  Chaotic motion in time of a number of macroscopic systems has been analyzed,
in the framework of scale relativity, as motion in a fractal space with
topological dimension 3 and geodesics with fractal dimension 2. The motion
equation is then Schr\"odinger-like and its interpretation in fluid mechanics
gives the well-known Euler and Navier-Stokes equations. We generalize here this
formalism to the study of a system exhibiting a chaotic behavior both in space
and time. We are thus lead to consider macroscopic fluid properties as issuing
from the geodesic features of a fractal `space-time' with topological dimension
4 and geodesics with fractal dimension 2. This allows us to obtain both a
motion equation for the fluid velocity field, which exhibits then three
components while only one is necessary for the description of an ordinary
fluid, and a relation between their three curls. The physical properties of
this solution suggest it could represent some three-dimensional chaotic
behavior for a classical fluid, tentatively turbulent if particular conditions
are fulfilled. Different ways of testing experimentally these assumptions are
proposed.
