On a new type of solving procedure for Laplace tidal equation

In this paper, we present a new approach for solving Laplace tidal equations (LTE) which was formulated first by S. V. Ershkov ["A Riccati-type solution of Euler-Poisson equations of rigid body rotation over the fixed point," Acta Mech. 228(7), 2719 (2017)] for solving Poisson equations: a new type of the solving procedure for Euler-Poisson equations (rigid body rotation over the fixed point) is implemented here for solving the momentum equation of LTE, Laplace tidal equations. Meanwhile, the system of Laplace tidal equations (including continuity equation) has been successfully explored with respect to the existence of an analytical way for presentation of the solution. As the main result, a new ansatz is suggested here for solving LTE: solving the momentum equation is reduced to solving a system of 3 nonlinear ordinary differential equations of 1st order with regards to 3 components of the flow velocity (depending on time t), along with the continuity equation which determines the spatial part of solution. Nevertheless, a proper elegant partial solution has been obtained due to invariant dependence between temporary components of the solution. In addition to this, it is proved here that the system of Laplace tidal equations does not have the analytical presentation of a solution (in quadratures) in the case of the nonzero fluid pressure in the oceans, as well as nonzero total gravitational potential and the centrifugal potential (due to planetary rotation). © 2018 Author(s).