Analytic solutions for along-channel velocity through an estuarine cross-section with laterally varying depth are compared to observations from an array of current meters deployed over a nearly triangular cross-section of the James River estuary. Analytic results suggest that the transverse structure of along-channel velocity at this cross-section is primarily due to simple density-driven circulation modified by bathymetry. Comparisons of analytic solutions for the amplitude and phase of tidal velocity to observations suggest that linear models which include realistic lateral depth variation should also incorporate across-channel variation in eddy viscosity. Solutions for various contributions to mean velocity are then derived which incorporate a power-law dependence of eddy viscosity on local depth. Comparison to observations from the James River suggests that density-induced circulation is the dominant contribution to along-channel mean velocity and that riverine discharge also provides a measurable contribution. Nonlinear tides may account for much of the remaining discrepancy between observations and the linear analytic solution. Finally, applications of an existing three-dimensional numerical model of the James River suggest (i) that inclusion of Coriolis acceleration does not greatly effect the cross-sectional distribution of along-channel mean velocity, and (ii) that the form of across-channel variation in eddy viscosity in the analytic model is consistent with the behavior of the numerical model's more sophisticated turbulence closure scheme.