feat(cfd): root-mean-square interior vorticity#413
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Add FlowSolution::rms_vorticity(), the root-mean-square interior vorticity:
omega_rms = sqrt(<omega^2>) (1/s)
the magnitude scale of the central-difference vorticity, completing the
peak / mean / rms vorticity-statistics set (mirrors the pressure family's
mean / std / rms_pressure). It relates to the enstrophy by
omega_rms = sqrt(2E/A) (enstrophy is 1/2 integral(omega^2 dA)), and is
always >= |mean vorticity| (Cauchy-Schwarz). Mirrors the mean_vorticity
interior stencil; returns 0 for a grid too small (nx < 3 or ny < 3).
Analytic test rms_vorticity_is_the_root_mean_square_interior_vorticity
(uniform shear u(y)=gamma*y, omega = -gamma everywhere):
(a) analytic: omega_rms = |omega| = gamma = 2;
(b) threads enstrophy (non-tautological, different code path):
omega_rms = sqrt(2E/A);
(c) rms >= |mean| (Cauchy-Schwarz), equality for the uniform field;
(d) grid too small for an interior difference -> 0.
Pure method on FlowSolution, no lib.rs change. cfd-native 123 lib tests
(was 122), cargo clippy --all-targets -D warnings clean.
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What
Adds
FlowSolution::rms_vorticity()— the root-mean-square interior vorticity:// omega_rms = sqrt(<omega^2>) (1/s)Why
The vorticity family has
max_vorticity(peak),mean_vorticity(#400, area-average),circulation, andenstrophy, but no RMS magnitude.omega_rmscompletes the peak / mean / rms vorticity-statistics set — mirroring the pressure family'smean/std/rms_pressure(#394). It relates to theenstrophybyomega_rms = sqrt(2E/A)(enstrophy is1/2 * integral(omega^2 dA)), and is always>= |mean vorticity|by Cauchy-Schwarz. Mirrors themean_vorticityinterior central-difference stencil; returns0for a grid too small (nx < 3orny < 3).Test
rms_vorticity_is_the_root_mean_square_interior_vorticity(uniform shearu(y)=gamma*y,omega = -gammaeverywhere):omega_rms = |omega| = gamma = 2;omega_rms = sqrt(2E/A);0.Pure method on
FlowSolution, nolib.rschange.valenx-cfd-native123 lib tests (was 122);cargo clippy -p valenx-cfd-native --all-targets -- -D warningsclean. Research-grade post-processing reducer.