TM No. 377 



Time-variable wave perturbations upon the suspended OMDUM system may also 

 have biased the velocity data. (Examine the heuristic covariance model of 

 equation (V-k6) or (V- i +7)«) What effect would instrument motion have upon the 

 ability of the instrument to measure the amplitude of the u and w components? 

 Assuming the ideal orbital motions associated with deep water waves (see 

 equations (II-5) and (U-6)), the amplitudes A u and A w in equation (V-U5) would 

 be identical for intermediate or shallow water waves. 



For simplicity, assume that the roots of the variances ( 0"u. and U^ ) are 

 indicative of the approximate response of OMDUM III to a single wave system whose 

 frequency is indicated by the <£^ and ^^ spectral peaks. Then the measurements 

 obtained with the OMDUM system show that A w generally ranged from 1.1 A u to above 

 3 A u (see table V-l). This effect seems to indicate a damping of the horizontal 

 motion response, rather than an amplification of the vertical response. This is 

 because the vertical stability of the suspended meter and counterweights far 

 exceeded the horizontal stability (see chapter IV"). Damping of the amplitude A. u 

 in expression (V-47) would, if anything, bias the covariance u 4 'w' Hfoward lower 

 values. This disproportion of the u and w amplitudes is something of an enigma. 

 It has already been suggested that part of this inequality of amplitudes was 

 caused by the presence of multi-directional wave trains. However, this does not 

 explain the disproportion between A u and A w in the OMDUM I measurements in 

 Narragansett Bay (see spectra in figure IV-2). Here, there was no swell present, 

 and the OMDUM I system was held rigidly from a large vertical pipe. Hence, over 

 and above the effects of other wave trains and of meter motion due to a non-rigid 

 suspension, either the ducted meter configuration inherently distorts the oscil- 

 latory wave motions, or a true disproportion does indeed exist in the waves 

 (which was suggested in the last section). 



A simple estimate of the wave perturbation on the meter should help to 

 assess the biasing in the horizontal amplitude A u . Assume that the wave period 

 T is k seconds, and that the height H is about 1 meter for the ambient wind wave. 

 The horizontal excursion of a wave particle at the sea surface can be computed 

 from equation (II-9), with the amplitude of the surface wave given as H = 1 meter. 

 The wave particle travels this distance in 2 seconds, giving an average velocity 

 of 50 cm sec~l„ (Actually, of course, the velocity is of a sinusoidal nature.) 



From observations of the OMDUM instrument, the largest visual estimate of 

 its horizontal excursion in response to wave faces (which are maximum at a wave 

 crest and act in the +u direction) was about 10 cm, or an average of about 

 5 cm sec~l„ This indicates that the amplitude could be reduced by about 10 

 percent. This effect would show up (in relation (V-U7) for the covariance) in 

 both the variance 0"J^ and in A u and A w . 



It should be remembered that the particle displacement and the velocity 

 components decrease exponentially with depth. If the drag of the u velocity is 

 roughly proportional to u^ (see Prandtl, 1952), then the force attenuates as 

 the square of the exponential function (shown in equation (II-5)). This increase 

 in the stability of the instrument with depth was noticed. At 0.5 to 1.0 meter 

 beneath the trough, the suspension appeared completely stable with no observable 

 swing. 



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