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The evolution of jets showers in high energy nuclear collisions is influenced in various ways by the presence of a surrounding medium. The interaction of jet constituents with the medium can happen during the partonic stage of the jet, during hadronization, and even during its hadronic stage. We demonstrate how flow of the ambient medium in a direction transverse to the jet can introduce both dipole and quadrupole defomations. We propose to analyze then= 1 andn= 2 harmonic deformations of soft and semi-hard hadrons or subjets in a jet with respect to the jet core using the method ofq-vectors. We discuss simulations which show how the transverse shapes and their preferred angles evolve when the ambient environment of jets changes from the vacuum to a parton medium without flow and finally to a medium with various rates of transverse flow. Our study includes the effects of both flow during the development of the parton shower and hadronization. The existence of dipole deformations, and the correlation of the angles of dipole and quadrupole deformations could constitute promising experimental signals for the presence and size of ambient transverse flow.