ABSTRACT Jets from active nuclei may supply the heating which moderates cooling and accretion from the circum-galactic medium. While steady overpressured jets can drive a circulatory flow, lateral energy transfer rarely exceeds 3 per cent of jet power, after the initial bow shock has advanced. Here, we explore if pulses in high-pressure jets are capable of sufficient lateral energy transfer into the surrounding environment. We answer this by performing a systematic survey of numerical simulations in an axisymmetric hydrodynamic mode. Velocity pulses along low Mach jets are studied at various overpressures. We consider combinations of jet velocity pulse amplitude and frequency. We find three flow types corresponding to slow, intermediate, and fast pulsations. Rapid pulsations in light jets generate a series of travelling shocks in the jet. They also create ripples which propagate into the ambient medium while a slow convection flow brings in ambient gas which is expelled along the jet direction. Long period pulses produce slowly evolving patterns which have little external effect, while screeching persists as in non-pulsed jets. In addition, rapid pulses in jets denser than the ambient medium generate a novel breathing cavity analogous to a lung. Intermediate period pulses generate a series of bows via a bellows action which transfer energy into the ambient gas, reaching power efficiencies of over 30 per cent when the jet overpressure is sufficiently large. This may adequately inhibit galaxy gas accretion. In addition, such pulses enhance the axial out-flow of jet material, potentially polluting the circum-galactic gas with metal-enriched interstellar gas.