Consider an average significant wave height of 3m and dominant period of 10s. Depth of closure is …

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BlackTom AI · Accepted Answer

To tackle this problem, we start by identifying the given data: average significant wave height Hs = 3 m and dominant period T = 10 s. A standard step in wave-depth questions is to determine the deep-water wavelength for the given dominant period, since many empirical or semi-empirical depth relations are expressed in terms of the wavelength.

First, estimate the deep-water wavelength L0 for T = 10 s using the deep-water dispersion relation approximated by L0 ≈ g T^2 / (2π), where g ≈ 9.81 m/s^2. Plugging in T = 10 s gives L0 ≈ (9.81 × 100) / (6.283) ≈ 981 / 6.283 ≈ 156 m. This provides a baseline scale for the wave field in deep water.

Next, apply a commonly used empirical rule for the depth of closure (Dc) in coastal engineering contexts, which relates Dc to the wavelength. A frequently used approximate relation is Dc ≈ 0.13 × L0. While various empirical coefficients exist depending on sediment, wave type, and exposure, 0.13 is a standard ballpark value for many wave-transport depth assessments.

Calculating with the 0.13 factor: Dc ≈ 0.13 × 156 m ≈ 20.28 m. This result is very close to 20.25 m, which aligns with the option presented in the question.

Now consider the other options:
- 2.25 m: This would require a much smaller fractional coefficient of L0 (about 0.0145). That coefficient is not typical for depth of closure estimates tied to wave wavelength, making this choice inconsistent with the standard relation used here.
- 10.23 m: This corresponds to a coefficient of roughly 0.0656 × L0. While a lower coefficient might be used in some specific contexts, it does not match the commonly adopted Dc ≈ 0.13 L0 scale for the given T and L0.
- 17.89 m: This would imply a coefficient around 0.114 × L0. Though closer to 0.13 than 0.065, it still deviates from the standard 0.13 factor used for a typical depth-of-closure estimate based on L0 for these wave parameters.

In summary, by estimating the deep-water wavelength from the dominant period and applying the conventional Dc ≈ 0.13 L0 relationship, Dc comes out to about 20.3 m, which corresponds to the 20.25 m option. The other choices arise from using incorrect or non-standard coefficients in the Dc ≈ k × L0 form, or from mixing up the proportionality constant, and thus are not supported by the typical approach for a 10 s, 3 m wave system.

CVEN90051_2025_SM2 Module #3 Practice Quiz

Consider an average significant wave height of 3m and dominant period of 10s. Depth of closure is …

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