Previously we found that large amplitude r -modes could decay catastrophically due to nonlinear hydrodynamic effects .
In this paper we found the particular coupling mechanism responsible for this catastrophic decay , and identified the fluid modes involved .
We find that for a neutron star described by a polytropic equation of state with polytropic index \Gamma = 2 , the coupling strength of the particular three-mode interaction causing the decay is strong enough that the usual picture of the r -mode instability with a flow pattern dominated by that of an r -mode can only be valid for the dimensionless r -mode amplitude less than O ( 10 ^ { -2 } ) .