Generation of intermediately-long sea waves by weakly sheared winds

TL;DR

This study models sea-wave instability under hurricane winds, revealing that traditional models underestimate wave growth rates and highlighting the importance of accurate wind roughness data for predicting wave behavior.

Contribution

It introduces a refined numerical model incorporating experimental wind roughness data, improving wave growth rate predictions under hurricane conditions.

Findings

Traditional models underestimate wave growth rates by 5-50 times.

Wind roughness significantly affects wave instability predictions.

Maximum instability occurs at specific wavelengths due to drag reduction.

Abstract

The present study concerns the numerical modeling of sea-wave instability under the effect of logarithmic-wind profile in hurricane conditions. The central point of the study is the calculation of the wave growth rate, which is proportional to the fractional input energy from the weakly-sheared (logarithmic) wind to the wave exponentially varying with time. It is shown for hurricane conditions that the Miles-type stability model based on the Charnock's formula with the standard constant coefficient underestimates the growth rate ~5 to 50 times as compared with the model employing the roughness adopted from experimental data for hurricane winds. The drag reduction with wind speed at hurricane conditions coupled with the similar behavior of the dimensionless gravity acceleration, leads to the minimum in the maximal growth rate and the maximum in the most unstable wavelength.