. Compendium of meteorology. Meteorology. FORECASTING OCEAN WAVES 1085 a more accurate formulation of the transfer expression, no energy is added on the basis of either the Airy or the Stokes theory if the waves move faster than the wind. The validity of Stokes' expression for mass trans- port in the case of waves on a rotating globe has also been questioned.' If the waves are conservative, that is if they maintain their identity, the knowledge from theory of the way in the wind is divided in a certain fixed manner between the energies required to increase wave height and wave period. The solu
. Compendium of meteorology. Meteorology. FORECASTING OCEAN WAVES 1085 a more accurate formulation of the transfer expression, no energy is added on the basis of either the Airy or the Stokes theory if the waves move faster than the wind. The validity of Stokes' expression for mass trans- port in the case of waves on a rotating globe has also been questioned.' If the waves are conservative, that is if they maintain their identity, the knowledge from theory of the way in the wind is divided in a certain fixed manner between the energies required to increase wave height and wave period. The solution of the resulting system of differ- ential equations leads to a relationship between wave steepness and wave age. 5 = m and, finally, to the relationships (l)-(4) above. (13) 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 30Q«. 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 DECAY DISTANCE,D, IN NAUTICAL MILES Fig. 3.—Wave-decay relationships in practical form for use in forecasting. which energy advances with the wave form leads to the following differential equations: Steady state: CdE Edc 2 dx + 2 dx Transient state: dE EdC dt + C dt = Rt =fc Rn — Rt ± Rff (11) (12) where the positive sign is used for C ^ U and the nega- tive sign for C > U. Actually the waves comprising sea cannot be conservative and the equations apply at best only approximately. Since the wave energy is related to the wave height, the two unlaiowns in the equations above may be con- sidered as wave height and wave velocity and the knowns as distance and time. An additional equation is obtained by assuming that the energy transferred from 3. F. Ursell, "The Theoretical Form of Ocean Swell on a Rotating ; Admiralty Research Laboratory, , February 1947 (unpublished). The relationship between 5 and /3 is particularly use- ful in comparison with wave observations. Many of the observations available for the first checkin
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