Waterway affects the hydraulics is unknown. The average current speed, V, 

 through the entrance is given by 



- ^ tidal prism ^2) 



12) (\> 



For the values above, an average speed is 0.05 foot per second. If a sinus- 

 oidal variation is assumed, the maximum velocity is ir/2(0.05). 



(2) Long Wave Method . Because some material has been deposited in 

 the entrance channel, average speeds are probably higher than 0.05 foot per 

 second. Therefore, the second approach is to consider speeds associated with 

 propagation of the tidal wave through the entrance, rather than those produced 

 hydraulically. From small-amplitude theory, the maximum horizontal orbital 

 velocity, u x> of a shallow-water wave is given by 



(3) 



where a is the amplitude of a wave whose period equals the tidal period, g 

 is the acceleration of gravity, and d is the depth. For a = 0.9 foot and 

 d = 38 feet: u^^^^^ = 0.82 foot per second, which is considerably greater than 

 the hydraulic speed found using equation (2). 



(3) Harbor Resonance Model. The effects of other long wave action in 

 the harbor were considered by applying Ippen and Goda's (1963) harbor reso- 

 nance model. Their model provides acceptable results over a large range of 

 values of kd (k = wave number = 2ir/L, L = wavelength, d = half of the harbor 

 width) for relatively large values of the reflection coefficient (between 0.8 

 and 0.9). The theory is based on the following assumptions: 



(a) The harbor is excited by a regular wave train moving normal 

 to the coastline. 



(b) All boundaries are perfectly reflecting. 



(c) The water depth is constant and equal, both inside and out- 

 side the harbor. 



(d) Small -amplitude wave theory is applicable. 



(e) The harbor entrance is small compared to the wavelength 

 (kc/2 < 1; c = width of the harbor entrance). 



For tida.l periods, no amplification of the tidal range was predicted. 

 However, for waves of the periods shown in Table 1, significant amplification 

 could occur. Unfortunately, the coarseness of the tidal data precluded 

 performing a spectral analysis to determine if energy is present in the gulf 

 at these periods. 



Galveston District has proposed modifications to the harbor and entrance 

 which roughly double the present channel width, jetty spacing, and cross- 

 sectional area, and increase the authorized depth from 45 to 50 feet. Using 



26 



