Approximation of the hydrostatics equation in numerical conservative models using a non-linear equation of state

Approximation of the hydrostatics equation is considered using a state equation in the form of a quadratic polynomial of temperature and salinity. It is shown that in this case the traditional approximation fails to obey the law of energy conservation in the numerical model. A difference analogue to the hydrostatics equation is derived which has the required property. The results of the calculation are presented.Translated by V. Puchkin.