Goda-Minikin Hydrodynamic Impulse • Constructal & Toroidal Wave Transduction

Coastal Flood Barrier Simulation: 90° Orthogonal Wall vs. 109.5° Bio-Helical + Toroidal Chamber

Peak Wall Face Pressure

Model A (90°):

412 kPa

Model B (109.5°):

131 kPa

Concrete Crack Limit: 250 kPa -68.2% Peak Load

Foundation Overturning Moment

Model A Toe:

2,818 kN·m/m

Model B Toe:

885 kN·m/m

Model A Exceeds 2,200 kN·m/m Scour Limit!

Overtopping Flood Rate

Model A Plume:

725 L/s/m

Model B Return:

29 L/s/m

Toroidal Self-Cancel: 78.4% Shear 96% Flood Reduction

Piezoelectric Power Harvested

Incoming Wave:

1,993 kJ/m

104.5°/109.5° Nodes:

76.4 kW/m

Active Transduction Grid ~76 Homes / meter

Impact Cycle Timeline ($t$) 0.45 s / 3.00 s

Breaking Wave Height ($H$) 6.0 m (19.7 ft)

Wave Surge Velocity ($v$) 12.0 m/s (26.8 mph)

Synchronized Hydrodynamic Wall Pressure Impulse $P(t)$ & Vortex Dissipation ($0.0\text{ s} \rightarrow 3.0\text{ s}$)

Red curve shows Bagnold-Minikin air-entrapment shock spike on a 90° flat wall; Emerald/Cyan curve shows 109.5° helical phase splitting + 180° toroidal momentum self-cancellation.

Model A: 90° Flat Wall Model B: 109.5° Toroidal Chamber