It is well known that Rayleigh-Benard convection with perturbations yields Lagrangian chaotic transport, and the mechanism of inducing chaotic transport has been numerically clarified by lobe dynamics . On the other hand, the mechanism of such Lagrangian transport has not been enough studied by experiments. In our previous work , we made an experimental study to investigate the Lagrangian transport appeared in the two-dimensional Rayleigh-Benard convection by giving oscillation on the velocity fields and showed that there exist Lagrangian Coherent Structures (LCSs) which correspond to invariant manifolds of non-autonomous systems. We also showed that the LCSs entangle with each other around cell boundaries. In this paper, we further explore the global invariant structures of the perturbed Rayleigh-Benard convection by clarifying the details on the LCSs and explain how the fluid transport obeys lobe dynamics. Finally, we propose a novel Hamiltonian model for the two-dimensional perturbed Rayleigh-Benard convection that enables to elucidate the global structures detected by experiments.