Adrien - Saturday, August 10, 2024

Where does the ocean dissipate the energy it receives from prevailing winds?

Numerical simulations show that hydrodynamic friction near the coasts plays a crucial role in explaining the stabilization of the mean flow of the ocean in the North Atlantic.


In the ocean, energy sources are well known, primarily being the action of prevailing winds on the sea, and to a lesser extent, flows created by differences in temperature or salinity. Thus, the oceanic circulation in the North Atlantic is generally described by a large-scale clockwise vortical flow, the North Atlantic gyre (of which the Gulf Stream is a component), which overlaps with the trade winds blowing westward near the equator and the westerly prevailing winds at our latitudes.

However, identifying the regions where energy is dissipated remains a largely open problem because the dissipation processes occur at small scales of the flow, which themselves result from the turbulent cascade, supposedly redistributing the large-scale injected energy to smaller scales in a complex manner.


To study the role of the coasts in these dissipation processes, a collaboration of researchers from the Physics Laboratory of ENS de Lyon (LPENSL, CNRS / ENS de Lyon) and the Institute of Environmental Geosciences (IGE, CNRS / INRAE / IRD / Université Grenoble Alpes) revisited a classic model that describes the emergence of oceanic gyres with intensified western boundary currents, such as the Gulf Stream in the North Atlantic or the Kuroshio in the Pacific. This model describes a two-dimensional flow forced by winds, a simplification justified by the fact that the aspect ratio of an ocean (thickness divided by characteristic lateral size) is close to that of a sheet of paper on a planetary scale.

Using numerical simulations, researchers show that oceanic gyres persist where viscous dissipation terms are very small, with an energy dissipation rate that remains constant, independent of the fluid's viscosity. This phenomenon of dissipative anomaly is well known in three-dimensional space flows but is surprising in the context of two-dimensional flow.


The ocean is modeled as a square ocean basin 3,100 miles (5,000 km) on each side, an idealized version of the North Atlantic.
Left: in the limit of low dissipation, the ocean appears at every moment like a sea of vortices.
Right: when this flow is averaged over very long times, the vortices disappear, and an intensified oceanic gyre is observed along the western edge.
Colors indicate the direction of the vortices' rotation.
© Lennard Miller, Bruno Deremble, and Antoine Venaille / IGE / Grenoble, LPENSL / CNRS.

Indeed, in three dimensions, large vortices destabilize and create smaller vortices, and so on, efficiently reaching dissipative scales. In two dimensions, as long as there are no lateral walls, an opposite phenomenon is known to occur: small vortices coalesce to form very stable large vortices, eventually forming a gigantic vortex that occupies the entire ocean basin, with the total energy continuously increasing due to ineffective dissipation.


To prevent the emergence of such unrealistic vortices, existing ocean models must account for 3D effects or add dissipation terms such as friction with the seabed.

This study shows for the first time that these giant vortices cannot form in 2D ocean models that account for lateral walls where velocity drops to zero: low-energy oceanic gyres persist, overlapped by a vigorous gas of localized and intense vortices created along the coasts. Therefore, it is not necessary to invoke an additional dissipation mechanism to explain the stabilization of gyre flows in a turbulent regime.

This work is a first step toward studying the oceanic energy cycle in more realistic models that consider ocean stratification. It is published in the journal Physical Review Fluids.

Reference:
Gyre turbulence: Anomalous dissipation in a two-dimensional ocean model,
Lennard Miller, Bruno Deremble, and Antoine Venaille, Physical Review Fluids, published on May 3, 2024.
Doi: 10.1103/PhysRevFluids.9.L051801
Open archive: arXiv
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