High-resolution modelling of near-inertial waves in the ocean

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


The combination of the ocean's density stratification and the earth's rotation results in the existence of waves, termed inertia-gravity waves, which propagate through the whole depth of the ocean and make a large contribution to its energy. Most of the energy of inertia-gravity waves is in fact contained in the waves with the lowest frequencies: these are the inertial waves at the centre of this project. Inertial waves, which are generated by wind at the ocean's surface, are highly energetic and susceptible to instabilities which induce turbulence and mixing. Because they are the primary source of vertical mixing below the immediate top layer of the ocean, inertial waves are crucially important for the dispersion of pollutants and for biological activity. More surprisingly perhaps, they are also crucial in establishing the density stratification of the deep ocean. As a result, they have a strong influence on the large-scale circulation of the ocean and thereby on the earth's climate. It is therefore very important that the numerical models that are used for climate predictions take into account the effect of inertial waves. This is challenging, however. Because the scales of the inertial waves are much smaller than the typical scales of the ocean's circulation, it is not possible for climate models to describe fully (i.e., to resolve) the details of the motion associated with the waves. Instead, the models must represent the large-scale, global effect of the waves and relate this effect to the processes which they describe well, such as the surface winds and large-scale currents. This is the role of parameterisation schemes, which are one of the most important (and delicate) components of climate models.

To be accurate and robust, these parameterisation schemes must be based on a sound understanding of the unresolved phenomena they represent. This project will build this understanding for wind-generated inertial waves. It will start by the development of a new numerical model specifically dedicated to the study of inertial waves. This model makes a number of simplifications tailored to inertial waves; thanks to these simplifications, its computational cost is much lower than that of traditional models. It will therefore provide a unique, highly efficient tool for the study of inertial waves. It will be benchmarked against the results of more costly models and against a series of measurements made by drifters floating near the ocean's surface. The propagation of inertial waves through the ocean will then be examined. Three specific aspects will be considered: the influence of currents with small vertical scales, the scattering and dissipation of the waves near the bottom topography, and the direct large-scale forcing induced by dissipating inertial waves. This will lead to a greatly improved understanding of the dynamics of inertial waves and pave the way for the design of parameterisation schemes to be implemented in climate models and in regional ocean models.

Planned Impact

In addition to the academic beneficiaries above, the following beneficiaries can be identified:

1. Climate scientists who rely on general circulation models as their main tool for the prediction of future climate and for the analysis of mitigation scenarios. They will be able to implement the new parameterisation schemes that we expect to flow from the results of the research and will benefit from the improvements in model performances that these will bring about.

2. Decision makers who act on the advice of the climate scientists in 1, and the general public whose lives will be affected by the future climate. They will benefit from the more reliable predictions derived from improved climate models.

3. Environmental agencies, industries which pose a pollution risk for the ocean and, by extension, decision-makers and the general public: they will benefit from the better representation of turbulent mixing in regional ocean models that may result from the research.
Description 1. Study of the Young-Ben Jelloul model of near-inertial waves has identified a new energy-like conservation law. This can exploited to explain the observed concentration of near-inertial activity in anticyclones at the surface of the ocean (joint work with Oliver Buhler, Courant).

2. A model based on Wigner-function representation has been developed to explain the relative inefficient scale cascade of near-inertial waves in complex flows (modelled here by random fields).

3. A model of the coupling between near-inertial waves and mesoscale motion has been derived and studied. This model is based on the generalised Lagrangian mean theory. It has enabled the identification of a new mechanism of interaction whereby large-scale near-inertial waves forced by wind extract energy from the mesoscale motion as their scale gets reduced by advection and refraction by the mesoscale flow. The mechanism is very interesting: there is a great deal of uncertainty about the processes that dissipate mesoscale energy, and the mechanism identified could be a significant player. (Joint work with PhD student J-H Xie).
Exploitation Route Models motivated by 3 above are currently being developed at Scripps. The mechanism described in 3 will be taken into account in global energy budgets of the ocean.
Sectors Environment

Description NSFGEO-NERC
Amount £280,000 (GBP)
Organisation Natural Environment Research Council 
Sector Public
Country United Kingdom
Start 07/2018 
End 07/2021
Title Scattering of inertial waves by random flows 
Description This dataset contains a matlab code that simulates the Young and Ben Jelloul equation for inertial waves propagating in a 2D flow. Also attached is a program to generate a 2D gaussian random flow, and a routine to calculate the eigenvalues of the scattering operator (see article arxiv.org/abs/1510.00784 ) 
Type Of Technology Software 
Year Produced 2016 
Open Source License? Yes