MASS TRANSPORT AND THERMAL UNDULATIONS 

 CAUSED BY LARGE AND SMALL SCALE VARIABILITY 

 IN THE STOKES' MASS TRANSPORT DUE TO 

 RANDOM WAVES "'" 



Hong Chin 



Assistant Research Scientist 



and 



Willard J. Pierson, Jr. 



Professor of Oceanography 



New York University 



The Stokes' mass transport is a well know^n second order 

 effect for irrotational monochromatic periodic surface waves. 

 It shows up most clearly in a Lagrangian analysis of wave 

 motion to second order. However, when a continuous spectrum 

 of frequencies and directions for surface waves is considered, 

 this mass transport becomes variable at both the synoptic 

 oceanographic scale and at temporal scales of five to twenty 

 minutes. It is therefore possible to use the directional wave 

 spectra obtained by both presently available and nearly com- 

 pleted wave forecasting models to compute mass transport 

 current fields and possible thermocline undulations caused 

 by this effect. 



The currents prove to be comparable at times to those 

 caused by Ekman theory, except that they grow and shrink 

 in direct response to the waves that are present. 



Second order nonlinear interactions produce difference 

 frequencies and difference wave numbers that yield long 

 period slow vertical and horizontal oscillations. Except 

 for the shear at a region of strong density variation that 

 occurs for internal waves, these motions have many features 

 similar to internal wave motions and may easily be mistaken 

 for them in a stratified fluid. Much of the apparent thermal 

 unrest in the oceans may well be due to these second order 

 wave effects, and, as such, a description of them is an 

 easily obtained extension of present gravity wave forecast- 

 ing models. 



INTRODUCTION 



Since the early work of G. G. Stokes in 1847, it has generally 



tContribution 79 of the Geophysical Sciences Laboratory, Depart- 

 ment of Meteorology and Oceanography, New York University. 



398 



