Arguments could ensue as to whether their closure for eddy viscosity provides the correct magnitude in any particular case, but the patch for the ill-posedness would remain intact as grid sizes dropped. ❋ Unknown (2007)
I am sure MM4 has hundreds of references too in many journals internationally, and the results speak to the issue of posedness themselves. ❋ Unknown (2007)
If there is overturning caused by numerics, physics, or ill posedness in the hydrostatic system, the model must be stabilized either by large dissipation or an ad hoc adjustment to reinstate the hydrostatic balance and usually both. ❋ Unknown (2007)
So, for example, if Gerry is correct in his stability analysis the ill-posedness Gerry describes suggests would cause the slightest difficulty when modeling flow past airfoils, pipe flow or many engineering flows. ❋ Unknown (2007)
Only when pressure was applied because of the ill posedness of the IBVP for that system did the mesoscale models switch to the nonhydrostatic system. ❋ Unknown (2007)
Using a mathematical perturbation of smooth, large-scale atmospheric flow in the presence of vertical shear (jet stream), Browning and Kreiss (1984) showed that the hydrostatic equations can lead to unbounded exponential growth (ill posedness) and the non-hydrostatic equations can lead to rapid exponential growth on the time scale of a few hours when the wave length resolved by a numerical model approaches 10 km. ❋ Unknown (2007)
In the previous discussions of chaos, dissipation, and ill-posedness in the comments listed above in this post, there was little mention of the thermal effects of physical dissipation in the fluid motions of interest. ❋ Unknown (2007)
Once we have these facts, we can discuss analytically the posedness and accuracy of the process. ❋ Unknown (2007)
I find it amusing that you are unable to answer basic questions about the coupled climate model that you supposedly code for IPCC, but claim to know so much about ill posedness. ❋ Unknown (2007)
The ill posedness of the IBVP for the hydrostatic system was shown mathematically in 1976. ❋ Unknown (2007)
If a hydrostatic model is being used at 10 km, then the dissipation must be much larger than in the real atmosphere in order to hide the ill posedness. ❋ Unknown (2007)
Hovering above everything we have the ill posedness of Jerry and the ominous interactions between resolved and unresolved dimensions that are arbitrary numerical artefacts anyway due to computer power considerations . ❋ Unknown (2007)
And at finer resolutions the hydrostatic model blows up even sooner as expected from the ill-posedness. ❋ Unknown (2007)
So, if the eddy viscosity acts as a patch to cover ill-posedness, then LES may work at large grid sizes and then stop working as the grid sizes drop because, to use a metaphor, the bandaid gets taken off. ❋ Unknown (2007)
You seem to have numerical accuracy, numerical stability, ill posedness and fast exponential growth confused. ❋ Unknown (2007)
Will you provide additional information relative to the basis of the ill-posedness of hydrostatic models? ❋ Unknown (2007)
This modification was made in order to overcome the ill posedness of the hydrostatic system for open boundary problems IBVP in the midlatitudes so that the approximate system could be used to supply accurate, well posed boundary conditions for fine mesh limited area models. ❋ Unknown (2007)
Auxiliary differential equation models can also affect the well- or ill-posedness of the overall equation system. ❋ Unknown (2007)
The latter, although in some agreement with the nonhydrostatic model at the lower resolution up to 12 hr all runs start with the same balanced large-scale initial conditions, in the higher resolution run blows up because of the ill-posedness of the hydrostatic system as expected from the mathematical theory in the reference cited above. ❋ Unknown (2007)
Were you able to link to the plots and how readable are the basic contour lines in the plots except for the fourth one which is a mess because of the ill posedness. ❋ Unknown (2007)
