The tradeoff between analyzability and expressiveness is a key factor when choosing a suitable dataflow model of computation (MoC) for designing, modeling, and simulating applications considering a formal base. A large number of techniques and analysis tools exist for static dataflow models, such as synchronous dataflow. However, they cannot express the dynamic behavior required for more dynamic applications in signal streaming or to model runtime reconfigurable systems. On the other hand, dynamic dataflow models like Kahn process networks sacrifice analyzability for expressiveness. Scenario-aware dataflow (SADF) is an excellent tradeoff providing sufficient expressiveness for dynamic systems, while still giving access to powerful analysis methods. In spite of an increasing interest in SADF methods, there is a lack of formally-defined functional models for describing and simulating SADF systems. This article overcomes the current situation by introducing a functional model for the SADF MoC, as well as a set of abstract operations for simulating it. We present the first modeling and simulation tool for SADF so far, implemented as an open source library in the functional framework ForSyDe. We demonstrate the capabilities of the functional model through a comprehensive tutorial-style example of a RISC processor described as an SADF application, and a traditional streaming application where we model an MPEG-4 simple profile decoder. We also present a couple of alternative approaches for functionally modeling SADF on different languages and paradigms. One of such approaches is used in a performance comparison with our functional model using the MPEG-4 simple profile decoder as a test case. As a result, our proposed model presented a good tradeoff between execution time and implementation succinctness. Finally, we discuss the potential of our formal model as a frontend for formal system design flows regarding dynamic applications.