W2: Scattering and Refraction of Low-Mode Internal Tides by Interaction With Mesoscale Eddies

Principal investigators: Dr. Janna Köhler (MARUM/University of Bremen), Prof. Dirk Olbers (MARUM/University of Bremen), Prof. Monika Rhein (MARUM/University of Bremen), Prof. Jin-Song von Storch (Max Planck Institute for Meteorology)

Internal gravity waves in the ocean are generated by tides, wind, and interaction of currents with rough seafloor topography. Models predict a global energy supply for the internal wave field of about 0.7–1.3 TW by the conversion of barotropic tides at mid-ocean ridges and abrupt topographic features. Winds acting on the oceanic mixed layer contribute 0.3–1.5 TW and mesoscale flow over rough topography adds an additional amount of 0.2 TW. Globally, 1–2 TW are needed to maintain the observed stratification of the deep ocean by diapycnal mixing that results from the breaking of internal waves. Ocean circulation models show significant impact of the spatial distribution of internal wave dissipation and mixing on the ocean state, e.g. thermal structure, stratification, and meridional overturning circulation.

The scattering and refraction of low-mode internal tides by interactions with mesoscale eddies provides a direct and important energetic link between mesoscale processes and the internal wavefield. Despite their relevance for the geographical distribution and intensity of mixing in the ocean, these processes have not been well studied or understood. In the second phase of the TRR181 W2 aims to improve our understanding of the involved processes and to quantify the eddy-induced changes in the magnitude, direction, and vertical structure of internal tides in the mid-latitude ocean.

For this we will combine
(a) In-situ observations to infer eddy-induced refraction and changes in the vertical structure and magnitude of the internal tides, dissipation rates from finestructure, and spectral energy transfers.
(b) An ICON-o telescope simulation with a resolution of up to O(500m) that will include tides, resolve higher vertical modes and simulate interactions between eddies and internal tides.
(c) Kinetic equations in a modal framework, evaluated for different parameters of the eddy field to estimate the energy transfer between tide and eddies.

The Walvis Ridge region in the southeast Atlantic (Fig. 1) is chosen as a representative for the mid- latitude open ocean as here energetic low-mode \(M_{2}\) internal tides propagate away from the ridge and cross the path of eddies in the form of both Agulhas rings and other mesoscale features.

Fig. 1: M2 internal tide energy flux from STORMTIDE in the background showing the energetic low-mode internal tides generated at Walvis Ridge. Green stars denote positions of the planned moorings, white dots those of the PIES. The main pathway of the eddies is shown as blue shading, the black box denotes the focus area of the CRC SONETT cruise.

Low-mode internal waves in the ocean possess a simple vertical structure, and hold a large part of the total energy of the internal wave field. They are able to travel basin-wide before they are dissipated. The spatial distribution of mixing related to internal wave dissipation affects the global overturning circulation in numerical models, but the observation as well as the representation of internal waves in ocean general circulation models (OGCMs) is still challenging.

To improve our understanding of the life cycle of internal waves, we studied the radiated low mode internal waves including processes operating along their paths. To identify sources and sinks, as well as to quantify the contribution to local dissipation, in-situ hydrographic measurements were combined with observations of internal wave energy fluxes based on satellite altimetry and STORMTIDE. STORMTIDE is a 1/10°-simulation from the Max-Planck Institute Ocean Model (MPIOM) forced by the full lunisolar tidal potential that resolves low-mode internal waves. A realistic surface forcing with 6-hourly wind stress was included in STORMTIDE2, currently the only global OGCM that is driven by tidal and wind forcing. The region of in-situ observations was south of the Azores in the NE Atlantic, where the satellite altimetry and STORMTIDE show beams of converging low mode internal waves generated at a seamount chain.

The modal structure of the internal tide energy flux is important for the ratio of local (close to the generation site) to remote energy dissipation, as low-mode internal waves are less prone to breaking and more likely to propagate over large distances compared to waves with a complex vertical structure. Our in-situ observations show that even close to the generation site, the energy flux is primarily contained in the first mode and thus likely to propagate over long distances before dissipating. Superposition of modes 1 and 2 captures over 84% of the total energy flux, indicating that OGCMs that resolve the first two modes are potentially able to capture the main characteristics of internal tide energy fluxes related to topography on scales typical for seamounts.

Fig. 1: (left) M2 internal tide energy flux from in-situ observations (red arrows) and STORMTIDE (background); (right) comparison of internal tide energy fluxes in STORMTIDE and from satellite altimetry: STORMTIDE shows high values close to the generation sites, while in the altimetry higher fluxes persist over longer distances. Adapted from Köhler et al. 2019.

The direct comparison of the energy fluxes from the in-situ measurements, satellite altimetry, and OGCM shows that in-situ fluxes are generally higher than the corresponding fluxes in STORMTIDE and those derived from altimetry (Fig 1). Differences between in-situ data and altimetry are expected since the spatial resolution of satellite data limits the resolution of the inferred energy fluxes. The long-range propagation of the internal tides observed in altimetry generally agrees with the results from the in-situ measurements, although the in-situ energy fluxes are more variable and show a less monotonic decrease away from the generation sites. STORMTIDE resolves small scale structures in the energy flux distribution, but high energy fluxes are restricted to the vicinity of the generation sites.

The simulated internal-tide generation was further quantified in a more detailed way, requiring 3-dimensional high-resolution data, not easily achievable from available observations. We showed, using STORMTIDE2, that the \(M_{2}\)internal tide generation is characterized by a systematic pressure drop from the upstream to the downstream side of an obstacle (seamount, ridge), consistent with theoretical considerations. Generation is affected by both the tidal velocity and the topographic slope, although the former is dominant. This dominance arises not only because the internal-tide generation varies linearly with topographic slope but essentially quadratically with tidal velocity, but also because the tidal velocity can change up to one order of magnitude from the top to the foot of a high ridge. STORMTIDE2 shows that the intense generation occurs near the summits of the major high underwater ridges and rises, leading to an \(M_{2}\)internal-tide generation being strongest above 1200 m and weakening drastically below 3000m.

Fig. 2: (a) Eddy kinetic energy (EKE) at the mooring location (30.48°N, 30.12°W) from the moored current meters and from CMEMS satellite data (red line in b). (b) Modal decomposition of observed energy flux of the semidiurnal internal tide. Different background colors indicate eddy activity: yellow = surface eddy; blue = subsurface eddy; white = no eddy. From Löb et al. 2020.

While the in-situ study region south of the Azores was chosen because of the unimpaired spreading of internal tides after generation, a mooring time series reveals the presence of eddies during two time periods (Fig. 2): one surface intensified eddy with a maximum horizontal velocity of approx. 20 cm s-1, and a weaker subsurface one. The temporal variability in the time series of energy flux is dominated by two factors: A strong coupling of the flux magnitude to the spring-neap variability in the barotropic tidal forcing (Fig. 2), and the decrease of energy flux during phases of higher eddy kinetic energy. Especially the surface-intensified eddy is correlated with a significant weakening of the energy flux compared to the time period with no eddy activity (Fig. 2). A potential transfer of internal tide energy from modes 1 and 2 into higher mode internal waves would result in a changed ratio of local to remote energy dissipation and hence be important for the global distribution of internal wave energy.

Whether the decrease in the low-mode internal tide energy flux observed in the mooring time series is due to increased dissipation, refraction or scattering of energy into higher modes is the subject of the 2nd phase.

Investigating internal wave energy fluxes

In my current work, I also look into the impact of mesoscale motion on the energy flux in this dataset.

Jonas Löb, PhD W2

My name is Jonas and I am a PhD Student in the subproject W2 “Low mode waves” in the working group Oceanography at the University Bremen. In this project I calculate low mode internal wave energy fluxes from mooring measurements and compare the results with measurements from satellite altimetry and a 1/10° ocean model (STORMTIDE2). Energy flux is an important quantity for these models because its divergence identifies sources and sinks.

Internal gravity waves occur all over the stratified ocean and can be grouped in different categories varying on their generation mechanism. I focus mainly on internal tides in the semidiurnal frequency M2 generated by the barotropic tides over rough topography. Internal tides are a response of the astronomical gravitational forces of the ocean via oscillations in the sea surface elevation with horizontal tidal currents through the entire water column. These waves in the stratified ocean take the form of standing vertical oscillations of horizontal currents, called modes. The “zeroth” (barotropic) mode of horizontal velocity corresponds to horizontal ocean currents that are uniform from top to bottom. The first depth dependent (baroclinic) mode is characterized by flow in one direction at the top and in the opposite direct at the bottom. Higher modes have a more complicated vertical structure and their phase speed decreases with increasing mode number. The vertical structure of a mode can be calculated by the stratification, and velocity profiles can be fitted onto a linear combination of these modes. Low mode motions contain appreciable energy but quickly propagate away laterally. To study these low mode internal waves, we deployed a mooring inside a tidal beam in the eastern North Atlantic, south of the Azores, where a seamount chain stands out as a generation site for internal tides. In our study region the energy flux correlates reasonably well in direction, coherent – uncoherent portioning and mode ratio between mooring and model time series and satellite data. With regard to the total energy flux, the model and satellite observations underestimate the flux compared to the in situ data.

In my current work, I also look into the impact of mesoscale motion on the energy flux in this dataset. A surface eddy was crossing the mooring, and in the process dampening the energy flux in the first two modes by about one third, while a passing subsurface eddy dampened the energy mainly in the second mode. These observations support the idea that eddy interactions transfer energy from low modes into higher modes that can lead to increased dissipation. An open question is how much of the energy converted from lower to higher modes result in local dissipation, which is a crucial information in creating energy consistent ocean-climate models.

The fate of low mode internal tides

The major goal of our subproject is to study the fate of low mode internal tides and the processes that operate along their pathways.

Janna Köhler, Postdoc in W2

I am an observational physical oceanographer working as a Postdoc at the University Bremen. Prior to joining the TRR I mainly studied temporal variability of internal waves using time series of moored instruments, and related the observed changes in the internal wave energy to generation processes such as topography-current interaction or energy input into the internal wave field by the wind.

In the TRR I am part of the subproject W2 “Energy transfer through low mode internal waves”. Low mode internal waves possess a major part of the entire energy of the internal wave field, which makes them an important component of the oceanic energy pathways.

The major goal of our subproject is to study the fate of low mode internal tides and the processes that operate along their pathways. A seamount south of the Azores provides a good study case for these processes, as it is one of the main generation sites of internal tides in the Atlantic. Here we will conduct shipboard measurements and deploy a mooring for about one year to study spatial and temporal variability of internal tide energy. We will then compare the observed spatial and temporal variability along the tidal beam with output of dedicated runs of the STORMTIDE model carried out by our project partners at the MPI in Hamburg.


M2 internal tide energy flux from the STORMTIDE model (Müller 2013) with the planned cruise track (white line) and mooring position (black triangle). References: Müller, M. "On the space-and time-dependence of barotropic-to-baroclinic tidal energy conversion." Ocean Modelling 72 (2013): 242-252.