The mass dependence of the transverse flow for $Z=1$--5 fragments from the collisions of $^{40}\mathrm{Ar}+^{27}\mathrm{Al}, ^{40}\mathrm{Ar}+^{48}\mathrm{Ti}$, and $^{40}\mathrm{Ar}+^{58}\mathrm{Ni}$ at 47 MeV/nucleon is investigated experimentally in this article. The transverse flow values are determined using the in-plane components of the fragment transverse momenta, where three conventional methods, i.e., the kinetic flow tensor method, the transverse momentum analysis method, and the azimuthal correlation method, are applied to reconstruct the reaction plane in an event-by-event basis. It is demonstrated from the comparison of the present experimental mass dependent flow measurements and the model simulations using an improved antisymmetrized molecular dynamics model that the experimentally observed abnormal $\ensuremath{\alpha}$ transverse flow enhancement is closely related to the reaction plane reconstruction procedure in the flow extraction. We further investigate the physical existence of the abnormal $\ensuremath{\alpha}$ flow behavior using a two-particle azimuthal correlation method, which allows us to provide the relative flow magnitude information with an identification of fragment charge number without the knowledge of the reaction plane differing from the three conventional methods. It is found that the relative flow magnitudes deduced from the two-particle azimuthal correlation functions with an identification of $Z$, with the correction for the recoil effect imposed by the momentum conservation, show a monotonically increasing trend as a function of fragment charge number, with no exception of the $\ensuremath{\alpha}$ flow enhancement. These results, in addition to those from the improved antisymmetrized molecular dynamics model simulations, definitely provide experimental evidences for the inexistence of the abnormal $\ensuremath{\alpha}$ flow behavior in the heavy-ion collisions at the present incident energy region in nature.
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