TM No. 377 



Procurement of Statistical and Physical Parameters — In the previous 

 sections the various definitions of the statistical parameters were pre- 

 sentedo This section considers them as they apply to the data obtained 

 from the wave measurements and serve as a "basis for the auto»spectra and 

 cross-spectra calculations. The two configurations of wave meters — the 

 orthogonally mounted (CMDUM) and linearly mounted (LIMDUM) systems «- pre- 

 sent specific types of data. It is therefore proper to clearly define the 

 modes of measurement of the two systems „ 



1. Vector Representation . Picture an ocean whose surface contains wind 

 waves moving in the +>C direction,, The problem is to measure the motion in the 

 XZ plane , normal to the horizontal wave crests (see figure I1I-4). The 

 Eulerian vector representation of the two-dimensional, time -variable,, particle 

 velocity at a geographical position and as a function of depth is: 



V <^x>y.= H ^4 oYo 4-Kujfr^. (III . 53) 



X and Y are the fixed coordinates and, for brevity, will be neglected in 

 further formulation. The XY plane defines the mean free surface of the ocean, 

 and Z is measured positive upward. Using the orthogonal or the linear wave 

 meters, there are several ways to measure the wave motions. These are shown 

 schematically in figure III-4. 



With the OMDUM system, the horizontal and vertical velocities (u and w) 

 are measured simultaneously at n meters below the wave troughs. These 

 components are written as : 



Note the inference, from the initial statement that the waves are moving 

 in the -f X direction, that the u and w velocities are associated with a single 

 wave train. This is not actually the casej and, as shown in chapter V, deter- 

 mining the origin of the motions detected with the wave meters can be difficult. 

 Spectrum estimates of the record, however,, render much assistance in the analysis. 



With the LIMDUM system a pair of horizontal or vertical velocities are 

 measured simultaneously at two depths on the Z axis (figure 111=4). The nota- 

 tion for the pair of horizontal components is; 



nA.C^-6) **o 4A(&*yt) . (HI-55) 



For the vertical components the rotation iss 



/^. ^ (III- 56) 



62 



