; • TM No. 377 



desired, was done with a Benson-Lehner model J electro-plotter (manufactured 

 by Data Instruments, Division of Telecomputer Corp., North Hollywood, Calif o)c 

 Upon removal of any had point cards, the data are ready for linear interpola- 

 tion. 'This produces the velocity data as an equi-spaced time series, which 

 is necessary for subsequent spectral analysis. 



The linear interpolation is graphically portrayed at the top of figure 

 III-2. Straight lines are drawn connecting the uninterpolated velocities 

 V/j Vj.', Vj'j . . . V^ • ■ • located on the time axis at T,\ TV, Tj^ . . . TV . . . 

 These velocities, in general, are unequally spaced. A sequence of new velo- 

 city values is then obtained at equi-spaced time intervals AT C Thus, a new 

 velocity distribution is formed of v,,^, v 3j . . ,V„'» • * (The Fortran program 

 for linear interpolation is listed in the appendix E. ) The time series of 

 interpolated pairs ('Itv^tf) or of similar velocity components (%,/ki, ofyt^tyi) 

 is now in a form for statistical analysis, including estimation of mean 

 values, verianee, and calculation of the various spectral parameters shown 

 in figure III-l. A discussion of possible errors due to interpolation and a 

 graphic comparison with uninterpolated data are presented later in this chapter. 



Correction Program for the OMDUM III Data — In chapter II a method was 

 suggested for making corrections to the vertical and horizontal velocity data 

 pairs obtained from the OMDUM III system. 'This correction was found to be 

 possible, since the bias, which produces a possible 10-12 percent error in 

 the values, can be determined fairly accurately as a function of the ratio 

 of the magnitudes of the uncorrected velocity pairs (%&/). 



To apply these correction procedures, one must use the linearly inter- 

 polated data pairs because the ratio computation requires simultaneous 

 velocity components. The first velocities obtained from the raw data ( V* ) 

 are not equi-spaced in time, and would not be simultaneously in the u and a* 

 records. The punch cards listing the interpolated velocity data along with 

 the curve fitting data allowed evaluation of the correction factor for each 

 velocity component. This factor is a known .function of the magnitude of 

 their ratio (i.e.,'!*^,). The ratio actually determines an angle 9 for the 

 UL component, applying the appropriate correction; and, since the detectors 

 are orthogonally mounted, the appropriate correction for 90°=© is applied to 

 the UJ component. The values of the corrected velocity components are then 

 suitable for final analysis. The Fortran computer program and a description 

 of the orthogonal velocity corrections is presented in appendix E. 



Data from the Fr ee Surf ace, Elevation Wave Staff System 



Two records of free surface fluctuation data, which were obtained from 

 the wave staff system (discussed in chapter IV) installed by the U. S. Army 

 Corps of Engineers on the southeast leg of the 3EELS tower, were processed 

 in order to compare some free surface wave spectra with those of wave parti- 

 cle velocity motions. The output of the recording system provides both a 

 magnetic tape and a pen and ink analog record of the time variable position of 

 the free surface tr\ on the vertical wave staff. Copies of pen and ink records 



h6 



