In this study, we examine the results obtained by the Finite-volume Coastal Ocean Circulation Model (FVCOM) regarding the effects of eddy viscosity and bathymetry on the three-dimensional (3D) Lagrangian residual velocity (LRV) in a narrow bay. The results are cast in terms of two nondimensional numbers: the ratio of friction to local acceleration ( δ) and the ratio of the minimum depth over shoals to the maximum depth in the channel ( ε). The ratio δ depends on the eddy viscosity and mean depth. For a given eddy viscosity, when ε > 0.5, the along-estuary LRV tends to be vertically sheared and when ε < 0.5, the exchange is laterally sheared. When ε << 1, the structure of the 3D, depth-integrated, and breadth-averaged LRV changes only slightly as δ increases. For ε values between 0.33 and 0.5, the structure of the 3D LRV is mainly laterally sheared. In the same ε range, the 3D and depth- integrated LRV exhibit reversed structures from high to low δ values. In addition, the breadth-averaged LRV weakens the typical two- layered circulation when δ decreases. When ε is 1, the two-layered vertical structure reverses direction, and a three- layered vertical structure develops in the outer bay as δ decreases.