A sigma coordinate ocean circulation model is employed to study flow trapped to a tall seamount in a periodic f-plane channel. In Part I, errors arising from the pressure gradient formulation in the steep topography/strong stratification limit are examined. To illustrate the error properties, a linearized adiabatic version of the model is considered, both with and without forcing, and starting from a resting state with level isopycnals. The systematic discretization errors from the horizontal pressure gradient terms are shown analytically to increase with steeper topography (relative to a fixed horizontal grid) and for stronger stratification (as measured by the Burger number). For an initially quiescent unforced ocean, the pressure gradient errors produce a spurious oscillating current that, at the end of 10 days, is approximately 1 cm s−1 in amplitude. The period of the spurious oscillation (about 0.5 days) is shown to be a consequence of the particular form of the pressure gradient terms in th... Abstract A sigma coordinate ocean circulation model is employed to study flow trapped to a tall seamount in a periodic f-plane channel. In Part I, errors arising from the pressure gradient formulation in the steep topography/strong stratification limit are examined. To illustrate the error properties, a linearized adiabatic version of the model is considered, both with and without forcing, and starting from a resting state with level isopycnals. The systematic discretization errors from the horizontal pressure gradient terms are shown analytically to increase with steeper topography (relative to a fixed horizontal grid) and for stronger stratification (as measured by the Burger number). For an initially quiescent unforced ocean, the pressure gradient errors produce a spurious oscillating current that, at the end of 10 days, is approximately 1 cm s−1 in amplitude. The period of the spurious oscillation (about 0.5 days) is shown to be a consequence of the particular form of the pressure gradient terms in th...