In the context below
"In Pidduck [8, 9] it was suggested that the water compressibility be taken into account to resolve the instantaneity paradox in the well-known Cauchy-Poisson problem. Pidduck described the water flow as isothermal and weakly compressible just as it appears in CMA-SPH. A linear analysis was performed verifying that the weakly compressible model captures the depth decaying incompressible solution to leading order with accuracy of order $O(1/c^2)$. However, it was shown that given appropriate initial and boundary conditions, the weak compressibility assumption also permits an infinite set of essentially non-attenuating high-frequency depth oscillatory acoustic modes that depend on c and the water depth".
Any sort of help is appreciated, Thanks