Internal waves in the ocean and atmosphere
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 (or here).
Some of our recent work has shown that internal waves generated by tides at the ocean bottom can act to energise the upper ocean eddy field. We are now investigating these internal wave - eddy energy exchanges in the laboratory. Student projects are available on this topic.
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.
Our paper has recently been published in Journal Geophysical Research: Oceans.
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 now 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.
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 oscialltory 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 seperately therefore gives an incorrect answer. We have published new theory (Shakespeare 2020) describing this coupling and are conducting laboratory experiments to verify the theoretical results.
Student projects are available on this topic, including using our long internal wave tank in the GFD Lab.
The dynamics and thermodynamics of the sea surface
The ocean stores the vast majority of the climate system's anthropogenic heat and carbon dioxide. All this heat and CO2 enters through the ocean surface in various ways - but these are poorly understood and poorly represented in models. This work is about understanding the energy and momentum balance operating at the sea surface including the transfers of momentum through the surface, and the interaction of blackbody (longwave) radiation with the sea surface.
A schematic of the different height-scales of sea surface processes is shown below:
This project includes experimental work in the GFD Lab using our custom-built temperature and humidity controlled wind tunnel, theoretical investigations, data analysis and modelling.
A key question to be addressed is "What sets the maximum surface temperature of the ocean?". It is well known that the maximum surface temperature of the ocean is approximately 33 degrees C (see below image), and has been the same value throughout the observational record. So a natural question is: what sets this value, and will it change in a warming climate?
Why is this an important question? Because the ocean surface temperature sets the air temperature in coastal regions. Thus, if the ocean surface temperature warms, so does the air temperature - and if the air temperature increases too much the "human adaptability limit" may be breached. This limit, shown below, is when the combination of air temperature and humidity is too high (defined by a dew point exceeding 35 degrees C) such that humans cannot lose heat via evaporation (sweating), and thus cannot survive outdoors.
Current climate models predict this limit will be breached in some regions by the year 2100: but should we believe these model results? Here we seek to understand the underlying physics.
This is collaborative work with Prof. Michael Roderick. Student projects are available.
Life cycle of spontaneously generated internal waves
Internal waves can be generated spontaneously from unbalaced flow near the ocean surface. Recently we can been examining the energy budget and life cycle of such waves in the ocean, and how they interact with the other (non-wave) flow. As the waves are generated they draw energy from the jets and eddies near the surface. The waves propagate downwards as a concentrated band of energy flux (shown in blue). Some of this energy is lost to dissipation and mixing. However, much of the energy is reflected back off the bottom into an upgoing wave flux (shown in red), Again, some energy is dissipated, but the majority is re-absorbed the near-surface jets and eddies (in a different location to where it was emitted). This "wave life cycle" conflicts the classical picture where energy fluxes are always from jets, eddies and other large-scale flow TO waves, with minimal feedback. What does this new paradigm mean for the ocean energy budget and mixing?
Curved density fronts and eddies: "Cyclogeostrophic frontogenesis"
This project seeks to address the role of curvature in modifying the dynamics of frontal systems. I have developed a simplified axi-symmetric mathematical description of a 'front' --- or equivalently a perfectly circular eddy (Shakespeare 2016). An example of how such a system adjusts from some initial motionless state to a final, balanced state is shown in the image below. The eddy slumps outwards and accelerates until a balance is achieved between the Coriolis, pressure and centripetal forces (known as 'cyclogeostrophic balance').
Curvature has the effect of introducing an asymmetry between eddies (fronts) that have a core warmer than the surrounding fluid and those that have a core colder than the surrounding fluid. Warm-cores have large horizontal flow speeds and are more likely to break down (and do so more rapidly) than cold-cores. However, vertical flow speeds associated with frontal sharpening at of a cold-core is stronger than for a warm-core.
Frontogenesis and wave generation at fronts
(My PhD thesis on this topic is available here)
Frontogenesis is just fancy way of saying "front formation". Fronts, in this context, are regions of sharp density contrast that occur in the ocean and atmosphere boundary layers. They are typically associated with large vertical velocities. In the atmosphere this implies rapidly rising air, and therefore the potential for heavy rain or snow. In the ocean, the large vertical velocities are important for the vertical transport of nutrients, heat and carbon dioxide between the ocean surface and interior.
My frontogenesis research is focused around the following broad areas:
Mechanisms: Frontal sharpening can occur as a result of an initial imbalance. For example, rapid heating of the atmosphere boundary layer can create a thermal imbalance. The boundary layer system then responds in a wave-like manner, similar to the motion of a pendulum displaced from its mean position. The oscillations cause a squeezing together of density surfaces on the boundaries; this is sometimes called "unbalanced frontogenesis". (Blumen, 2001). Frontogenesis can also result from a large scale squeezing of an initially weak density front. For example, weather fronts in the troposphere form due to the squeezing (convergence) between atmospheric high and low pressure systems. In the ocean, eddies and gyres play a similar role. This is sometimes called "balanced frontogenesis" (Hoskins and Bretherton, 1972) or strain-driven frontogenesis. (see Shakespeare and Taylor, 2013)
Scale dependence: As noted above, weather systems, eddies, ocean gyres, etcetera, can all provide strain fields that act to drive frontogenesis. Obviously, each of these flows has a very different "scale". We quantify this scale by the Rossby number, Ro, of the structure (e.g. eddy/gyre). How do the dynamics of frontogenesis depend on this parameter? Of particular interest here is the occurrence of frontogenesis on the ocean submesoscale (typically 1-10km) where Ro is order one. Previous theories have been unable to describe this regime. We find that submesoscale frontogenesis is associated with strong spontaneous wave generation and very large vertical velocities. (see Shakespeare and Taylor, 2014)
Inertia-Gravity Wave generation: The emission of waves from frontal zones provides a potential pathway for the loss of energy from large-scales flows (e.g. mesoscale eddies) , and ultimate dissipation by wave breaking (which also drives mixing). There are a number of mechanisms of wave generation at fronts:
- Initial conditions: *Unbalanced* initial conditions (or equivalently a sudden change in forcing) trigger an adjustment process whereby the system releases energy through wave emission. (see Shakespeare and Taylor, 2013 & 2014)
- Spontaneous: Waves can also be generated spontaneously from a front as strain forces a collapse to small scales. The magnitude of this generation is strongly controlled by the value of the Rossby number, Ro, mentioned above. Spontaneous wave generation associated with frontogenesis may be responsible for the formation of squall lines, which are lines of intense upwelling (and often heavy rainfall) located ahead of atmospheric cold fronts (see Shakespeare and Taylor, 2014). The mechanism of generation is very similar to that of lee wave generation at a rigid obstacle. Waves are generated at the front and trapped in a distinctive "palm-frond" pattern as seen in the simulation shown above (Shakespeare and Taylor 2015 has the details).
Conceptual model of the large-scale ocean circulation
The ocean transports and stores huge quantities of heat, salt, carbon dioxide and many other tracers. This transport is achieved via the Meridional Overturning Circulation. The ocean's role in future climatic changes is closely tied to how this circulation responds to changing surface forcing from the atmosphere. In this project we develop a very simple analytic model of the MOC in the Atlantic basin by parametrising the key processes driving the system and applying simple conservation laws. A schematic of the model is shown in the adjoining figure. Using this model we can test how the the ocean circulation will respond to changes in Southern Ocean winds, as well as the pattern and strength of surface buoyancy fluxes. See Shakespeare and Hogg 2012.
Mode water formation via cabbeling
Cabbeling is the process where two water masses of equal density mix to create a denser water mass owing to non-linearities in the seawater equations of state. Cabbeling is likely to be signficant at Temperature-Salinity (TS) fronts with large temperature contrasts such as the Gulf Stream, Kuroshio, and Subantarctic fronts. Previous work has suggested that cabbeling by itself (i.e. unforced small-scale mixing along density surfaces) will not drive significant water mass transformation. However, this work did not consider the presence of background confluent flows at many of these fronts due to the action of ocean gyres and mesoscale eddies. The confluent flow is able to balance small-scale mixing and give rise to a steady state water mass transformation. We develop a simple idealised model to demonstrate these dynamics (see Thomas and Shakespeare 2015).
More recently we have run idealised numerical simulations in MITgcm (http://mitgcm.org) to illustrate the process (Shakespeare and Thomas 2017) . These simulations resolve the submesoscale eddies that drive mixing and confirm that cabbeling can account for a large fraction of observed mode water formation. A set of 25,000 flow-following parcels from one of these simulations is shown in the image above. The colours indicate the density of the water parcels (red = light, blue = heavy). The large-scale eddy field pushes the parcels in towards the front, which becomes unstable around 50 days, leading to rapid mixing and densification via cabbeling (note the rapid change in the parcel density: colour changes from red to blue).
Some key results:
- Cabbeling at a strained fronts such as the Subantarctic Front or Gulf Stream north wall can drive significant mode water formation. We develop a simple first-order scaling for the water mass transformation.
- Numerical simulations confirm that cabbeling can drive large water mass transformations.
- The cabbeling mechanism is likely play a first-order role in setting the properties of mode waters in the oceans.