A dynamical systems approach is taken to explain the dynamics of two classes of ‘gap-leaping’ geophysical flow as well as the hypersonic second-mode instability. First, in the context of a loop current system, it is shown that multiple steady flow patterns with hysteresis exist and appear to satisfy a cusp catastrophe geometry of solutions. Which state the system assumes (looping or leaping or periodic eddy shedding) and when transitions between states occur, will be discussed in terms of fundamental vorticity advection and dissipation. Second, a global perspective of Gulf of Maine circulation leads to a new mechanism for Scotian Shelf Water crossover events. Finally, by considering an idealized system and an analogy with harmonic oscillators, a fundamental mechanism for the hypersonic second-mode instability is proposed.