Two mass points, initially at the same orbital location, are displaced to two new orbits close by. Mass point is orbiting at inner radius , while mass point orbits at outer radius . They are connected by a massless spring. Assume, as would be the case for a Keplerian disk, that orbits more rapidly than . The string stretches and builds up tension T .
T pulls backwards on and forwards on .
Thus continuously loses angular momentum, while continuously gains the same. This means that cannot remain in orbit and must drop down to a yet lower orbit. Similarly, acquires too much angular momentum to stay in orbit and must move outwards. T goes up, and the process runs away. This is the essence of the weak-field instability in differentially rotating systems.