tag:blogger.com,1999:blog-7729093380675162051.post5426810446228402472..comments2021-03-22T09:11:17.119+11:00Comments on moyhu: Lorenz attractors, fluids, chaos and climate.Nick Stokeshttp://www.blogger.com/profile/06377413236983002873noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-7729093380675162051.post-9507012938393796882016-11-21T07:38:14.497+11:002016-11-21T07:38:14.497+11:00If you want to see pretty pictures, head over here...If you want to see pretty pictures, head over here:<br /><a href="https://forum.azimuthproject.org/discussion/comment/15591/#Comment_15591" rel="nofollow">https://forum.azimuthproject.org/discussion/comment/15591/#Comment_15591</a><br /><br />The model is a biennial "attractor" (sorry that I have to condescend to that terminology) of ENSO. The beauty is that two completely non-overlapping intervals reveal precisely the same underlying periodic process.<br /><br />Lorenz may have hampered progress in modeling physical processes for generations as he implied that climate followed such extremely non-linear modes. The truth lies somewhere in-between the purely linear and highly nonlinear. This is the world of the Mathieu and Hill equations which are widely known in solid-state physics, astrophysics, and in (lo-and-behold) engineering hydrodynamics. In many regimes these are solvable and deterministic.<br /><br />Perhaps time to give up the toy models and move to something more practical.<br /><br />In particular, this premise is arguable:<br /><br /><i>"Importantly, it is an autonomous (no t on RHS) first-order differential equation."</i><br /><br />This implies that the process is a completely resonant phenomenon, not subject to boundary conditions. What would make one think that spontaneous processes would occur on the scale of the Pacific Ocean?<br /><br /><br />@whuthttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-30457085826448039292016-11-20T08:27:53.135+11:002016-11-20T08:27:53.135+11:00"Probably an inaccurate analogy, but even sin...<i>"Probably an inaccurate analogy, but even since watching Gavin Schmidt's lecture on chaos and climate I've wondered if the two attractors of the Lorenz equations might be analogous to the two quasi-steady states of a glaciated Arctic and Antarctic vs. their ice-free equivalents."</i><br /><br />This is likely true. On a much finer time scale, the ENSO "attractor" is a biennial Mathieu modulation of the wave equation, which is forced by angular momentum wobbles of the Earth and due to lunar gravitational forcing. The wobble is partly the Chandler wobble measured at the North Pole which is a flattening of the pole. There is also a wobble due to the triaxial nature of the earth and that is related to an equatorial flattening. That wobble is ~14 years. These wobbles are both sensitive to distribution of mass. The lunar forcing is of course not related to the distribution of mass.<br /><a href="https://forum.azimuthproject.org/discussion/1471/qbo-and-enso#latest" rel="nofollow">https://forum.azimuthproject.org/discussion/1471/qbo-and-enso#latest</a><br /><br /><br /><br />@whuthttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-7856523030574945212016-11-16T23:31:01.071+11:002016-11-16T23:31:01.071+11:00Probably an inaccurate analogy, but even since wat...Probably an inaccurate analogy, but even since watching Gavin Schmidt's lecture on chaos and climate I've wondered if the two attractors of the Lorenz equations might be analogous to the two quasi-steady states of a glaciated Arctic and Antarctic vs. their ice-free equivalents.<br /><br />There is a surprising amount of details that seem to be necessary to have our current ice-age prone climate state, including a southern polar continent, a restricted northern polar ocean basin, the rise of the Tibetan Plateau and the closing of the Panama Isthmus.Magmanoreply@blogger.com