FLUCTUATIONS: AN OVERVIEW 



Ira Dyer 



Department of Ocean Engineering 

 Massachusetts Institute of Technology 

 Cambridge, Massachusetts 



The study of fluctuations is hampered by a diversity of 

 definitions and language. I propose that theories and 

 experiments be distinguished as to 1) Averaging Algo- 

 rithms, 2) Source/Receiver Motion, and 3) Ocean Dynamics. 

 Confusions in the interpretation or comparison of recent 

 results can be reduced thereby. Several results are 

 discussed within this framework. 



More particularly, a format for studying short- time- 

 averaged amplitude (envelope) fluctuations is proposed. 

 Envelope statistics for phase random processes are well 

 known for sample sets with fixed mean; these statistics 

 change significantly for sample sets with varying mean, 

 as is often the case for sets extending over time dura- 

 tions and spatial extents involved in detection by typical 

 sonars. The format includes metrics such as the fluctu- 

 ation (fading) period, the fluctuation (interference) 

 scale, and more generally their corresponding spectra. 

 Some recent results are discussed in these terms. 



There is no clear, accepted way to distinguish between various 

 categories of fluctuations. This paper addresses, therefore, the 

 question of time series that may be observed in the ocean; it applies 

 equally to spatial series that may also be observed in the ocean in 

 the study of coherence. Figure 1 defines certain terms of importance 

 to time series; a comparable set of definitions exists for the 

 spatial series. 



Two quantities are typically of interest: the amplitude, which 

 may be the decibel level, A (or the intensity, I, or the RMS value, 

 Ipj), and the phase, 0, which could just as well be the tilt angle 

 or the bearing angle. 



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