Fig. 5- The Ekman current meter. 



strictly justifiable simulation of a condition of 

 63.2$> response. Then 



r 129° 

 r a 



dt 



and 



v._t,o sinf 



t = ±- log e tan 1 



129" 



3-8 



(6) 



(7) 



If we use a velocity of 1.0 fps and a radius, r, 

 of 20 inches, corresponding to the Ekman current 

 meter shown in Fig. 5> we obtain a time constant 

 of 6.3 seconds. During part of the period water 

 flows through the meter backward. In the Ekman 

 meter reverse turns are subtracted but in most 

 electrically registering meters the rotor has no 

 directional discrimination and the registration 

 of velocity is always positive. Current meters 

 with small radii of rotation and those with 

 hydrofoil sections for tail fins will have bet- 

 ter characteristics. Particularly good is the 

 Von Arx current meter which uses two Garbell 

 fins on either side of a cylindrical body and 

 probably the most satisfactory device is a small 

 sensitive direction vane such as used in the 

 Snodgras s met er . 7 



A practical problem is to inquire what happens 

 to a meter like the Ekman meter in the continu- 

 ally oscillating currents in waves near the sur- 

 face, which is similar to the case of a rapidly 

 fluctuating suspension. The calculation requires 

 only minor modification to that above but is 

 sensitive to the boundary conditions. Here it 

 is assumed that the meter will carry out a sym- 

 metrical rotary oscillation reaching a maximum 

 conformity to the current direction at the end 

 of each half -cycle. 



The results of this calculation are shown in 

 Fig. 6 for the Ekman current meter in a recipro- 

 cating current corresponding to the particle 

 velocity of 5-foot sinusoidal waves at the 



WATER VELOCITY 



ORIENTATION OF METER 



APPARENT VELOCITY 

 I |_ 



TIME ANGLE 



Fig. 6. Response of current meter with tail fin 

 to rapidly reciprocating current. 



surface. It is interesting that the result is 

 independent of the period of the wave and depends 

 only on the ratio of wave height to the radius 

 of rotation of the meter fin. In Fig. 6 the 

 apparent velocity is shown as negative when the 

 water flows backward through the rotor. In this 

 idealized case the Ekman meter would sum current 

 flow to zero in one cycle whereas electrically 

 registering meters would count all the flows as 

 positive although the independently registered 

 direction, if it were registered continuously, 

 would give indication of a spurious result. 

 Discrete registrations of direction could lead to 

 confusion, depending on the frequency of sampling, 

 unfortunately, the real situation is worse since 

 most meters are not equally sensitive to forward 

 and reverse flows and the time-integral of vel- 

 ocity will not be exactly zero even if direction 

 could be properly incorporated. Rapidly respond- 

 ing meters will behave much better. The negative 

 excursions of the apparent velocity will be 

 smaller and the orientation of the meter will be 

 near 0° and l80° during a larger fraction of the 

 cycle. Such meters, however, will not be immune 

 to the accumulation of apparent flow registration 

 due to their front-to-back asymmetry and the 

 many times repeated oscillations. 



Integration of such cyclic fluctuations to 

 zero over an integral number of complete cycles 

 theoretically is possible if the velocity sensor 

 is equally sensitive from all directions, the 

 direction sensor extremely rapid in response, 

 and the sampling sufficiently frequent . In the 

 general case, in which fluctuations are rotary, 

 it is necessary to carry out vector-integrations 

 continually, either in the current meter itself 

 or from the record at a later date. This requires 

 that the velocity and direction be associated as 

 vectors. If they are dissociated, it generally 

 is impossible to integrate. 



Of existing current meters, the Snodgrass meter 

 (Fig. 7) in its continuously recording form is 

 closest to having the desired characteristics 



l»+3 



