L3: Meso- to Submesoscale Turbulence in the Ocean

Principal investigators: Dr. Alexa Griesel (Universität Hamburg), Dr. Maren Walter (MARUM/University of Bremen)

The energy cycle in ocean models is still biased due to the large uncertainty regarding how processes in the mesoscale and submesoscale regimes are represented. Since mesoscale turbulence is largely geostrophic, it features an energy transfer towards larger scales. In contrast, submesoscale turbulence can contain both geostrophic and ageostrophic dynamics which makes the direction of the energy flux less clear. Measuring the kinetic energy spectrum in the ocean is challenging, since gridded satellite data are unable to resolve the subdeformation scales, and shipboard measurements are limited to a few regions. Lagrangian floats are globally available, can connect a range of scales from 10 m to 1000 km and hence are a unique source of information on mesoto submesoscale turbulence.

The goals of L3 are to observe the upper-ocean energy spectrum by using Lagrangian surface drifters, and other available observations, to investigate the direction of the energy flux in different dynamical conditions, and to quantify energy dissipation (transfer) rates. High-resolution models will serve as a Euclidean supplement and a testbed for the interpretation of the observations.

In the first phase, we assessed turbulence regimes with a focus on the Benguela upwelling region. Using a new scaling method and with adequate subsampling of the deployed surface drifters, we estimated a consistent energy transfer rate and identified an inverse cascade for scales 30-500 km close to the upwelling current. In addition, we assessed quasigeostrophic linear theory for the parameterization of the effects of mesoscale eddies and produced global maps of eddy diffusivities from an eddying ocean model that can be used to assess the parameterization of mesoscale eddies in the diffusive limit.

In the second phase, we will extend the Lagrangian analyses and apply the structure-function diagnostic (in addition to the classical Lagrangian dispersion estimates) in an area offshore from the Benguela region that is characterized by high internal tide and eddy activity but without a deep baroclinic current. In a concerted effort (targeted measurements with gliders, ship ADCP, drifters) we will quantify horizontal wavenumber spectra for the upper ocean in theWalvis Ridge Region in close collaboration with W5 and W2. The subsampling methods developed from the analyses in the Benguela and Walvis Ridge regions, together with high-resolution modelling, will be used to extrapolate to the global ocean using the global drifter program.

This project will complement L2 from the observational side and by different statistical analysis. This project will complement T2 in the quantification of wavenumber spectra and cascade directions. It will serve as input on the spatial variability of dissipation rates for T2. This project will supply M3 with a global map of inverse cascade rates to improve and constrain backscattering schemes.

Oceanic eddies, fluctuations on scales on the order of one km to hundreds of km, derive their energy primarily from baroclinic instability processes. It is common to parameterize this loss of available potential energy of the balanced flow in ocean models by an additional eddy-driven advection velocity, or, equivalently a skew diffusivity. In addition, eddies also mix tracers along isopycnals, which is implemented as along-isopycnal diffusion with isopycnal diffusivity. Eddy diffusivities currently are specified in coarse ocean models without connection to the energy budget, and, more fundamentally, it is unclear to what extent, where and on what scales the downgradient eddy-diffusion model is appropriate at all. Rotational components of the eddy fluxes associated with the advective terms in the eddy variance equation are generally large, so that production and dissipation of eddy energy do not balance locally.

Dispersion statistics from Lagrangian numerical particles deployed in the Southern Ocean of an eddying ocean model. Left: Lagrangian diffusivities (upper panel) and Lagrangian velocity autocovariance (lower panel) as a function of time lag at three depth levels for a region southwest of Australia. Right: Lagrangian integral time scale (upper panel) and Lagrangian diffusivity (lower panel) diagnosed from the numerical particle dispersion in bins as a function of depth and longitude along the main jets of the Antarctic Circumpolar Current. The black line is the steering level depth where enhanced mixing is expected from linear theory (from Griesel et al., 2015).

Our main questions are:

  • What is the spatial and temporal variation of eddy-mean flow interactions and scale dependence of eddy diffusivities on a global scale and in one key observational region of the ocean, the Benguela upwelling Current?
  • What are the limits and validities of the eddy diffusion model and consequences for energy-consistent parameterizations of eddy-mean flow interactions across a range of eddy scales?

To address these questions we will use Lagrangian particle statistics in both eddying ocean models and observations to assess the spatial and temporal variability of eddy diffusivities, eddy-mean flow interactions, and submesoscale processes, and to quantify dispersion regimes on different scales to assess the eddy-diffusion model and get insight into energy cascades. In-situ observations and a Lagrangian drifter experiment at the upwelling front in the Benguela current system will  serve as the major observational reference to study the lifetime of meso- and submesoscale features, as well as their dissipation in the interior ocean. Results from the analyses of observations and eddying ocean models will be used to construct energy-consistent parameterizations that use prognostic equations of eddy kinetic energy, taking non-localness into account.

Exemplary sea surface temperature from satellite data off Namibia (MODIS; spatial resolution 4~km) on 5th of January 2012. The blue and green colours clearly show the cold coastal upwelling region as well as the inhomogeneous front at the western boundary of the upwelling system. White colour marks regions which are covered by clouds (no data). Orange stars mark the locations of Walvis Bay (WB) and Luederitz (L).
Snapshot of Sea surface height in January 2000 in the eddying Parallel Ocean Program (POP) model in the Namibian upwelling zone showing cold-core eddies propagating westward encountering warm-core eddies that have propagated from the Agulhas region. Also shown are some of the surface trajectories of the numerical floats.

During the cruise to the Benguela upwelling region off the coast of Namibia from Nov 15- Dec 10, we deployed 37 surface drifters that captured the meso- to submesoscale variability close to the boundary current and along the sampled filament. Together with high-resolution submesoscale permitting modelling of that region and the global eddy-permitting POP we pursued the following goals:

Investigating eddy diffusivitites and eddy-mean flow interactions

Our observational data will serve the model as a reference that includes smaller scales that the model is not able to cover.

Julia Dräger-Dietel, Postdoc in L3

In September 2016 I started working as a postdoctoral researcher in the subproject L3 Diagnosing and parameterising the effects of eddies at the Universität Hamburg with Kerstin Jochumsen from Experimental Oceanography and Alexa Griesel from Theoretical Oceanography. Having a background in nonlinear dynamics and statistical physics in application to complex systems, I am strongly attracted by the aim of our research project and by the possibility to work within an inspiring interdisciplinary research network as created by the TRR181 with its great possibilities for exchange with scientists of different fields.

A major link to my former research consists in the analysis of trajectories (derived from in situ experiments or modeled by stochastic processes) and more specifically the analysis of broad (non Gaussian) Langrangian statistics of absolute and relative dispersion. The goal of our research subproject L3 is the quantification of eddy diffusivities and eddy-mean flow interactions by using Langrangian particles statistics in both eddying ocean models and observations. Its aim is to develop and to test energy consistent parameterisations of meso- and sub-mesoscale processes for the global ocean with a focus on 100 km -1 km scales.

At the beginning I developed and tested float deployment strategies by means of the high resolution POP model. In November/December 2016 our cruise with the RV Meteor took place in the atlantic-sea off the african coast. The cold upwelling front off Namibia's coast in the area of Luderitz has a highly irregular structure due to eddies and filaments, finger-like structures of cold upwelling water pushing west into the warm surface waters offshore (see Figure 1). In our field experiment we explored mesoscale and submesoscale structures within a filament by satellite-tracking 37 surface drifters which we released in groups of triplets. As a first result we find that, due to the underlying rich mesoscale system, the dispersion statistics are very different depending on the location of release. While the drifters of the group released at the southern border of the filament separate slower (Figure 2a), the drifters in the group released closer to the upwelling system at the northern border of the filament separate faster from each other and follow distinct paths within the complex surface currents (Figure 2b). Currently our research focuses on the relative dispersion of drifter pairs (and its corresponding probability density function) as its properties depend on the kinetic energy spectrum. The statistical analyzing of single particle dispersion and the comparison of our findings with dispersion statistics of ocean model will be a next step. Here our observational data will serve the model as a reference that includes smaller scales that the model is not able to cover.

More Information about the research cruise on RV Meteor (M132) including reports, posters and videos of the scientific work have a look have a look at our TRR181 homepage.

Figure 1. Namibia from satellite. The blue colors show the cold upwelling area off Lüderitz and a cold filament (green and yellow).
Figure 2a
Figure 2b