Identifying Instabilities in Complex Fluid Dynamical Systems with Adaptive-Ensemble Bred Vectors

A new concept of bred vectors (BVs) has been developed to computationally study the spatial patterns and time evolution of the nonlinear instabilities in turbulent fluid dynamical systems by finding the error signatures and establishing their connections with the predictability characteristics of instabilities such as convective, baroclinic, thermal-acoustic modes. A turbulent fluid dynamical system with high degrees of unsteadiness has a finite limit of predictability and a strong sensitive dependence on initial conditions. Initially, in small amplitude, dynamically significant instabilities will inevitably bring about fundamental changes in global flow behaviors in a finite time. Consequently, the inherent instabilities will deteriorate the prediction and potentially result in valueless information. This study will provide new insight on the identification of spatial and temporal signatures of instabilities and potenially assist in the development of flow control methods.