1084 
Steady state: 
gHr/U? = figF/U?), (1) 
Cr/U = fo(gF/U*), (2) 
Transient state: 
gHz/U? = fs(gta/U), (3) 
Cr/U = fa(gta/U). (4) 
Height and period of swell at the end of the decay 
distance and travel time are determined from the decay 
MARINE METEOROLOGY 
The assumption is made that energy is transferred 
from wind to waves by normal pressure and tangential 
stress. Following Jeffreys, the expression used for the 
mean rate of energy transfer per unit area as a result of 
normal wind pressure is 
2 
Ry = + = sp(U — C)? &C, (8) 
where the sign is positive for U > C and negative for 
U < C. Thus, a transfer expression which depends upon 
variations in pressure along the surface is introduced, 
WIND VELOCITY, U, IN KNOTS ——> 
SSsaaan 
ak lia 
= === 5 
Sa glee eases 
DURATION ,tg ,IN HOURS 
Fic 2—Transient state wave-generation relationships in practical form for use in forecasting. 
distance and the period at the end of the fetch accord- 
ing to: 
Hy/Hr= fs(D/gTr’), (5) 
Tp/Tr = fo(D/gTr*), (6) 
to/Tr = f;(D/gTr°). (7) 
Relationships (1)-(7) are translated into practical 
graphs for use in forecasting? (examples are presented 
in Figs. 2 and 3). 
The basis of the theory is the development of equa- 
tions which express the energy budget between wind 
and waves. Use is made of results from two hydro- 
dynamical theories of irrotational waves: (1) the Airy 
theory of waves of small amplitude, and (2) Stokes’ 
theory of waves of finite amplitude. Certain constants 
which occur in the solution are evaluated empirically. 
2. R. 8. Arthur, ‘‘“Revised Wave Forecasting Graphs and 
Procedures.”’ Scripps Institution of Oceanography Wave Report 
No. 73, March 1948 (unpublished). These forecasting relation- 
ships, as revised according to [24], are to be included in a forth- 
coming manual on wave forecasting to be issued by the Hydro- 
graphic Office. 
although use is made of hydrodynamical theories which 
assume constant pressure along the surface. 
For the tangential stress, the form 
tr = 7pU?, (9) 
where y? = 2.6 X 10-, is introduced with the under- 
standing that wind velocities are great enough so that 
the sea surface is hydrodynamically rough. The expres- 
sion for Ry is derived using the horizontal component 
of particle velocity at the surface from the Airy theory, 
but on this basis no energy is transferred by tangential 
stress. However, if the average surface mass transport 
velocity, w’ = 76°C, from the Stokes theory is utilized, 
the mean rate of energy transfer per unit area by 
tangential stress is 
L 
Re - [ PA da ee CUE ao) 
0 
and on the basis of this expression a transfer of energy 
from wind to waves is possible even if the waves move 
faster than the wind. Further investigation of this 
point is indicated because if the difference between the 
wind velocity and the horizontal component of particle 
velocity is introduced in the expression for r, seemingly 
