Transporting and storing hydrogen is a complex technological task. A typical problem relates to the need to minimize the strength of fluid motion and heat transfer near the walls of the container. In this work this problem is tackled numerically assuming an infinite cavity of pipe square cross-section, located in a constant external temperature gradient. In particular, a method based on the application of vibrations to suppress the gravitational convection mechanism is explored. A parametric investigation is conducted and the limits of applicability of the method for small Grashof numbers (10e4) are determined. It is shown that it is possible to minimize the intensity of the vibrogravitational flow for any values of the problem parameters if correction factors are specified. The results obtained can be applied in technological processes associated with the transportation, storage and use of hydrogen: pumping the working fluid through pipes, storage in tanks, as well as flow processes in the combustion chambers of power plants.