TY - JFULL AU - Eiichi Sasaki and Shin-ichi Takehiro and Michio Yamada PY - 2013/3/ TI - Bifurcations and Chaotic Solutions of Two-dimensional Zonal Jet Flow on a Rotating Sphere T2 - International Journal of Physical and Mathematical Sciences SP - 208 EP - 215 VL - 7 SN - 1307-6892 UR - https://publications.waset.org/pdf/10566 PU - World Academy of Science, Engineering and Technology NX - Open Science Index 74, 2013 N2 - 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. ER -