Flutter response of bladed disks is a quite an important problem in modern designs of low pressure turbines, but, even for tuned configurations, it is not fully understood yet. Some research work suggests that, in a tuned rotor, the flutter induced vibration state that sets in consists of just a single traveling wave mode, while others show flutter states composed of several traveling waves active at the same time. Many of these studies were performed using conceptual models, such as mass-spring systems or asymptotically reduced models. In this work, a high fidelity bladed disk model is integrated into the time domain for the case of a realistic aerodynamically unstable low pressure turbine. In this configuration, the only nonlinear effect is the friction present at the blade disk attachment, which is responsible for the saturation of the flutter growth, and it is also the only mechanism that allows the interaction among the different unstable traveling wave modes. A case with multiple unstable modes of the same modal family is studied first. After that, the study is extended to a case where modes of different modal families are unstable and have similar aerodynamic instability levels. The interaction of unstable modes from different modal families is studied, we believe, for the first time, as previous flutter analyses were restricted to the interaction of unstable modes from the same family.