  We study cosmological perturbations in a brane-world scenario where the
matter fields live on a four-dimensional brane and gravity propagates in the
five-dimensional bulk. We present the equations of motion in an arbitrary gauge
for metric perturbations in the bulk and matter perturbations on the brane.
Gauge-invariant perturbations are then constructed corresponding to
perturbations in longitudinal and Gaussian normal gauges. Longitudinal gauge
metric perturbations may be directly derived from three master variables
(separately describing scalar, vector and tensor metric perturbations) which
obey five-dimensional wave-equations. Gaussian normal gauge perturbations are
directly related to the induced metric perturbations on the brane with the
additional bulk degrees of freedom interpreted as an effective Weyl
energy-momentum tensor on the brane. We construct gauge-invariant perturbations
describing the effective density, momentum and pressures of this Weyl fluid at
the brane and throughout the bulk. We show that there exist gauge-invariant
curvature perturbations on the brane and in the bulk that are conserved on
large-scales when three-dimensional spatial gradients are negligible.
