What the study found
Internal waves moving through a horizontal shear layer can grow and break through two distinct mechanisms: refraction by the shear can make the waves steeper, or advection of the background flow can increase streamwise velocity perturbations. The authors also found that a dimensionless perturbation energy ratio, F, can be used to predict which mechanism is more important.
Why the authors say this matters
The study suggests that identifying whether steepening or momentum advection dominates may help explain how wave breaking develops in shear flows, and how energy, momentum, and mixing are transferred among the wave, the background flow, and turbulence. The findings indicate that the character of breaking is linked to the resulting dissipation and mixing properties.
What the researchers tested
The researchers studied internal waves propagating in a background shear flow with shear direction orthogonal to gravity. They used ray-tracing theory to predict wave properties where instability occurs, and they tested those predictions with fully nonlinear direct numerical simulations across a range of wave-breaking dynamics.
What worked and what didn't
The theory gave good qualitative agreement with the simulations, even though the simulations departed substantially from the theory's underlying assumptions. When F was small, waves became locally steep and kinetic and potential energy stayed approximately equipartitioned; in that case, instabilities were expected to arise from a combination of shear and convection. As F increased, kinetic energy became dominant and breaking was increasingly driven by enhanced vertical shear.
What to keep in mind
The abstract does not provide detailed limitations beyond noting substantial departures from the theory's assumptions in the simulations. The summary is limited to internal waves in a horizontal shear layer with shear orthogonal to gravity.
Key points
- Internal waves in a horizontal shear layer can break through either steepening by refraction or momentum advection by the background flow.
- A dimensionless perturbation energy ratio, F, was constructed to estimate which breaking mechanism is more important.
- Small F was associated with locally steep waves and roughly balanced kinetic and potential energy.
- Larger F was associated with kinetic-energy dominance and breaking increasingly driven by enhanced vertical shear.
- Direct numerical simulations showed good qualitative agreement with the ray-tracing theory despite substantial assumption mismatches.
- Wave breaking produced significant turbulent dissipation, sometimes greatly exceeding the initial wave energy.
Disclosure
- Research title:
- Internal-wave breaking depends on two shear-driven mechanisms
- Image credit:
- Photo by Landiva Weber on Pexels
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