  Fish exhibit various patterns of collective motion, in which individual fish
sense the gravitational field and tend to move horizonally. We study the effect
of gravity on the collective patterns by incorporating suppression of vertical
motion in an agent-based model. The gravitational factor induces a tornado
which is a vertically and highly elongated form of a torus, The vortex axis
becomes almost identical to the vertical axis even when the gravitational
factor is weak compared to the interaction between fish. We also obtained a
vertically elongated polarized school with high frontal density. Our results
clarify the effect of gravity on the shape of clusters, individual-level
motion, and mobility of the entire cluster.
