Internal waves

The ocean is a sea of internal gravity waves. Similar to the gravity waves that propagate over the ocean surface and break along our coastlines, internal waves propagate great distances through the ocean interior. These waves are generated at the ocean surface and the seafloor by a variety of mechanisms. As the waves propagate, they interact with the ocean currents, jets and eddies. These interactions often involve an exchange of energy either to the internal waves (amplifying them) or away from the waves (weakening them). The location and direction of these energy exchanges tell us about the pathways by which energy moves through the ocean system from the very largest scales where it is injected by tides and winds, to the very smallest scales where it is dissipated as heat. A general introduction to internal waves can be found in my Physics Today article here.

Internal waves and coral

Can the mixing driven by internal waves create localised refuges for coral as the climate warms? Myself -- and collaborators at the National Centre for Atmospheric Research in the USA -- have been looking at this problem using high resolution numerical modelling of the Indonesian seas. Our results are consistent with observations showing healthier corals in coastal regions exposed to internal waves and tides (Schmidt et al, 2016).Thus, internal waves may provide a mechanism to create localised refuges for coral as the climate warms, since coral in these refuges will experience reduced heat stress and bleaching. See our paper in the Journal Geophysical Research: Oceans.

Lagrangian Filtering

Quantifying the interactions of internal waves with other flows requires a method of uniquely identifying the internal wave component in flow fields output from numerical simulations. Our group has developed a novel technique for doing this called Lagrangian filtering -- which is available as a parallelised Python package (see GitHub for the latest version and documentation). I describe more about this method in a conference presentation which you can watch on YouTube. A methods paper is published in JAMES

Internal wave generation in the presence of both steady and oscillatory flows

The generation of internal waves at mountains on the seafloor is an important source of bottom-intensified mixing and a sink of geostrophic momentum. The flow over these mountains is almost always a combination of an oscillatory component due to the ocean tides, and a steady component due to the slower mean and eddying ocean flows.  Previous work has considered wave generation by either one or the other flows, but not both together. However, it turns out the the two are coupled, and considering them separately therefore gives an incorrect answer. We have published new theory (Shakespeare 2020) describing this coupling and have conducted laboratory experiments to verify the theoretical results (Dossmann et al, 2020).

Wave-mean interactions

Internal waves often exchange energy with other flows in via so-called 'wave-mean interactions'. This energy can be transferred in either direction, depending on the details of the situation. In recent work, I have demonstrated a robust mechanism by which internal waves generated by the tide at hills on the seafloor can consistently lose their energy to the upper ocean eddy field, amplifying eddy energy and decreasing eddy lifetimes. I describe this as the 'wave forcing' of the ocean eddy field and it may play a key role in eddy lifecycles in regions with strong tides.

Recent papers:

• Shakespeare, Callum J. "Eddy acceleration and decay driven by internal tides." Journal of Physical Oceanography (2023)
• Rama, Jemima, Callum J. Shakespeare, and Andrew McC. Hogg. "Importance of background vorticity effect and Doppler shift in defining near‐inertial internal waves." Geophysical Research Letters (2022)
• Shakespeare, Callum J., Brian K. Arbic, and Andrew McC. Hogg. "Dissipating and reflecting internal waves." Journal of Physical Oceanography (2021)
• Shakespeare, Callum J., Angus H. Gibson, Andrew McC. Hogg, Scott D. Bachman, Shane R. Keating, and Nick Velzeboer. "A New Open Source Implementation of Lagrangian Filtering: A Method to Identify Internal Waves in High‐Resolution Simulations." Journal of Advances in Modeling Earth Systems (2021)
• Shakespeare, Callum J., Brian K. Arbic, and Andrew McC. Hogg. "The Impact of Abyssal Hill Roughness on the Benthic Tide." Journal of Advances in Modeling Earth Systems 13.5 (2021)
• Shakespeare, Callum J. "Interdependence of internal tide and lee wave generation at abyssal hills: Global calculations." Journal of Physical Oceanography (2020)
• Shakespeare, Callum J., Brian K. Arbic, and Andrew McC. Hogg. "The drag on the barotropic tide due to the generation of baroclinic motion." Journal of Physical Oceanography 50.12 (2020)
• Shakespeare, Callum J., and Andrew McC Hogg. "On the momentum flux of internal tides." Journal of Physical Oceanography (2019) 

Longwave radiation and climate sensitivity

All objects emit radiation: hotter objects (like the sun) emit shorter wavelengths, while cooler objects (like the atmosphere on Earth) emit longer wavelengths. This 'longwave radiation' from the air above is one of the major components in the balance of energy fluxes at the Earth's surface, which determine the air temperature we all experience. It is well known that as CO₂ levels rise in the atmosphere, longwave radiation increases, and it is sometimes argued that this enhanced radiation represents an independent forcing of the surface (e.g., this is assumed in standalone ocean, land and ice-sheet models). However, our recent work in the Journal of Climate shows that over 90% of the increase in longwave is a indirect feedback due to increases in the surface temperature. Therefore, to ensure accurate, physically correct results, all models should include these feedback effects. This analysis uses a classic forcing-feedback approach to the surface energy budget, building on a semi-analytical model for downwelling longwave radiation we developed in related work (see papers below). Recently, my student Koh Kawaguchi has updated this model to more accurately include the effects of clouds. I talk about some of this work in an RSES School Seminar here.

Recent papers:

• Kawaguchi, Koh, Callum J. Shakespeare, and Michael L. Roderick. "CO2 dependence in global estimation of all‐sky downwelling longwave: Parameterization and model comparison." Geophysical Research Letters (2024)
• Shakespeare, Callum J., and Michael L. Roderick. "Diagnosing instantaneous forcing and feedbacks of downwelling longwave radiation at the surface: a simple methodology and its application to CMIP5 models." Journal of Climate (2022)
• Shakespeare, Callum J., and Michael L. Roderick. "The clear‐sky downwelling long‐wave radiation at the surface in current and future climates." Quarterly Journal of the Royal Meteorological Society (2021)

Air-sea fluxes, boundary layer process and atmospheric dynamics

The vast majority of the Earth's heat capacity is within the global oceans. As such, climate change (on long timescales) is really about ocean change, with the atmosphere then equilibrating with the ocean through the transfer of heat energy across the air-sea interface. Therefore, a precise and accurate representations of air-sea fluxes (e.g., longwave and shortwave radiation, sensible and latent heat transfer) is critical to the accurate modelling of climate change. As one part of this work, we are conducting experimental work in the CFP Lab focused on testing and improving the 'bulk formulae' used to calculate these fluxes of heat and moisture across the air-sea interface. In another, we are investigating constraints on air-sea fluxes and near-surface air properties imposed by the moist convection over the ocean surface; for instance, explaining the rather remarkable fact that the relative humidity near to ocean surface is always approximately 80%.

Recent papers:

• Shakespeare, Callum J., and Michael L. Roderick. "The probability distribution of relative humidity in the lower troposphere." Quarterly Journal of the Royal Meteorological Society (2025)
• Roderick, Michael L., and Callum J. Shakespeare. "Technical note: An assessment of the relative contribution of the Soret effect to open water evaporation." Hydrology and Earth System Sciences (2025)
• Shakespeare, Callum J., and Michael L. Roderick. "What Controls Near‐Surface Relative Humidity Over the Ocean?" Journal of Advances in Modeling Earth Systems (2024)
• Roderick, Michael L., Chathuranga Jayarathne, Angus J. Rummery, and Callum J. Shakespeare. "Evaluation of a wind tunnel designed to investigate the response of evaporation to changes in the incoming long-wave radiation at a water surface." Atmospheric Measurement Techniques (2023)

Ice-ocean interactions

The rate at which Antarctica's giant ice sheet melts depends critically on turbulent processes occurring at the centimetre scale. My PhD student Jim Sweetman has been using laboratory experiments to investigate how different environmental factors (such as the stratification and surface waves) impact these finescale dynamics at the ice-ocean interface and thereby modulate melting.

In other work, we are examining how sea ice grows under different conditions (such as on the side vs. bottom of a floe) and seeking to better understand the thermodynamic properties of the ice. Sea ice has a very complicated structure owing to the inclusion of pockets and channels of salty brine within the ice matrix, which makes this a challenging endeavour.

Recent papers:

• Stewart, Kial D., William Palm, Callum J. Shakespeare, and Noa Kraitzman. "The sensitivity of sea-ice brine fraction to the freezing temperature and orientation." Annals of Glaciology (2024)
• Sweetman, James K., Callum J. Shakespeare, Kial D. Stewart, and Craig D. McConnochie. "Laboratory experiments of melting ice in warm salt-stratified environments." Journal of Fluid Mechanics (2024)