inviscid

The discussions remind me of the massless beams, frictionless planes, and inviscid/incompressible flows that dot the physics and engineering pedagogy: very useful to a point, and wildly inaccurate past that point.

Roll Over, Ricardo, Arnold Kling | EconLog | Library of Economics and Liberty 2009

Now the unforced viscous, incompressible NS equations are not the equations that describe the climate, but the body of work does indicate that there is a vast mathematical difference between the inviscid and viscous cases, and the impact of using an incorrect kind or size of viscosity in an attempt to compute the continuum solution with the correct kind and size of kinematic viscosity.

Exponential Growth in Physical Systems #2 « Climate Audit 2007

I consider the inviscid Navier-Stokes Eulerian equations as the basic

Exponential Growth in Physical Systems #2 « Climate Audit 2007

It is my recollection that the Lorenz equations were derived from the inviscid atmospheric equations using just the interaction of the lowest 3 spectral modes.

Exponential Growth in Physical Systems #2 « Climate Audit 2007

I ran inviscid tests of a hydrostatic and nonhydrostatic model at fine resolutions.

Exponential Growth in Physical Systems #2 « Climate Audit 2007

The main point of the original thread (#1) was that the basic inviscid system (essentially the inviscid compressible Navier-Stokes equations with only gravitational and Coriolis forces included) numerically approximated in all weather prediction and climate models has mathematical problems in the continuum system that prevent any meaningful numerical convergence.

Exponential Growth in Physical Systems #2 « Climate Audit 2007

I seem to recall that Ed used an approximation of the inviscid system.

Exponential Growth in Physical Systems #2 « Climate Audit 2007

The original equations that Ed Lorenz derived were an extremely simplified version of the interaction of several spectral modes of the inviscid equations of motion and could hardly be called an accurate approximation of the full system of equations.

Exponential Growth in Physical Systems #2 « Climate Audit 2007

Except for the very smallest turbulent scales, the continuum system to all intent and purposes is inviscid.

Exponential Growth in Physical Systems #2 « Climate Audit 2007

Thus numerical methods cannot converge to the correct continuum solution in either of these (almost) inviscid, unforced cases let alone with inaccurate forcing terms (parameterizations).

Exponential Growth in Physical Systems #2 « Climate Audit 2007