present in the fetch or to account for waves generatedby a rapidly changing wind.. E value. E is equal to the sum of the squares ofthe individual amplitudes of the individual sine wavesthat make up the actual waves. Since it is proportionalto the total energy accumulated in these waves, it is usedto describe the energy present in them and in severalformulas involving wave energy.l Co-cumulative spectra. The co-cumulativespectra are graphs in which the total accumulated energyis plotted against frequency for a given wind speed. Theco-cumulative spectra have been devised for twosituations: a fetch limited wind and a duration timelimited wind.l Upper limit of frequencies (fu). The upper limitof frequencies represents the lowest valued frequenciesproduced by a fetch or that are present at a forecast point.This term gets its name from the fact that the periodassociated with this frequency is the period with thehighest value.The waves associated with thisfrequency are the largest waves.l Lower limit of frequencies (fL,). The lower limitof frequencies represents the highest value frequenciesproduced by a fetch or that are present at a forecast point.This term gets its name from the fact that the periodassociated with this frequency is the period with thelowest value. The waves associated with this frequencyare the smallest waves.. Filter area. That area between the fetch and theforecast point through which swell waves propagate.This area is so termed because it filters the frequenciesand permits only certain ones to arrive at a forecast pointat a forecast time.l Significant frequency range. The significantfrequency range is the range of frequencies betweenthe upper limit of frequencies and the lower limitof frequencies.The term significant range isused because those low-valued frequencieswhose E values are less than 5 percent of thetotal E value and those high-valued frequencieswhose E values are less than 3 percent of thetotal E value are eliminated because of insignificance.The significant range of frequencies is used todetermine the range of periods present at the forecastpoint.l Propagation. Propagation as applied to oceanwaves refers to the movement of the swell through thearea between the fetch and the forecast point.. Dispersion. The spreading out effect caused bythe different group speeds of the spectral frequencies inthe original disturbance at the source. Dispersion canbe understood by thinking of the different speeds of thedifferent frequencies. The faster wave groups will getahead of the slower ones; the total area covered isthereby extended. The effect applies to swell only.l Angular spreading. Angular spreading resultsfrom waves traveling radially outward from thegenerating area rather than in straight lines or banksbecause of different wind direction in the fetch.Although all waves are subject to angular spreading, theeffect of such spreading is compensated for only withswell waves because the spreading effect is negligiblefor sea waves still in the generating area. Angularspreading dissipates energy.Wave SpectrumThe wave spectrum is the term that describesmathematically the distribution of wave energy withfrequency and direction. The wave spectrum consistsof a range of frequencies.Remember that ocean waves are composed of amultitude of sine waves, each having a differentfrequency. For purposes of explanation, thesefrequencies are arranged in ascending order from left toright, ranging from the low-valued frequencies on theleft to the high-valued frequencies on the right, asillustrated in figure 6-3.A particular range of frequencies, for instance, from0.05 to 0.10 does not, however, represent only sixdifferent frequencies of sine waves, but an infinitenumber of sine waves whose frequencies range between0.05 and 0.10. Each sine wave contains a certainamount of energy, and the energy of all the sine wavesadded together is equal to the total energy present in theocean waves. The total energy present in the oceanwaves is not distributed equally throughout the range offrequencies; instead, in every spectrum, the energy isconcentrated around a particular frequency (fmax), thatcorresponds to a certain wind speed. For instance, fora wind speed of 10 knots (kt) fcnax is 0.248; for 20 kt,0.124; for 30 kt, 0.0825; for 40 kt, 0.0619. For moreFigure 6-3.-A typical frequency range of a wave spectrum.6-4