  We study the orientational order of an immobile fish school. Starting from
the second Newton's law, we show that the inertial dynamics of orientations is
ruled by an Ornstein-Uhlenbeck process. This process describes the dynamics of
alignment between neighboring fish in a shoal, a dynamics already used in the
literature for mobile fish schools. Firstly, in a fluid at rest, we calculate
the global polarization (i.e. the mean orientation of the fish) which decreases
rapidly as a function of the noise. We show that the faster a fish is able to
reorient itself, the more the school can afford to reorder itself for important
noise values. Secondly, in the prescence of a stream, each fish tends to orient
itself and swims against the flow: the so-called rheotaxis. So even in the
presence of a flow, it results in an immobile fish school. By adding an
individual rheotaxis effect to alignment interaction between fish, we show that
in a noisy environment, individual rheotaxis is enhanced by alignment
interactions between fish.
