W6: Spectral Energy Fluxes by Wave-Wave Interactions

Principal investigators: Prof. Carsten Eden (Universität Hamburg), Prof. Dirk Olbers (MARUM/University of Bremen), Prof. Nedjeljka Žagar (Universität Hamburg)

The two main wave modes − gravity waves and Rossby waves − govern the circulation in atmosphere and ocean. Although their linear properties are well understood, the role of wave-wave interactions is unknown to a large extent, but it is certainly of major importance for energy transfers in the atmosphere and ocean. In both the atmosphere and ocean, the energy exchange is governed by the same mechanism of the triad interactions, which this subproject aims at understanding better. An improved understanding will be achieved by focusing on the nonlinear interactions involving

  1. internal gravity waves and Rossby waves in the mid-latitude ocean, and
  2. the most energetic waves in the tropical atmosphere.

By focusing on the two unique dynamical regions on the globe – the tropics and mid-latitudes – and by sharing ideas, methods and cross-validation, the results of this subproject will underline not only the energy transfers within and between different wave types but also the transfer to small-scale turbulence by wave breaking in the ocean, from the tropics to extratropics, and from the troposphere to the middle atmosphere. Better understanding and quantification will contribute to improvements in:

  1. parameterizations of wave-wave interactions (subprojects W1, W4, W2, S2),
  2. interpretation of regime decomposition and momentum fluxes (L2),
  3. quantification of the energy cycle in the ocean and atmosphere (W2, L2), and
  4. model evaluation using novel metrics (S1).

Furthermore, wave interactions in the tropics and their intimate coupling to convection will contribute new understanding towards balance theory for the tropics.

IWEM – The Internal Wave Energy Model

We developed the novel numerical Internal Wave Energy Model (IWEM) based in the radiative transfer equation to study the propagation and refraction of internal gravity waves (IGWs) in a meso-scale eddy in the ocean. In its full complexity IWEM includes six dimensions, three in physical x and three in wavenumber k space, in addition to the time dimension, see Fig1. The simulations we present in Sebastia Saez et al. 2023 are the first ones, to our knowledge, to comprehensively describe the evolution of the full IGW spectrum inside a meso-scale coherent eddy, within the WKBJ-approximation, and detail the effects of wave propagation, reflection, refraction, interaction with the mean flow and breaking related to wave dissipation by vertical and horizontal refraction.

Interactions between IGWs and meso-scale eddies, which evolve at much slower time scales, are important for the energy transfers in the ocean, however, these interactions make it challenging to separate, diagnose and quantify the associated oceanic processes. We analyse the free evolution (during six days) of the Garret-Munk model as typical IGW spectrum in the presence of an idealised, stationary, coherent, and cyclonic meso-scale eddy structure motivated from observations in the Canary Current System, which we think is representative for a typical coherent eddy at mid-latitudes, see Fig 2 a).

In Fig 2 b), we show that lateral shear leads to wave energy gain due to a developing horizontal anisotropy in the IGW spectrum outside the eddy and at the rim, while vertical shear leads to wave energy loss which is enhanced at the eddy rim. Wave energy loss by wave dissipation due to vertical shear dominates over horizontal shear. Our results show similar behaviour of the internal gravity wave in a cyclonic as well as an anticyclonic eddy.

Wave dissipation by vertical wave refraction occurs predominantly at the eddy rim near the surface, where waves break and mix density, which can have wide ranging effects on the ocean’s circulation. Related vertical diffusivities are comparable to estimates based on the Munk's Abyssal Recipe. These results are important to understand the ocean’s mixing and energy cycle, and to develop eddy and wave parameterisations.


Fig 1 - Schematic of IWEM, where the physical and wavenumber is represented with open horizontal and wavenumber boundaries (red arrows). Waves dissipate by vertical wave refraction at the vertical wavenumber cut-off (1) and by horizontal wave refraction at the horizontal wavenumber cut-off (2).
a) Speed of the cyclonic eddy. b) Wave energy density after six days of simulation.

Research Stay in San Diego by Pablo Sebastia Saez (May 23)

California Dreamin’

Nods, smiles… How’re the waves? This is the perfect conversation starter for an oceanographer spending the summer in California. Hella chillin, bro!

But let’s get to business… Just a little, after I’ll tell you about the fun part. During the summer of 2023 I spent almost two months at Scripps Institution of Oceanography in San Diego, California. The decision came to life after a brainstorming session with my supervisor on who (a topic-wise related and experienced researcher) and where (an oceanographic institute that could open new doors) could I visit, that could provide further, new, groundbreaking, specialized, state-of-the-art insights about internal gravity waves and their interaction with the background environment. And the winner was … (drum roll, please) Prof. Dr. William R. Young! After developing and proposing a feasable working structure for the research stay and several meetings…, after applying for the visa, finding accomodation, working myself through a whole load of paper work and packing my bags…, I was finally ready to catch this wave, ride it out, and let the californian vibe wash over me.

I went to the US with a clear and clean research topic, but as in surfing, sometimes it’s better to let the wave tune you into the right direction. During long eye-opening discussions with Prof. Young we stumble upon an unresolved problem within the direction of the scope of my dissertation, so we decided to reformulate the research question of my upcoming work.  Within the two months at Scripps I had the chance to get to know other PhDs, PostDocs and professors from various research disciplines. I took advantage and attended seminars offered by both visiting as well as in-house researchers. I joined social events organized by the institute. And I got the great opportunity to present my work, discuss my interests and raise awareness of the research done within TRR181. But most importantly, I came back to Hamburg with far more new and exciting research questions to be answered!

What I liked best?

I arrived in San Diego just on time for ‘May Gray and June Gloom’ with cloudy and cool weather, but we slowly drifted into the summer season with plenty Sunkissed mornings and sunset wave rides. These together with endless nature getaways, road trips around Southern California and the legendary TGF were the highlights of this amazing journey! There remains naught else for me to express but my gratitude to the TRR181.

  • Sebastia Saez, P., Eden, C. & Chouksey, M. (2024). The evolution of internal gravity waves in meso-scale eddies. J. Phys. Ocean., accepted.

  • Mahó, S.I., Vasylkevych, S. & Žagar, N. (2024). Excitation of mixed Rossby-gravity waves by wave-mean flow interactions on the sphere. Quarterly Journal of the Royal Meteorological Society, under revision. 

  • Chouksey, M., Eden, C., Masur, G. & Oliver, M. (2023). A comparison of methods to balance geophysical flows. J. Fluid Mech. 971, A2, doi: https://doi.org/10.1017/jfm.2023.602

  • Olbers, D., Pollmann, F., Patel, A. & Eden, C. (2023). A model of energy and spectral shape for the internal gravity wave field in the deep-sea – The parametric IDEMIX model. J. Phys.Oceanogr. 53(5), doi: https://doi.org/10.1175/JPO-D-22-0147.1.

  • Denamiel, C., Vasylkevych, S., Žagar, N., Zemunik, P. & Vilibić, I. (2023). Destructive potential of planetary meteotsunami waves beyond the Hunga Tonga–Hunga Ha’apai volcano eruption. B. Am. Meteorol. Soc. 104(1), E178–E191, doi: https://doi.org/10.1175/BAMS-D-22-0164.1.

  • Chouksey, M., Eden, C. & Olbers, D. (2022). Gravity Wave Generation in Balanced Sheared Flow Revisited. J. Phys. Oceanogr. 52, 1351–1362, doi: https://doi.org/10.1175/JPO-D-21-0115.1.

  • Eden, C., Olbers, D. & Eriksen, T. (2021). A closure for lee wave drag on the large-scale ocean circulation. J. Phys. Oceanogr. 51(12), doi: https://doi.org/10.1175/JPO-D-20-0230.1.