A Restricted Nonlinear Study of Laminar-Turbulent Transition

We apply the restricted nonlinear (RNL) model to investigate K-type transition. The RNL model equations comprise a streamwise averaged mean interacting with a limited number of streamwise varying perturbation modes which lead to a reduced representation of the dynamics. We take advantage of the model tractability by interrogating the transient energy growth of each mode in this reduced representation during transition. When compared to direct numerical simulations (DNS), the RNL model is shown to predict greater energy and transition earlier. However, the reduced dynamics of the RNL model follow a similar transition process to DNS and reproduces salient streak and roll flow features. In this framework we vary the streamwise wavenumber support of the RNL dynamics to isolate and assess the role of scale interactions during transition.