TM No. 377 



measurement, the concept of mean value and stationarity, so important to 

 spectrum evaluation, has more significance when applied to w(t) observations than 

 to u(t). The random oscillation mode of a fluid is thus more amenable (than a 

 random drift process) to examination by a Eulerian time series measurement. For 

 example, it is easier to measure and interpret a spectrum of wave heights than it 

 is to measure and interpret a spectrum of ocean currents. 



The estimate of the two-dimensional components in the XZ plane of a particular 

 wave train is rendered difficult in another respect. The u component detector has 

 been shown in calibrations to be sensitive to the direction of flow. This can be 

 clearly seen in measuring the u and w components of a uniform train of ocean waves. 

 Assume in figure V-6A that the output of the motion detector or current meter is 

 proportional to the cosine of the angle between the azimuth of the detector and 

 the direction of the waves. Now, if 'M.o is "the amplitude of the horizontal velocity 

 component function oscillating both in time and space, then its value is a function 

 of the azimuth of the detector and is given by: 



11(e) ^u cos & 



(v-5) 



The variance obtained will be: 



OZ t O) = U Z cos x e 



(v-6) 



The variance is proportional to the wave energy, so that the spectral functions 

 would have a similar relationship to 0. On the other hand, the response of the 

 vertical motion detector will be independent of the value of 0, or: 



Ouj = constant. (V-7) 



The essential difference here (shown in figure V-6b) is that the particle subjected 

 to random oscillation is virtually bounded along the Z coordinate by the interplay 

 of pressure forces, gravity, and, to a lesser extent, shear stresses. Particles 

 experiencing random drift move in a less predictable way, with much weaker shear 

 and pressure forces acting upon them in a somewhat random manner. A fairly 

 sophisticated interpretation may therefore be required to explain observed 

 differences between the two velocity records. As an example, if both a swell and 

 a wind wave motion are present, and if the swell is not moving in a coincident 

 direction to the wind wave (at which the horizontal sensor has been aimed), then 

 the swell motion plus the wind wave motion are detected by the vertical sensor. 

 However, some of the horizontal flow component of the swell is filtered out. 



Figure V-k appears to bear out this analysis. The u meter of the OMDUM III 

 system was aimed at the wind waves coming from the west. The result is that small 



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