@article{(Open Science Index):https://publications.waset.org/pdf/10566,
	  title     = {Bifurcations and Chaotic Solutions of Two-dimensional Zonal Jet Flow on a Rotating Sphere},
	  author    = {Eiichi Sasaki and  Shin-ichi Takehiro and  Michio Yamada},
	  country	= {},
	  institution	= {},
	  abstract     = {We study bifurcation structure of the zonal jet flow the
streamfunction of which is expressed by a single spherical harmonics
on a rotating sphere. In the non-rotating case, we find that a steady
traveling wave solution arises from the zonal jet flow through Hopf
bifurcation. As the Reynolds number increases, several traveling
solutions arise only through the pitchfork bifurcations and at high
Reynolds number the bifurcating solutions become Hopf unstable. In
the rotating case, on the other hand, under the stabilizing effect of
rotation, as the absolute value of rotation rate increases, the number
of the bifurcating solutions arising from the zonal jet flow decreases
monotonically. We also carry out time integration to study unsteady
solutions at high Reynolds number and find that in the non-rotating
case the unsteady solutions are chaotic, while not in the rotating cases
calculated. This result reflects the general tendency that the rotation
stabilizes nonlinear solutions of Navier-Stokes equations.},
	    journal   = {International Journal of Physical and Mathematical Sciences},
	  volume    = {7},
	  number    = {2},
	  year      = {2013},
	  pages     = {209 - 215},
	  ee        = {https://publications.waset.org/pdf/10566},
	  url   	= {https://publications.waset.org/vol/74},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 74, 2013},
	}