S. A. Thorpe

Bio: S. A. Thorpe is an academic researcher from Bangor University. The author has contributed to research in topics: Internal wave & Boundary layer. The author has an hindex of 20, co-authored 21 publications receiving 3276 citations. Previous affiliations of S. A. Thorpe include National Institute of Oceanography, India.

Turbulence and mixing in a Scottish Loch

Abstract: It is nearly three-quarters of a century since E. R. Watson (1904) and E. M. Wedderburn (1907) made the observations in Loch Ness which showed conclusively, and for the first time, that large bodies of water contain beneath their surface the wave motions which have now come to be known as internal waves. The observations and theory of these waves have developed much since those days, but the Loch is still very useful as a site in which to observe and examine phenomena which are also found in other bodies of water, particularly the ocean. In particular the Loch provides a large-scale natural ‘laboratory’ in which a variety of small-scale phenomena associated with turbulence in a stratified fluid may be studied. Observations have been made with a novel profiling instrument which measures the horizontal velocity of the water and its temperature, from which the density may be inferred. These observations serve to illustrate a variety of local conditions which occur in calm weather, as the Loch responds to the wind and during the passage of an internal surge. Analysis of the records is conducted in terms of an intermittency index (the fraction of fluid in which the density decreases with depth), the Richardson number and a length scale which characterizes the vertical scale of the regions which are found to be unstably stratified. Semi-empirical formulae for the eddy diffusion coefficient and the rate of dissipation of kinetic energy in the turbulent motion are examined to see whether they are consistent with observations. No universal value of the Richardson number is found, but this may be a consequence of the rather low values of Reynolds number found in the Loch thermocline.

The Turbulent Ocean

Abstract: The subject of ocean turbulence is in a state of discovery and development with many intellectual challenges. This book describes the principal dynamic processes that control the distribution of turbulence, its dissipation of kinetic energy and its effects on the dispersion of properties such as heat, salinity, and dissolved or suspended matter in the deep ocean, the shallow coastal and the continental shelf seas. It focuses on the measurement of turbulence, and the consequences of turbulent motion in the oceanic boundary layers at the sea surface and near the seabed. Processes are illustrated by examples of laboratory experiments and field observations. The Turbulent Ocean provides an excellent resource for senior undergraduate and graduate courses, as well as an introduction and general overview for researchers. It will be of interest to all those involved in the study of fluid motion, in particular geophysical fluid mechanics, meteorology and the dynamics of lakes.

Experiments on the instability of stratified shear flows: immiscible fluids

Abstract: When a long rectangular tube containing two immiscible fluids is slightly tilted away from the horizontal, a uniformly accelerating flow is produced with shear at the interface. The presence of shear leads to instability, which is characterized by the spontaneous and rapid growth of almost stationary waves if the fluid depths are equal and the density difference small. The conditions for the onset of Kelvin-Helmholtz instability, taking account of the accelerating flow and the presence of a velocity transition region at the interface, are investigated theoretically and comparison made with observations. The time at which instability occurs is quite well predicted by this theory, but the wavelength of the unstable waves is rather greater than predicted in the accelerating flow. The difference between the predictions and observations may be the result of finite amplitude effects or of the development of Tollmien-Schlichting instability before Kelvin-Helmholtz.

A method of producing a shear flow in a stratified fluid

Abstract: When the end of a long closed horizontal tube containing a stratified fluid is raised, a laminar accelerating flow begins. The flow is two-dimensional in the central portion of the tube, and, in this region, it is predictable, at least until the onset of instability. The occurrence of instability, its nature, and the subsequent transition to turbulence, are described qualitatively. The apparatus may be used for the study of a variety of other internal hydraulic phenomena with applications to meteorology and oceanography.

An Introduction to Ocean Turbulence

Abstract: This textbook provides an introduction to turbulent motion occurring naturally in the ocean on scales ranging from millimetres to hundreds of kilometres. It describes turbulence in the mixed boundary layers at the sea surface and seabed, turbulent motion in the density-stratified water between, and the energy sources that support and sustain ocean mixing. Little prior knowledge of physical oceanography is assumed. The text is supported by numerous figures, extensive further reading lists, and more than 50 exercises that are graded in difficulty. Detailed solutions to the exercises are available to instructors online at www.cambridge.org/9780521859486. This textbook is intended for undergraduate courses in physical oceanography, and all students interested in multidisciplinary aspects of how the ocean works, from the shoreline to the deep abyssal plains. It also forms a useful lead-in to the author's more advanced graduate textbook, The Turbulent Ocean (Cambridge University Press, 2005).

Turbulence, Coherent Structures, Dynamical Systems and Symmetry

Abstract: Preface Part I. Turbulence: 1. Introduction 2. Coherent structures 3. Proper orthogonal decomposition 4. Galerkin projection Part II. Dynamical Systems: 5. Qualitative theory 6. Symmetry 7. One-dimensional 'turbulence' 8. Randomly perturbed systems Part III. 9. Low-dimensional Models: 10. Behaviour of the models Part IV. Other Applications and Related Work: 11. Some other fluid problems 12. Review: prospects for rigor Bibliography.

Local and global instabilities in spatially developing flows

Abstract: The goal of this survey is to review recent developments in the hydro­ dynamic stability theory of spatially developing flows pertaining to absolute/convective and local/global instability concepts. We wish to dem­ onstrate how these notions can be used effectively to obtain a qualitative and quantitative description of the spatio-temporal dynamics of open shear flows, such as mixing layers, jets, wakes, boundary layers, plane Poiseuille flow, etc. In this review, we only consider open flows where fluid particles do not remain within the physical domain of interest but are advected through downstream flow boundaries. Thus, for the most part, flows in "boxes" (Rayleigh-Benard convection in finite-size cells, Taylor-Couette flow between concentric rotating cylinders, etc.) are not discussed. Further­ more, the implications of local/global and absolute/convective instability concepts for geophysical flows are only alluded to briefly. In many of the flows of interest here, the mean-velocity profile is non-

Coherent structures and turbulence.

Abstract: This is a personal statement on the present state of understanding of coherent structures, in particular their spatial details and dynamical significance. The characteristic measures of coherent structures are discussed, emphasizing coherent vorticity as the crucial property. We present here a general scheme for educing structures in any transitional or fully turbulent flow. From smoothed vorticity maps in convenient flow planes, this scheme recognizes patterns of the same mode and parameter size, and then phase-aligns and ensemble-averages them to obtain coherent structure measures. The departure of individual realizations from the ensemble average denotes incoherent turbulence. This robust scheme has been used to educe structures from velocity data using a rake of hot wires as well as direct numerical simulations and can educe structures using newer measurement techniques such as digital image processing. Our recent studies of coherent structures in several free shear flows are briefly reviewed. Detailed data in circular and elliptic jets, mixing layers, and a plane wake reveal that incoherent turbulence is produced at the ‘saddles’ and then advected to the ‘centres’ of the structures. The mechanism of production of turbulence in shear layers is the stretching of longitudinal vortices or ‘ribs’ which connect the predominantly spanwise ‘rolls’; the ribs induce spanwise contortions of rolls and cause mixing and dissipation, mostly at points where they connect with rolls. We also briefly discuss the role of coherent structures in aerodynamic noise generation and argue that the structure breakdown process, rather than vortex pairing, is the dominant mechanism of noise generation. The ‘cut-and-connect’ interaction of coherent structures is proposed as a specific mechanism of aerodynamic noise generation, and a simple analytical model of it shows that it can provide acceptable predictions of jet noise. The coherent-structures approach to turbulence, apart from explaining flow physics, has also enabled turbulence management via control of structure evolution and interactions. We also discuss some new ideas under investigation: in particular, helicity as a characteristic property of coherent structures.

Ozone depletion: ultraviolet radiation and phytoplankton biology in antarctic waters.

Abstract: The springtime stratospheric ozone (O3) layer over the Antarctic is thinning by as much as 50 percent, resulting in increased midultraviolet (UVB) radiation reaching the surface of the Southern Ocean. There is concern that phytoplankton communities confined to near-surface waters of the marginal ice zone will be harmed by increased UVB irradiance penetrating the ocean surface, thereby altering the dynamics of Antarctic marine ecosystems. Results from a 6-week cruise (Icecolors) in the marginal ice zone of the Bellingshausen Sea in austral spring of 1990 indicated that as the O3 layer thinned: (i) sea surface- and depth-dependent ratios of UVB irradiance (280 to 320 nanometers) to total irradiance (280 to 700 nanometers) increased and (ii) UVB inhibition of photosynthesis increased. These and other Icecolors findings suggest that O3-dependent shifts of in-water spectral irradiances alter the balance of spectrally dependent phytoplankton processes, including photoinhibition, photoreactivation, photoprotection, and photosynthesis. A minimum 6 to 12 percent reduction in primary production associated with O3 depletion was estimated for the duration of the cruise.

Quasi–incompressible Cahn–Hilliard fluids and topological transitions

Abstract: One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. Following some previous work in this area, we suggest a physically motivated regularization of the Euler equations which allows topological transitions to occur smoothly. In this model, the sharp interface is replaced by a narrow transition layer across which the fluids may mix. The model describes a flow of a binary mixture, and the internal structure of the interface is determined by both diffusion and motion. An advantage of our regularization is that it automatically yields a continuous description of surface tension, which can play an important role in topological transitions. An additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the Euler (or Navier–Stokes) and the Cahn–Hilliard equations. The model takes into account weak non–locality (dispersion) associated with an internal length scale and localized dissipation due to mixing. The non–locality introduces a dimensional surface energy; dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes. In particular, we study a non–trivial limit when both components are incompressible, the pressure is kinematic but the velocity field is non–solenoidal (quasi–incompressibility). To demonstrate the effects of quasi–incompressibility, we analyse the linear stage of spinodal decomposition in one dimension. We show that when the densities of the fluids are not perfectly matched, the evolution of the concentration field causes fluid motion even if the fluids are inviscid. In the limit of infinitely thin and well–separated interfacial layers, an appropriately scaled quasi–incompressible Euler–Cahn–Hilliard system converges to the classical sharp interface model. In order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient, we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity.