Geostrophic Turbulence and Mechanical Energy Budgets from Satellite Altimetry
The University of Texas at Austin,
4412 Spicewood Springs Rd.,
Austin, TX 78759,
Utilizing over a decade of satellite observations of sea surface height we are studying the World Ocean’s kinetic energy cascade of the surface geostrophic flow. This has allowed for the first direct confirmation of one of the most fundamental predictions of geostrophic turbulence theory, but also challenged other aspects of the theory. It’s also providing new insight into the oceanic mechanical energy budget and sources of diapycnal mixing.
The last 38 years have seen considerable development in the theory and phenomenology of the geostrophic turbulence, the turbulence that governs large scale atmospheric and oceanic flow. Numerical simulations of simplified equations in idealized domains have remained the primary tool of investigation. While laboratory experiments helped to ground ideas in reality, questions of the applicability to real geophysical flows inevitably remained. Before the advent of satellite altimetry, there simply was not sufficient observational data to test these theories in the ocean, one of the major systems they’re supposed to describe. Using satellite altimeter data, we estimated the spectral kinetic energy flux, i.e. the flux of energy from scales with total horizontal wavelength greater than λ to scales with wavelength less than λ, for λ from several thousand km to less than a hundred km. Some of our key results are summarized below:
1) A near universal shape of the spectral kinetic energy flux was found that provides direct evidence of a source of kinetic energy near to or smaller than the deformation radius, consistent with linear instability theory. This suggests baroclinic instability is a ubiquitous source of kinetic energy everywhere except the equatorial region.
2) No inertial range was found, implying inertial range scaling, such as the established K-5/3 slope of spectral kinetic energy density, is not applicable to the surface geostrophic flow.
3) We also found a net inverse cascade (i.e. a cascade to larger spatial scale), consistent with strictly two-dimensional turbulence phenomenology. But stratified geostrophic turbulence theory predicts an inverse cascade for the barotropic mode only while energy in the large scale baroclinic modes is predicted to undergo a direct cascade towards the first mode deformation scale. Thus if the surface geostrophic flow is predominately the first baroclinic mode, as expected for oceanic stratification, then the observed inverse cascade contradicts geostrophic turbulence theory. Furthermore the inverse cascade arrest scale does not follow the Rhines scale, as one would expect for the barotropic mode. A revision of theory was proposed that resolved these conflicts. Subsequent idealized modeling experiments have confirmed the revision, providing an example of where satellite altimetry has successfully guided geostrophic turbulence research.
The measurement of the kinetic energy cascade and its interpretation in terms of geostrophic turbulence theory is finding its most immediate application in quantifying the mechanical energy budget of the World Ocean, and uncovering the pathways from large scale forcing to small scale dissipation. Key quantities, such as the conversion rate from gravitational potential to kinetic energy and the ratio of kinetic energy cascading to small scales versus large scales, that could not previously be measured, are now being estimated using satellite altimetry. This information is of great interest to understanding the source of diapycnal mixing responsible for driving the thermohaline circulation.