%0 Generic %1 rosenberg2017nonlinear %A Rosenberg, Kevin %A McKeon, Beverley J. %D 2017 %K 76d05-incompressible-navier-stokes-equations 76f20-dynamical-systems-approach-to-turbulence %T Nonlinear forcing in the resolvent analysis of exact coherent states of the Navier-Stokes equations %U http://arxiv.org/abs/1705.10824 %X The resolvent analysis of McKeon & Sharma (2010) recasts the Navier-Stokes equations into an input/output form in which the nonlinear term is treated as a forcing that acts upon the linear dynamics to yield a velocity response. The framework has shown promise with regards to producing low-dimensional representations of exact coherent states. Previous work has focused on a primitive variable output; here we show a velocity-vorticity formulation of the governing equations along with a Helmholtz decomposition of the nonlinear forcing term reveals a simplified input/output form in the resolvent analysis. This approach leads to an improved method for compact representations of exact coherent states for both forcing and response fields, with a significant reduction in degrees of freedom in comparison to the primitive variable approach.

@misc{rosenberg2017nonlinear, abstract = {The resolvent analysis of McKeon & Sharma (2010) recasts the Navier-Stokes equations into an input/output form in which the nonlinear term is treated as a forcing that acts upon the linear dynamics to yield a velocity response. The framework has shown promise with regards to producing low-dimensional representations of exact coherent states. Previous work has focused on a primitive variable output; here we show a velocity-vorticity formulation of the governing equations along with a Helmholtz decomposition of the nonlinear forcing term reveals a simplified input/output form in the resolvent analysis. This approach leads to an improved method for compact representations of exact coherent states for both forcing and response fields, with a significant reduction in degrees of freedom in comparison to the primitive variable approach.}, added-at = {2020-11-17T04:51:39.000+0100}, author = {Rosenberg, Kevin and McKeon, Beverley J.}, biburl = {https://www.bibsonomy.org/bibtex/27e4f1b1f65b310f359a93bcd54f92264/gdmcbain}, howpublished = {arxiv:1705.10824}, interhash = {d2c79f71174f427c256d71394e887b1f}, intrahash = {7e4f1b1f65b310f359a93bcd54f92264}, keywords = {76d05-incompressible-navier-stokes-equations 76f20-dynamical-systems-approach-to-turbulence}, timestamp = {2020-11-17T04:51:39.000+0100}, title = {Nonlinear forcing in the resolvent analysis of exact coherent states of the Navier-Stokes equations}, url = {http://arxiv.org/abs/1705.10824}, year = 2017 }