In the dispersion relation for waves in this regime, the hyperbolic tangent term approaches h, causing the phase speed to equal the square root of little g times h. For 10 points each:
[10m] Unidirectional waves in what regime are modeled by the Korteweg-de Vries (de VREEZE) equation?
ANSWER: shallow-water regime [or shallow-water waves; prompt on shallow]
[10e] The shallow-water limit occurs when this quantity is over 20 times the water depth. This quantity measured between two adjacent crests can be hundreds of kilometers for a tsunami.
ANSWER: wavelength [or length]
[10h] In a shallow-water wave, the path traced out by a moving particle is "flattened" and thus has this shape.
ANSWER: ellipse [or elliptical or oval-shaped]
<June Yin , Science - Physics - Any>