A working numerical model for oceanographic forecasting is being developed at the Department of Meteorology and Oceanography, New York University. In this paper we discuss a few aspects of physical problems in the basic model equations and boundary conditions. These are (1) realistic initial conditions which enable the forecasting model to track rapidly variable wind stresses and water properties imposed at the sea surface, (2) nonlinear eddy fluxes in the vertical direction, and (3) boundary mixing at lateral and bottom walls. In Problem (1), use is made of the results on theoretical models for the thermohaline circulation of the oceans to construct the realistic initial conditions. Thus the velocity and density fields are expressed by similarity forms that are valid in the interior of the ocean. In Problem (2), the dependence of the vertical eddy conductivity on water stratification is taken into account in the vertical flux of heat. The resultant diffusion process may describe realistic temperature profiles in the surface layer for a warming period. In Problem (3), two kinds of boundary mixing processes are studied. (Author).