Basil Wrigley Wilson

In 1965, Wilson proposed a method which can be used to approximate the significant wave height H_1/3 and period T_1/3 of wind waves generated by a constant wind of speed U blowing over a fetch length F.^[13][14] The units for these quantities are as follows:

• H_1/3 in metres (m)
• T_1/3 in seconds (s)
• U in metres per second (m/s)
• F in metres (m)

Under conditions were the wind blows for a sufficiently long time, for example during a prolonged storm, the wave height and period can be calculated as follows:

${\displaystyle gH_{1/3}/U^{2}=0.30\left\{1-\left[1+0.004\left(gF/U^{2}\right)^{1/2}\right]^{-2}\right\}}$

${\displaystyle gT_{1/3}/(2\pi U)=1.37\left\{1-\left[1+0.008\left(gF/U^{2}\right)^{1/3}\right]^{-5}\right\}}$

In these formulae, g denotes the acceleration due to gravity, which is approximately 9.807 m/s². The wind speed U is measured at an elevation of 10 metres above the sea surface. Wilson's formulae apply when the duration of the wind blowing is sufficiently long, as when the wind blows for only a limited time, waves cannot attain the full height and period corresponding to the wind speed and fetch length. Work by Yoshimi Goda and other Japanese researchers subsequently provided modifications to the formulae to consider these effects.^[15][16][17]

Goda adapted Wilson's formula with a simple equation which is first used to calculate the minimum fetch (F_min):

${\displaystyle F_{\text{min}}=1.0t^{1.37}U^{0.63}}$

In this equation, t is the wind duration (in hours) and U is the wind speed, in metres per second. If F > F_min, then the wave growth is limited by the wind duration, and F_min is used instead of F in Wilson's equations. If F < F_min, the wave growth is limited by fetch length, and F is used.^[15]

Wilson was recognised during his career with several awards, including the American Society of Civil Engineers Arthur M. Wellington Prize (1952), Norman Medal (1969), and the Moffatt-Nichol Harbor and Coastal Engineering Award (1983).^[18][19][20] He was also recognised by the Institution of Civil Engineers and South African Institution of Civil Engineers. In 1984, he was elected to the National Academy of Engineering.^[21]

He died in 1996 in Pasadena, California, survived by his wife and four children.^[1]