23. For physically modeling sediment transport processes predominantly driven by turbulence-induced 

 fluid velocities, there is increasing evidence that a dimensionless number, commonly referred to as the fall 

 velocity (or fall time) parameter, must to be kept similar in both prototype and model. This evidence is 

 reviewed below. 



Dimensionless Fall Speed Parameter 



24. Sediment grain size has often appeared in various dimensionless parameters intended for use in 

 characterizing observed features of the beach profile. For example, Iwagaki and Noda (1963) investigated 

 laboratory-formed beach profiles using the parameter Ho/d}, where Ho is the deep water wave height and d 

 is the sediment mean grain size diameter. 



25. More recently, increased attention has been given to a parameter referred to as the fall velocity 

 parameter, which is defined as 



— (1) 



where 



U = wave height 



vj = fall speed of the median sediment size 



T = wave period 



26. Strictly, the term velocity represents a vector quantity and should be replaced with speed because 

 the value of w is obtained as the fall distance divided by the fall time and hence represents an average 

 scalar speed in the vertical direction.^ For this reason the parameter given by Equation 1 will be referred 

 to as the fall speed parameter in this report. 



27. It appears that the use of the fall speed parameter was first proposed by Gourlay,^ who suggested 

 using the parameter for describing beach processes. Gourlay pointed out that H/w represented ". . . the 

 time taken for a sand particle to fall a distance equal to the wave height." If this time is large compared 

 with the wave period, he reasoned the particle would remain in suspension and move as suspended load. 

 Conversely, if the time is equal to or less than the wave period, then the sediment will move primarily as 

 bed load. Gourlay also suggested that a fall speed parameter value around unity could be critical value in 

 determining the different transport mechanisms leading to different profile types. 



28. Around the same time, several other investigators also examined their results in terms of the 

 dimensionless speed parameter. Nayak (1970, 1971) related beach slope with the parameter, and he noted 



'For convenience, symbols and abbreviations are listed in the Notation (Appendix F). 



^Philosophical lunchtime discussion with Dr. N. Kraus, CERC. 



•'M. R. Gourlay, 1968, "Beach and Dune Erosion Tests," unpublished report, Delft Hydraulic Laboratory, The Netherlands. 



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