| Title: |
Nonlinear evolution of the horizontal shear instability in stratified rotating fluids under the complete Coriolis acceleration. |
| Authors: |
Moisset, Camille; Billant, Paul; Park, Junho; Mathis, Stéphane |
| Source: |
Journal of Fluid Mechanics; 1/25/2026, Vol. 1027, p1-34, 34p |
| Subject Terms: |
KELVIN-Helmholtz instability; STRATIFIED flow; CORIOLIS force; FLOW instability; NONLINEAR mechanics; TURBULENCE; ROTATING fluid; CASCADES (Fluid dynamics) |
| Abstract: |
This paper investigates the nonlinear dynamics of horizontal shear instability in an incompressible, stratified and rotating fluid in the non-traditional $f$ -plane, i.e. with the full Coriolis acceleration, using direct numerical simulations. The study is restricted to two-dimensional horizontal perturbations. It is therefore independent of the vertical (traditional) Coriolis parameter. However, the flow has three velocity components due to the horizontal (non-traditional) Coriolis parameter. Three different scenarios of nonlinear evolution of the shear instability are identified, depending on the non-dimensional Brunt–Väisälä frequency $N$ and the non-dimensional non-traditional Coriolis parameter $\tilde {f}$ (non-dimensionalised by the maximum shear), in the range $\tilde {f}\lt N$ for fixed Reynolds and Schmidt numbers $ \textit{Re}=2000$ , $ \textit{Sc}=1$. When the stratification is strong $N\gg 1$ , the shear instability generates stable Kelvin–Helmholtz billows like in the traditional limit $\tilde {f}=0$. Furthermore, when $N\gg 1$ , the governing equations for any $\tilde {f}$ can be transformed into those for $\tilde {f}=0$. This enables us to directly predict the characteristics of the flow depending on $\tilde {f}$ and $N$. When $N$ is around unity and $\tilde {f}$ is above a threshold, the primary Kelvin–Helmholtz vortex is destabilised by secondary instabilities but it remains coherent. For weaker stratification, $N\leqslant 0.5$ and $\tilde {f}$ large enough, secondary instabilities develop vigorously and destroy the primary vortex into small-scales turbulence. Concomitantly, the enstrophy rises to high values by stretching/tilting as in fully three-dimensional flows. A local analysis of the flow prior to the onset of secondary instabilities reveals that the Fjørtoft necessary condition for instability is satisfied, suggesting that they correspond to shear instabilities. [ABSTRACT FROM AUTHOR] |
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| Database: |
Complementary Index |