Shear layer rollup#
The shear layer rollup is a 2-dimensional ideal incompressible flow (Euler flow). And the external body force is zero.
The flow is in a periodic domain \(\Omega = [0, 2\pi]^2\), and components of the initial velocity \(\boldsymbol{u}^0 = \begin{bmatrix}u^0 & v^0\end{bmatrix}^{\mathsf{T}}\) are
and
where \(\delta=\pi/15\) and \(\epsilon=0.05\).
![../../../_images/t048.png](../../../_images/t048.png)
Fig. 13 The vorticity field of the shear layer rollup flow at \(t\in\left\lbrace0,4,8\right\rbrace\) with contour lines for \(\left\lbrace\pm 1,\pm 2, \cdots, \pm 6\right\rbrace\).#
It is seen that two vorticity layers gradually roll up due to the initial perturbation in the velocity field.
For a phyem implementation of the shear layer rollup using the dual-field method introduced in
[Dual-field NS, Zhang et al.], click
phyem_slr.py
↩️ Back to 🌊 Navier-Stokes equations.