In this paper

the linear continuously tratified model of the abyssal circulation proposed by Pedlosky (1992) was extended to include the second order term -(γθ zzz ) in the vertical turbulent mixing parameterization of $$ - \overline {(w\prime \theta \prime )} _z = k_u \theta _{zz} - \gamma \theta _{zzz} $$

in whichk v is a vertical diffusion coefficient

and γ is the second order coefficient of turbulent mixing (or simply called γ-term and γ<0 is only allowed). The influence of the γ-term on the baroclinic structure of the abyssal circulation driven by upwelling out of the abyss was investigated. It was found that the γ-term has a noticeable influence on the baroclinic structure of the upwelling driven abyssal circulation. For uniform upwelling

it favors the baroclinic layering of the abyssal circulation in the eastern part of the basin

but prevents the layering in the west. In addition

this parameter was found to decrease the vertically averaging meridional velocity of the abyssal circulation from the west to the east on the southern boundary. For upwelling localized near the eastern boundary

the γ-term favors baroclinic layering of the abyssal circulation in the whole basin. Especially

on the southern boundary the γ-term could strengthen the vertically averaging meridional velocity in the west

but greatly weaken it in the east. The model presented here might be considered as an extension of the Pedlosky baroclinic model of the abyssal circulation.