Thomas Peacock

The formation and fate of internal waves in the South China Sea

Internal gravity waves, the subsurface analogue of the familiar surface gravity waves that break on beaches, are ubiquitous in the ocean. Because of their strong vertical and horizontal currents, and the turbulent mixing caused by their breaking, they affect a panoply of ocean processes, such as the supply of nutrients for photosynthesis, sediment and pollutant transport and acoustic transmission; they also pose hazards for man-made structures in the ocean. Generated primarily by the wind and the tides, internal waves can travel thousands of kilometres from their sources before breaking, making it challenging to observe them and to include them in numerical climate models, which are sensitive to their effects. For over a decade, studies have targeted the South China Sea, where the oceans’ most powerful known internal waves are generated in the Luzon Strait and steepen dramatically as they propagate west. Confusion has persisted regarding their mechanism of generation, variability and energy budget, however, owing to the lack of in situ data from the Luzon Strait, where extreme flow conditions make measurements difficult. Here we use new observations and numerical models to (1) show that the waves begin as sinusoidal disturbances rather than arising from sharp hydraulic phenomena, (2) reveal the existence of >200-metre-high breaking internal waves in the region of generation that give rise to turbulence levels >10,000 times that in the open ocean, (3) determine that the Kuroshio western boundary current noticeably refracts the internal wave field emanating from the Luzon Strait, and (4) demonstrate a factor-of-two agreement between modelled and observed energy fluxes, which allows us to produce an observationally supported energy budget of the region. Together, these findings give a cradle-to-grave picture of internal waves on a basin scale, which will support further improvements of their representation in numerical climate predictions.

Properties of the water column and bottom derived from Airborne Visible Infrared Imaging Spectrometer (AVIRIS) data

Using Airborne Visible Infrared Imaging Spectrometer (AVIRIS) data as an example, we show in this study that the properties of the water column and bottom of a large, shallow area can be adequately retrieved using a model-driven optimization technique. The simultaneously derived properties include bottom depth, bottom albedo, and water absorption and backscattering coefficients, which in turn could be used to derive concentrations of chlorophyll, dissolved organic matter, and suspended sediments in the water column. The derived bottom depths were compared with a bathymetry chart and a boat survey and were found to agree very well. Also, the derived bottom albedo image shows clear spatial patterns, with end-members consistent with sand and seagrass. The image of absorption and backscattering coefficients indicates that the water is quite horizontally mixed. Without bottom corrections, chlorophyll a retrievals were ∼50 mg m−3, while the retrievals after bottom corrections were tenfold less, approximating real values. These results suggest that the model and approach used work very well for the retrieval of subsurface properties of shallow-water environments even for rather turbid environments like Tampa Bay, Florida.

Tidal Conversion by Supercritical Topography

Calculations are presented of the rate of energy conversion of the barotropic tide into internal gravity waves above topography on the ocean floor. The ocean is treated as infinitely deep, and the topography consists of periodic obstructions; a Green function method is used to construct the scattered wavefield. The calculations extend the previous results of Balmforth et al. for subcritical topography (wherein waves propagate along rays whose slopes exceed that of the topography everywhere), by allowing the obstacles to be arbitrarily steep or supercritical (so waves propagate at shallower angles than the topographic slopes and are scattered both up and down). A complicated pattern is found for the dependence of energy conversion on e, the ratio of maximum topographic slope to wave slope, and the ratio of obstacle amplitude and separation. This results from a sequence of constructive and destructive interferences between scattered waves that has implications for computing tidal conversion rates for the global ocean.

Introduction to Focus Issue: Lagrangian Coherent Structures

The topic of Lagrangian coherent structures (LCS) has been a rapidly growing area of research in nonlinear dynamics for almost a decade. It provides a means to rigorously define and detect transport barriers in dynamical systems with arbitrary time dependence and has a wealth of applications, particularly to fluid flow problems. Here, we give a short introduction to the topic of LCS and review the new work presented in this Focus Issue.

Lagrangian coherent structures: The hidden skeleton of fluid flows

New techniques promise better forecasting of where damaging contaminants in the ocean or atmosphere will end up.

Low-mode Internal Tide Generation by Topography: An Experimental and Numerical Investigation

We analyse the low-mode structure of internal tides generated in laboratory experiments and numerical simulations by a two-dimensional ridge in a channel of finite depth. The height of the ridge is approximately half of the channel depth and the regimes considered span sub- to supercritical topography. For small tidal excursions, of the order of 1 % of the topographic width, our results agree well with linear theory. For larger tidal excursions, up to 15 % of the topographic width, we find that the scaled mode 1 conversion rate decreases by less than 15 %, in spite of nonlinear phenomena that break down the familiar wave-beam structure and generate harmonics and inter-harmonics. Modes two and three, however, are more strongly affected. For this topographic configuration, most of the linear baroclinic energy flux is associated with the mode 1 tide, so our experiments reveal that nonlinear behaviour does not significantly affect the barotropic to baroclinic energy conversion in this regime, which is relevant to large-scale ocean ridges. This may not be the case, however, for smaller scale ridges that generate a response dominated by higher modes.

Internal tide generation by arbitrary two-dimensional topography

To date, analytical models of internal tide generation by two-dimensional ridges have considered only idealized shapes. Here, we advance the Green function approach to address the generation of internal tides by two-dimensional topography of arbitrary shape, employing the Wentzel-Kramers-Brillouin (WKB) approximation to consider the impact of non-uniform stratifications. This allows for a more accurate analytical estimation of tidal conversion rates. Studies of single and double ridges reveal that the conversion rate and the nature of the radiated internal tide can be sensitive to the topographic shape, particularly around criticality and when there is interference between wave fields generated by neighbouring ridges. The method is then applied to the study of two important internal tide generation sites, the Hawaiian and Luzon Ridges, where it captures key features of the generation process.

Visualization of nonlinear effects in reflecting internal wave beams

Recent theoretical and numerical investigations predict that localized nonlinear effects in the overlapping region of an incoming and reflected internal wave beam can radiate higher-harmonic beams. We present the first set of experimental visualizations, obtained using the digital Schlieren method, that confirm the existence of radiated higher-harmonic beams. For arrangements in which the angle of propagation of the second harmonic exceeds the slope angle, radiated beams are visualized. When the propagation angle of the second harmonic deceeds the slope angle no radiated beams are detected, as the associated density gradient perturbations are too weak for the experimental method. The case of a critical slope is also reported.

An Experimental Investigation of Internal Tide Generation by Two-Dimensional Topography

Experimental results of internal tide generation by two-dimensional topography are presented. The synthetic Schlieren technique is used to study the wave fields generated by a Gaussian bump and a knife edge. The data compare well to theoretical predictions, supporting the use of these models to predict tidal conversion rates. In the experiments, viscosity plays an important role in smoothing the wave fields, which heals the singularities that can appear in inviscid theory and suppresses secondary instabilities of the experimental wave field.

Enhanced drag of a sphere settling in a stratified fluid at small Reynolds numbers

We present a combined experimental and numerical investigation of a sphere settling in a linearly stratified fluid at small Reynolds numbers. Using time-lapse photography and numerical modelling, we observed and quantified an increase in drag due to stratification. For a salt stratification, the normalized added drag coefficient scales as Ri 0.51 , where Ri=a 3 N 2 /(νU) is the viscous Richardson number, a the particle radius, U its speed, ν the kinematic fluid viscosity and N the buoyancy frequency. Microscale synthetic schlieren revealed that a settling sphere draws lighter fluid downwards, resulting in a density wake extending tens of particle radii. Analysis of the flow and density fields shows that the added drag results from the buoyancy of the fluid in a region of size (ν/N) 1/2 surrounding the sphere, while the bulk of the wake does not influence drag. A scaling argument is provided to rationalize the observations. The enhanced drag can increase settling times in natural aquatic environments, affecting retention of particles at density interfaces and vertical fluxes of organic matter.