NSFGEO-NERC: Stimulated Loss of Balance

Lead Research Organisation: University of Edinburgh
Department Name: Sch of Mathematics


Recent results obtained by the PIs show that the advection and refraction of near-inertial waves (NIWs) by mesoscale flow is necessarily accompanied by a transfer of energy from the mesoscale to NIWs: the presence of externally forced NIWs stimulates a loss of energy from the geostrophically and hydrostatically balanced component of the flow. This process, stimulated loss of balance (SLOB), should be contrasted with the much more studied and weaker process known as spontaneous loss of balance. The spontaneous version occurs at order one Rossby number and without externally forced waves. But the stimulated version is active even at small Rossby number and hence, we hypothesize, throughout the ocean. The main objectives of this proposal are to assess and develop the hypothesis that SLOB plays a major role in the mesoscale energy budget, and to investigate SLOB by components of the internal wave spectrum other than NIWs, particularly the internal tide (IT). This will be achieved by the development of new, phase-averaged models coupling the dynamics of internal waves with that of the balanced mesoscale flow, and through numerical solution of both these models and of the three-dimensional Boussinesq equations. The outcome will be a quantitative understanding of the role played by SLOB in the ocean energy budget.

Planned Impact

The ocean plays a key role in the Earth's climate through heat transport and carbon uptake. A quantitative understanding of ocean energetics is crucial to modeling its dynamics and predicting its future behaviour. In particular, the reliability of climate predictions depends on the ability of numerical models to accurately represent these pathways in current and future conditions. One outcome of the project will be a new understanding of the energy balance of the ocean and thus the proposed research will have an impact on climate models. Operational ocean models as well as climate models rely on parameterizations of the mixing associated with internal waves. Arguably, the wave feedback studied in this proposal should also be parameterized. Parameterizing either or both effects require a simplified representa- tion of the internal-wave dynamics, which is too fast to be resolved without imposing drastic timestep reduction. The phase-averaged models that we propose to derive represent a first step towards this simplified representation. They provide a rigorously derived foundation for parameterizations (which require further, heuristic simplifications for practical implementation, such as representing the entire wave spectrum by a few discrete components). Thus, by supporting the development of new, improved parameterizations, the proposed research can contribute to the improvement of ocean models and benefit their end-users including the shipping, fishing and energy industries. The project includes the modeling of the propagation of ITs in mesoscale flows. While this modeling is motivated by SLOB, it can have a strong impact on observational oceanography. Specifically, one of the obstacles to the accurate inference of sea-surface velocity from satellite altimetry is the (strongly aliased) tidal signal, especially when this signal loses spatial coher- ence as a result of interaction with and scattering by ocean macroturbulence. Overcoming this obstacle is a pressing need with the forthcoming SWOT mission.


10 25 50

publication icon
Kafiabad H (2019) Diffusion of inertia-gravity waves by geostrophic turbulence in Journal of Fluid Mechanics

publication icon
Gilbert A (2018) Geometric generalised Lagrangian-mean theories in Journal of Fluid Mechanics

publication icon
Kafiabad H (2021) Interaction of near-inertial waves with an anticyclonic vortex in Journal of Physical Oceanography

publication icon
Savva M (2018) Scattering of internal tides by barotropic quasigeostrophic flows in Journal of Fluid Mechanics

publication icon
Kafiabad H (2021) Wave-averaged balance: a simple example in Journal of Fluid Mechanics

Description The project has had two major outcomes. First, we have developed a model for the scattering of atmospheric and oceanic inertia-gravity waves that results from their interactions with eddies and currents. The model makes it possible to predict the energy of these waves as a function of their scale. Remarkably, the model predicts a distribution that matches long-unexplained observations in the atmosphere and ocean. In doing so, our theory provides strong support for the hypothesis that much of the energy at intermediate horizontal scales (from 500-50 km in the atmosphere, from 100 km to 10 km in the ocean) is contained in inertia-gravity waves. Second, we demonstrated how the interaction between oceanic inertial waves and vortices is described accurately by wave-averaged models, including in the nonlinear regime.
Exploitation Route The outcomes might be taken forward by atmosphere and ocean scientists who want to explain the observed distribution of energy as a function of scale. They might also lead to the development of new parameterisations, that is, representation of inertia-gravity waves in numerical models used for weather forecasting, climate prediction and operational oceanography.
Sectors Aerospace

Defence and Marine



Description NSFGEO-NERC
Amount £280,000 (GBP)
Organisation Natural Environment Research Council 
Sector Public
Country United Kingdom
Start 07/2018 
End 07/2021
Description Mecator Fellow of the DFG Research Centre TRR181 'Energy transfer in atmosphere and ocean' 
Organisation University of Hamburg
Country Germany 
Sector Academic/University 
PI Contribution As a result of the work on wave scattering funded by the grant, I was invited to be part of the DGF Research Centre TRR181 'Energy transfer in atmosphere and ocean' as a Mercator Fellow. This gives me access to all future activities of the research centre as well as some funding to attend these activities.
Collaborator Contribution We are currently interacting on a project about ocean diffusivities, with the partner supervising 2 MSc thesis on the topic.
Impact NA
Start Year 2020