Named after the French mathematician Augustin Louis Cauchy and from the article "Tibetan Singing Bowls," by Denis Terwagne and John W. M. Bush, published July 1, 2011, in Nonlinearity 24 R51–R66:
To simplify the acoustic analysis, one can approximate the glass or bowl by a cylindrical shell with a rigid base and an open top (figure 2(a)). The system can then be described in terms of 7 physical variables, the radius R, height H0, thickness a, Young’s modulus Y and density ρs of the cylindrical shell, and the frequency f and amplitude Δ of its oscillating rim. The system can thus be described in terms of 4 independent dimensionless groups, which we take to be R/H, Δ /a, Δ /R and a Cauchy number Ca = ρsf 2Δ2/Y that indicates the relative magnitudes of the inertial and the elastic forces experienced by the vibrating rim.
|"Lake in Tibet" from Orbit Trap|