For wind-generated waves, if F is the fetch (straight-line distance of open water in km), which empirical Stevenson relation gives the significant wave height H (in metres)?

Introduction / Context:Preliminary wave prediction in harbour planning often uses simple empirical relations that link wave height to fetch and wind conditions. Stevenson's formula provides a fast estimate of wave height from fetch alone, useful for early sizing of coastal structures before detailed spectral models are applied.

Given Data / Assumptions:

• F = fetch in kilometres (straight-line open-water distance).
• H = estimated wave height in metres for preliminary design.
• Empirical relation relies on typical wind exposures and equilibrium assumptions.

Concept / Approach:Stevenson's empirical expression commonly used in exam problems states: H (m) ≈ 0.34 * sqrt(F in km). The square-root dependence reflects diminishing returns in wave growth with increasing fetch, a pattern consistent with more advanced growth curves (e.g., SMB/JONSWAP) though those also depend on wind speed and duration.

Step-by-Step Solution:Select the formula with square-root dependence: H proportional to sqrt(F).Check coefficient: 0.34 is the standard value quoted for H in metres with F in km.Reject linear-in-F options which overpredict for large fetches.

Verification / Alternative check:Example: If F = 100 km, H ≈ 0.34 * sqrt(100) = 3.4 m, a realistic preliminary height. A linear formula would predict 34 m, which is not credible for typical wind seas.

Why Other Options Are Wrong:

• 0.20, 0.15, 0.42 * sqrt(F): coefficients not used in the standard Stevenson relation for this unit set.
• 0.34 * F: wrong functional dependence; gross overestimation at large F.

Common Pitfalls:Forgetting that units matter (F in km, H in metres); using linear dependence instead of square-root.

Final Answer:H = 0.34 * sqrt(F)