I can barely understand what you're saying here, so I won't comment beyond this reply.
The time scale is critical. If you look at any review of numerical weather prediction accuracy, such as the one I linked to above, you will see it's a key parameter. It's why 3-day forecasts are excellent and 7-day forecasts are not very good. Good 3-day predictability does not imply good 7-day predictability.
This is no different than the pictures of the state trajectories of the Lorenz system (http://en.wikipedia.org/wiki/Lorenz_attractor) starting from two nearby states, which stay together for a time, and then diverge suddenly.
It's true, the relevant laws are the Navier-Stokes differential equations, not simple laws like F = m a. But, we can observe the boundary conditions and propagate the system state forward in time. These equations do constrain the future dynamics.
The time scale is critical. If you look at any review of numerical weather prediction accuracy, such as the one I linked to above, you will see it's a key parameter. It's why 3-day forecasts are excellent and 7-day forecasts are not very good. Good 3-day predictability does not imply good 7-day predictability.
This is no different than the pictures of the state trajectories of the Lorenz system (http://en.wikipedia.org/wiki/Lorenz_attractor) starting from two nearby states, which stay together for a time, and then diverge suddenly.
It's true, the relevant laws are the Navier-Stokes differential equations, not simple laws like F = m a. But, we can observe the boundary conditions and propagate the system state forward in time. These equations do constrain the future dynamics.