  Let F be a riemannian flow on a closed manifold M. We study the behavior of
the first eigenvalues of the Hodge Laplacian acting on differential forms under
adiabatic collapsing of the flow. We show that the number of small eigenvalues
is related to the basic cohomology of F, and give spectral criteria for the
vanishing of the \'Alvarez class and the Euler class of F. We also define a
diophantine invariant of the flow wich is related to the asymptotical behavior
of the small eigenvalues. An appendix is devoted to arithmetic properties of
riemannian flows.
