition from Laminar Convection To Thermal Turbulence in a Rotating Fluid Layer, J. Fluid Mech., 1969, vol. 35, pp. 609–620.
Pedlosky, J., Geophysical Fluid Dynamics, New York: Springer, 1987.
Reshetnyak, M. and Hejda, P., Direct and Inverse Cascades in the Geodynamo, Nonlin. Processes Geophys., 2008, vol. 15, pp. 873–880.
Reshetnyak, M.Yu., Taylor Cylinder and Convection in a Spherical Shell, Geomagn. Aeron., 2010, vol. 50, no. 2, pp. 263–273.
Reshetnyak, M.Yu., The Pseudospectral Method in Thermal Convection Models of a Rotating Spherical Shell for Parallel Computers, Vychisl. Met. Progr. Nov. Vychisl. Tekhnol., 2011, vol. 12, pp. 77–84.
Sreenivasan, B. and Davidson, P.A., On the Formation of Cyclones and Anticyclones in a Rotating Fluid, Phys. Fluids. 2008, vol. 20, pp. 085104-1–085104-11.
Tabeling, P., Two-Dimensional Turbulence: A Physicist Approach, Phys. Reports, 2002, vol. 362, pp. 1–62.
Verma, M., Statistical Theory of Magnetohydrodynamic Turbulence: Recent Results, Phys. Reports, 2004, vol. 401, pp. 229–380.
Zeldovich, Ya.B., Ruzmaikin, A.A., and Sokoloff, D.D., Magnetic Fields in Astrophysics, New York: Gordon and Breach, 1983.