The transient airflow in a rigid, asymmetric monopodial sheep (ovine) tracheobronchial tree of up to 13 generations was investigated numerically. The lung geometry was segmented and reconstructed from computed-tomographic (CT) images. The flow characteristics in the image-based sheep airway were compared with the flow patterns produced by a Weibel-based model at prime locations. Boundary conditions were prescribed 1) a velocity profile from experimental data at the inlet and 2) zero pressure at the bronchial outlets. A mesh convergence study was carried out to establish confidence in the model predictions, and gross left-right ventilation was validated against experimental xenon wash-in-washout data. Detailed flow characteristics were investigated at three points in the breathing cycle: 1) peak inhalation, 2) peak exhalation, and 3) transition. Simulation results revealed fundamental differences between airflow in monopodial and bipodial branching airways. Compared with idealized bipodial flow, the flow in the sheep airway was asymmetric and highly vortical, especially during exhalation and transition. The streak lines during the inhalation phase suggest that the left and right upper lobes are ventilated by airflow in the peripheral region of the trachea. This work may contribute to understanding the interplay between structure and function in the lung.