Inherent Instabilities in the Kuramoto-Sivashinsky Equation

Add to your list(s) Download to your calendar using vCal

• Chris Sear ( DAMTP)
• Monday 07 February 2022, 15:00-16:00
• CMS, MR11.

If you have a question about this talk, please contact Alistair Hales.

There is evidence to suggest that the boundary-layer equations are not the high-Reynolds number limit of solutions to the Navier-Stokes equations. Numerical calculations by Brinckman and Walker show that at sufficiently high Reynolds number, a short-wavelength instability may appear before the separation time of solutions to the unsteady boundary-layer equations. Using the Kuramoto-Sivashinsky equation as a model for the problem with key similarities and one spatial dimension, we will show that a similar short-wavelength instability can arise before the shock formation time of the kinematic-wave equation. We will then show that this instability can be explained through tracking exponentially-small terms in the asymptotic solution structure, invisible to traditional matched asymptotics approaches. These terms, and their associated Stokes and anti-Stokes lines, can be found by tracking singularities of the kinematic-wave equation in the complex plane.

This talk is part of the Waves Group (DAMTP) series.

This talk is included in these lists:

• CMS, MR11
• Waves Group (DAMTP)

Note that ex-directory lists are not shown.