what is scale?
1. size of a bounded object (if boundaries well defined) cloud
2. sizes of "patches" in a continuum (defined how?)
3. Wavelength (for fluctiations of a continuous field)
Other folks: Markowski and Richardson Ch 1 (upcoming book)
0. Conventional: "a few times 100-102 km in space, minutes to a day (or an inertial period) in time.
1. Dynamical 1: Space scales between aspect ratio 1 and Rossby deformation radius
1a. Dynamical 1a: Time scales between 1/N and 1/f
2. Dynamical 2: Pretty well hysrostatic, but not quite geostrophic.
3. Dynamical 3: You can't ignore Coriolis forces (like for small scales), nor ageostrophic advection (like for synoptic/ large scales).
How do we deal with (describe, formalize) the problem of multiple scales (a continuum of scales)?
Fourier analysis
Definitions
http://en.wikipedia.org/wiki/Fourier_series
From bottom of wikipedia - graphs of converging series
http://mathworld.wolfram.com/FourierSeries.html
Intuitive (image processing oriented)
http://cns-alumni.bu.edu/~slehar/fourier/fourier.html
Table of FFT pairs - Gaussian is of special interest
http://mathworld.wolfram.com/FourierTransform.html
Lecture on image processing (too much)
http://www.archive.org/details/Lectures_on_Image_Processing