Derek D. Stretch

On the turbulent Prandtl number in homogeneous stably stratified turbulence

In this paper, we derive a general relationship for the turbulent Prandtl number Pr t for homogeneous stably stratified turbulence from the turbulent kinetic energy and scalar variance equations. A formulation for the turbulent Prandtl number, Pr t , is developed in terms of a mixing length scale L M and an overturning length scale L E , the ratio of the mechanical (turbulent kinetic energy) decay time scale T L to scalar decay time scale T ρ and the gradient Richardson number Ri. We show that our formulation for Pr t is appropriate even for non-stationary (developing) stratified flows, since it does not include the reversible contributions in both the turbulent kinetic energy production and buoyancy fluxes that drive the time variations in the flow. Our analysis of direct numerical simulation (DNS) data of homogeneous sheared turbulence shows that the ratio L M /L E ≈ 1 for weakly stratified flows. We show that in the limit of zero stratification, the turbulent Prandtl number is equal to the inverse of the ratio of the mechanical time scale to the scalar time scale, T L /T ρ . We use the stably stratified DNS data of Shih et al. (J. Fluid Mech., vol. 412, 2000, pp. 1―20; J. Fluid Mech., vol. 525, 2005, pp. 193―214) to propose a new parameterization for Pr t in terms of the gradient Richardson number Ri. The formulation presented here provides a general framework for calculating Pr t that will be useful for turbulence closure schemes in numerical models.

Southern African sea levels: corrections, influences and trends

The tidal records of existing South African and Namibian tide gauges are examined and corrected. Regional sea level trends vary, with the West Coast rising by +1.87 mm y−1 (1959-2006), the southern coast by +1.48 mm y−1 (1957-2006) and the East Coast by +2.74 mm y−1 (1967-2006). The effects of barometric pressure and vertical crustal movement changes on these trends are examined. The derived relationship between sea levels and barometric pressure changes varied between 5.71 and 7.67 mm hPa−1, significantly less than the theoretical inverse barometric correction. Barometric pressure has been dropping along the west coast at 1.63 hPa per decade (1987-2006), has remained fairly static along the southern coast and is rising at 0.30 hPa per decade (1970-2007) along the east coast of southern Africa. The West Coast barometrically corrected sea level trends show that most of the change can be attributed to falling barometric pressure, whereas along the East Coast, the barometric pressure increase is suppressing sea level by 0.2 mm y−1. Vertical crust movements vary, with the largest recorded movements of +1.11 ± 0.25 mm y−1 found along the East Coast. Movement rate reduces southwards. Eustatic sea level trends vary from +3.55 mm y−1 along the East Coast and +1.57 mm y−1 along the southern coast to +0.42 mm y−1 along the West Coast.

Ecology and Conservation of Estuarine Ecosystems: Lake St. Lucia as a Global Model

List of contributors Foreword Alan Whitfield Preface 1. South Africas first World Heritage Site Roger N. Porter 2. Management history Ricky H. Taylor 3. Geological history Greg A. Botha, Sylvi Haldorsen and Naomi Porat 4. The marine environment Allan D. Connell and Sean N. Porter 5. Catchment hydrology Derek D. Stretch and Andrew Z. Maro 6. The Wetlands William N. Ellery, Suzanne E. Grenfell, Michael C. Grenfell, Marc S. Humphries and Kirsten B. Barnes 7. Estuary and lake hydrodynamics Derek D. Stretch, Clint P. Chrystal, Robynne A. Chrystal, Christopher Maine and Justin J. Pringle 8. Groundwater hydrology Bruce E. Kelbe, Ricky H. Taylor and Sylvi Haldorsen 9. Physico-chemical environment Renzo Perissinotto, Nicola K. Carrasco and Ricky H. Taylor 10. Microalgae Renzo Perissinotto, Guy C. Bate and David G. Muir 11. Macrophytes Janine B. Adams, Sibulele Nondoda and Ricky H. Taylor 12. Benthic invertebrates Deena Pillay, Sarah J. Bownes and Holly A. Nel 13. Zooplankton Nicola K. Carrasco, Renzo Perissinotto and Hendrik L. Jerling 14. Penaeid prawns Anthony T. Forbes and Nicolette T. Forbes 15. Fish and fisheries Digby Cyrus 16. Birds Jane Turpie, Ricky H. Taylor, Meyrick Bowker and Caroline Fox 17. Crocodiles Xander Combrink, Jonathan Warner and Colleen T. Downs 18. Hippopotamuses Ricky H. Taylor 19. Alien and invasive species Nelson A. F. Miranda and Janine B. Adams 20. Food webs and ecosystem functioning Ursula M. Scharler and Fiona C. MacKay 21. Climate change impacts Andrew A. Mather, Derek D. Stretch and Andrew Z. Maro References Appendix: web page database, 1900-2010 Nuette Gordon Index.

Lagrangian mixing in decaying stably stratified turbulence

Direct numerical simulations are used to study mixing and dispersion in decaying stably stratified turbulence from a Lagrangian perspective. The change in density of fluid particles owing to small-scale mixing is extracted from the simulations to provide insight into the mixing process. These changes are driven by temporally and spatially intermittent events that are strongly suppressed as the stratification increases and overturning motions disappear. This occurs for times

THE BREACHING OF SAND BARRIERS AT PERCHED, TEMPORARY OPEN/CLOSED ESTUARIES — A MODEL STUDY

Nt \,{>}\, 2\upi

Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

, i.e. after one buoyancy period, where

PREDICTING EXTREME WAVE RUN-UP ON NATURAL BEACHES FOR COASTAL PLANNING AND MANAGEMENT

N

BREACHING TIMESCALES AND PEAK OUTFLOWS FOR PERCHED, TEMPORARY OPEN ESTUARIES

is the buoyancy frequency. The role of small-scale mixing processes in the density (or buoyancy) flux is analysed. After an initial transient, we find that diapycnal displacements due to mixing dominate the dispersion of fluid particles, even in weak stratification. The relationship between the diapycnal diffusivity and vertical dispersion coefficients is found to be strongly dependent on stratification. Models for the mixing following fluid particles are investigated. The time scale for the density changes due to small-scale mixing is shown to be approximately independent of

Diapycnal diffusivities in homogeneous stratified turbulence

N

Circulation patterns identified by spatial rainfall and ocean wave fields in Southern Africa

and instead remains linked to the energy decay time scale which is relatively insensitive to stratification. There are large changes in the structure of these flows as they evolve under the influence of buoyancy forces. We investigate these changes and their relationship to mixing. We find that strong mixing events are closely linked to the presence of overturning regions in the flow, and that they occur close to (but not within) these regions. The results reported here have implications for the development of improved models of diffusion in stably stratified turbulence.