Zonal flow (ZF) momentum balance in a three-dimensional, coupled drift-ion acoustic wave system is examined. In a three-dimensional system, conservation of potential vorticity (PV) is broken by fluctuating parallel flow compressibility. The coupling between PV fluctuation and fluctuating parallel flow compression defines a source/sink for fluctuating potential enstrophy density, and thus influences the wave momentum density and modifies the zonal momentum theorem. We show that perpendicular ZFs can be excited by stationary turbulence via compressional coupling, even in the absence of a driving force and potential enstrophy flux. The coupling drive involves both perpendicular and parallel dynamics, and does not require symmetry breaking in the turbulence spectrum. A new mechanism for ZF generation is thus revealed.