Question 1

How is the natural oscillation period of a harbor calculated?

Accepted Answer

The fundamental period of an open-ended (open entrance) rectangular harbor is T₁ = 4L/c, where L is the harbor length and c = √(gh) is the shallow water wave speed (h: water depth). The nth resonance period is Tₙ = 4L/((2n-1)c). For a closed-end (both ends sealed) harbor, Tₙ = 2L/(nc). Which case applies depends on the actual harbor geometry.

Question 2

What is Helmholtz resonance?

Accepted Answer

Helmholtz resonance occurs as the lowest-order mode when the harbor entrance is much smaller than the harbor basin (e.g., lagoons and inlets). The resonance frequency is f_H = (c/2π) × √(A_mouth/(L_channel × V_harbor)), where A_mouth is the entrance cross-sectional area, L_channel is the entrance channel length, and V_harbor is the harbor basin volume. The period can range from tens of minutes to several hours.

Question 3

What is the relationship between tsunamis and harbor resonance?

Accepted Answer

The typical period of tsunamis is 10 minutes to 2 hours. If the harbor's natural oscillation period falls within this range, resonance occurs and water level fluctuations inside the harbor can be amplified several to tens of times. In the 2011 Tohoku earthquake, several harbors suffered severe damage because their fundamental periods coincided with the tsunami period. Adjusting the natural period (by modifying breakwater length or water depth) is an important design countermeasure.

Question 4

How does changing water depth affect the natural period?

Accepted Answer

Since the shallow water wave speed c = √(gh), doubling the water depth (×4 in depth) doubles the wave speed and halves the natural period. For example, a harbor with h=10m (c=9.9m/s) and L=5km has T₁ = 4×5000/9.9 ≈ 2020s ≈ 34 min. At h=40m (c=19.8m/s), T₁ ≈ 17 min. Changes in water depth due to reclamation or dredging significantly affect resonance characteristics.

Harbor Resonance & Natural Period Calculator

Harbor Resonance Theory