  We introduce a quasi-local integral functional and scalar quasi-local
variables to examine a wide class of spherically symmetric inhomogeneous
spacetimes that generalize the Lemaitre-Tolman-Bondi (LTB) dust solutions
("LTB" spacetimes). By using these variables, we can transform the fluid flow
evolution equations into evolution equations for non-linear, covariant,
gauge--invariant perturbations of Friedman-Lemaitre-Robertson-Walker (FLRW)
cosmologies. In the linear limit, we obtain spherical perturbations in the
synchronous gauge under the long wavelength approximation. The formalism has a
significant potential for cosmological applications, as it allows one to
examine a wide variety of sources with different "equations of state",
generalizing known FLRW solutions to idealized but non-trivial and non-linear
inhomogeneous conditions. The quasi-local functional can be reformulated as a
weighed proper volume average distribution, with the weight factor given by a
scalar invariant related to the quasi-local mass-energy function. The
back-reaction terms, emerging in Buchert's proper averaging formalism, can be
expressed as differences between fluctuations of averaged and quasi-local
energy densities. By comparing this average with the weighed quasi-local one,
we can define a binding energy functional related to spatial gradients of the
averaged and quasi-local variables that appear in the back-reaction terms.
