Holland Gradient Wind Profile

Cyclostrophic and Coriolis balance are solved using the Holland (1980) relation:

V(r) = [ (B/ρ)·(Rmw/r)^B·Δp·e^(-(Rmw/r)^B) + (r·f/2)^2 ]^0.5 - (r·f/2)

where Δp = p_env - p_c, Coriolis parameter f = 2Ω sin(φ), and shape parameter B = 1.0 + (p_env - p_c)/100. Asymmetry is introduced by vector-adding the storm forward velocity V_f with boundary layer inflow angle turning (22° inward).

Wind-Stress Setup & Inverted Barometer Effect

Coastal storm surge η represents the sum of the inverse barometer rise and hydrodynamic wind piling across the bathymetric profile:

η_ib = 0.01 · (p_env - p_c) [meters]

∂η/∂x = (τ_wind,x - τ_bottom,x) / (ρ_w · g · (d + η))

Shallow shelves (e.g. Gulf of Mexico) yield deep cross-shelf integration paths and extreme surge. Steep Pacific coastal shelves dissipate deep ocean waves with lower peak surge but violent littoral breakers.

Landfall Asymmetry & Inundation Hazard

In the Northern Hemisphere, maximum storm surge universally concentrates in the right-front quadrant where forward translation vector constructively adds to tangential cyclonic winds, driving catastrophic onshore water piling.