TM No, 377 



between the two velocity fluctuations. What, if any, is the significance of a 

 phase lag or lead between two vertically separated velocity fluctuations within 

 the wind wave regime? In a discussion by Starr (19U8), it is suggested that 

 poleward transfer of angular momentum is associated with horizontal velocity 

 correlations. Velocity patterns which can perform this function are schematically 

 shown in figure V-U5A. These quasi-sinusoidal wave forms exhibit a northeast- 

 southeast tilt of the trough lines of isobars (which approximate the wind stream- 

 lines). Integration of the quasi- i nst antaneous u'v 1 around a latitude circle would 

 give a spatially averaged val ue of u'v' , interpreted as a net northward transfer 

 of eastward momentum (i.e., P u ! (v) ) . 



Starr (l96l) also considers the possibility that such tilted troughs in the 

 relative streamlines associated with wind waves may produce a downward momentum 

 transfer. Figure V-U5B shows a vertical section of an ocean wave (in the XZ plane) 

 in which the wave is propagating in the +x direction. The instantaneous material 

 surfaces or relative streamlines are shown as a function of depth. Since the 

 waves travel at a constant speed without change in shape, a steady state picture 

 may be obtained by the superposition of the phase speed (from left to right) on 

 all water particles. This addition of a uniform velocity field does not interfere 

 with the dynamic properties of the system (see further, Starr, 19^5). The wavy 

 lines represent the steady state streamlines relative to the moving wave. These 

 can be interpreted in a manner analagous to the previous diagram and show a net 

 downward transport of the downwind momentum. The significant feature is that a 

 phase advance with depth is required to bring about this transport. 



The spectral analyses of all LIMDUM I" data provide phase angle data (PHI) 

 as a function of frequency. These are tabulated in appendix B. If the order of 

 tabulation is ui (or W]_) followed by ug (or w2/ , then PHI gives the average phase 

 angle lead of the latter over the former. (Note that in some cases, the order 

 is reversed - u 2 followed by ujj.. The PHI must then be multiplied by a minus 

 sign.) 



The values of PHI near the peak frequencies of either the auto-spectra or 

 the coherence plots were examined for any indication of spatial phase lead by 

 the dominant motions as a function of depth. Unfortunately, the PHI relation- 

 ships show nearly an equal number of positive and negative values. In fact, the 

 values appear disturbingly random in both sign and magnitude; hence, no con- 

 clusions can be made regarding the phase evaluation. 



The tilting phenomenon can also be considered with respect to the elliptical 

 orbital motion depicted in figure V-U5C. The top of the semi-major axis is 

 tilted slightly backward. Since the wave is progressing, the Eulerian time 

 variation is that of a vector forming an elliptical pattern, with a negative co- 

 variance u'w' produced. To show this, simply integrate across a surface from A 

 to B. The net value of u'w' is negative, indicating downward transport of ( pu s ). 

 Note that such a tilted ellipse provides a variance of the w velocity component 

 that is larger than the u variance, This is in accordance with what was found 

 experimentally. 



