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The joint effects of planetary B, topography and friction on baroclinic instability in a two-layer quasi-geostrophic model
Sterl, M.F.; Palóczy, A.; Groeskamp, S.; Baatsen, M.L.J.; LaCasce, J.H.; Isachsen, P.E. (2025). The joint effects of planetary B, topography and friction on baroclinic instability in a two-layer quasi-geostrophic model. J. Fluid Mech. 1012: A1. https://dx.doi.org/10.1017/jfm.2025.10172
In: Journal of Fluid Mechanics. Cambridge University Press: London. ISSN 0022-1120; e-ISSN 1469-7645, meer
Peer reviewed article  
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Author keywords
    baroclinic flows; quasi-geostrophic flows; topographic effects
Auteurs  Top 
  • Sterl, M.F., meer
  • Palóczy, A.
  • Groeskamp, S., meer
  • Baatsen, M.L.J.
  • LaCasce, J.H.
  • Isachsen, P.E.
Abstract
    The quasi-geostrophic two-layer model is a widely used tool to study baroclinic instability in the ocean. One instability criterion for the inviscid two-layer model is that the potential vorticity (PV) gradient must change sign between the layers. This has a well-known implication if the model includes a linear bottom slope: for sufficiently steep retrograde slopes, instability is suppressed for a flow parallel to the isobaths. This changes in the presence of bottom friction as well as when the PV gradients in the layers are not aligned. We derive the generalised instability condition for the two-layer model with non-zero friction and arbitrary mean flow orientation. This condition involves neither the friction coefficient nor the bottom slope; even infinitesimally weak bottom friction destabilises the system regardless of the bottom slope. We then examine the instability characteristics as a function of varying slope orientation and magnitude. The system is stable across all wavenumbers only if friction is absent and if the planetary, topographic and stretching PV gradients are aligned. Strong bottom friction decreases the growth rates but also alters the dependence on bottom slope. In conclusion, the often mentioned stabilisation by steep bottom slopes in the two-layer model holds only in very specific circumstances, thus probably plays only a limited role in the ocean.
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