MATHEMATICAL SIMULATION OF GRAVITATIONAL
WAVES IN THE OCEAN IN THE APPROXIMATION OF
"SHALLOW WATER"

N. A. Kudryashov , Yu. I. Syts'ko , and
S. A. Chesnokov

UDC 532.59

Problems of the behavior of gravitational waves in 
the approximation of "shallow water" - motion of a solitary wave 
over the water surface, exit of a wave to the shore, passage of a 
solitary wave over a submerged rock - are solved. The solution 
of the first problem showed that in modeling the motion of a solitary 
(soliton-type) wave the "shallow water" approximation breaks down 
at a ratio of water depth to wavelength equal to 0.3. An analysis 
of the results of solution of the second problem indicates that the 
"shallow water" approximation cannot be used for calculation of the 
height of a wave in its exit to the shore but it can be used for estimation 
of the distance from the shore where the wave is turned over. It follows 
from the solution of the third problem that the "shallow water"
approximation is suited only for obtaining a qualitative picture
of the distortion of the profile of a wave in its motion over a rock.

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JEPTER7492017