The disappearance of Malaysia Airlines flight MH370 on the morning of 8 March 2014 is one of the great mysteries of our time. Perhaps the most relevant aspect of this mystery is that not a single piece of debris from the aircraft was found during the intensive surface search carried out for roughly 2 months following the crash. Difficulties in the search efforts, due to the uncertainty of the plane's final impact point and the time that had passed since the accident, bring the question on how the debris scattered in an always moving ocean, for which there are multiple data sets that do not uniquely determine its state. Our approach to this problem is based on the use of Lagrangian descriptors (LD), a novel mathematical tool coming from dynamical systems theory that identifies dynamic barriers and coherent structures governing transport. By combining publicly available information supplied by different ocean data sources with these mathematical techniques, we are able to assess the spatio-temporal state of the ocean in the priority search area at the time of impact and the following weeks. Using this information we propose a revised search strategy by showing why one might not have expected to find debris in some large search areas targeted by the Australian Maritime Safety Authority (AMSA), and determining regions where one might have expected impact debris to be located, which were not subjected to any exploration.