### Abstract

The analytical results of the nonlinear theory of wave packets are tested against experiments performed in a water tank and compared with the analytical results of the linear theory of low-amplitude waves and the theory of weakly nonlinear gravitational waves on the free fluid surface infinite in extent. The results of experiments and observations well-known in the literature are used for testing.

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Translated by E.A. Pushkar

## CLASSICAL EQUATIONS IN THE CURVILINEAR COORDINATES \(\sigma ,\theta \)

### CLASSICAL EQUATIONS IN THE CURVILINEAR COORDINATES \(\sigma ,\theta \)

Points \(P\) and *Q* are mentioned in the integral for the velocity potential; point \(P\) has the curvilinear coordinates \(\sigma ,\theta \) and point *Q* has the coordinates \({{\sigma }_{1}},\;{{\theta }_{1}}\) at \({{\sigma }_{1}} = 0\).

In the curvilinear coordinates the velocity potential can be written as follow:

where

Nonlinear equations (A2) and (A3) are, respectively, the kinematic condition on the free fluid surface and the pressure continuity condition on this surface

The conditions at infinity can be taken in the form:

Conditions (A4) guarantee that the perturbation source in fluid imparts finite energy to the fluid.

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Mindlin, I.M. Water Waves: Theory and Experiments.
*Fluid Dyn* **55**, 498–510 (2020). https://doi.org/10.1134/S001546282003009X

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DOI: https://doi.org/10.1134/S001546282003009X