Experiments on JT-60U and JET have shown that plasma configurations with shear reversal are prone to the excitation of unusual Alfvén eigenmodes by energetic particles. These modes emerge outside the TAE frequency gap, where one might expect them to be strongly damped. The modes often appear in bunches and they exhibit a quasi-periodic pattern of predominantly upward frequency sweeping (Alfvén Cascades) as the safety factor q changes in time. This work presents a theory that explains the key features of the observed unusual modes including their connection to TAE's as well as the modifications of TAE's themselves near the shear reversal point. The developed theory has been incorporated into a reduced numerical model and verified with full geometry codes. JET experimental data on Alfvén spectroscopy have been simulated to infer the mode numbers and the evolution of qmin in the discharge. This analysis confirms the values of q that characterize the internal transport barrier triggering in reversed shear plasmas.