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.

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Abstract. The erosion of a beach depends on various storm characteristics. Ideally, the risk associated with a storm would be described by a single multivariate return period that is also representative of the erosion risk, i.e. a 100 yr multivariate storm return period would cause a 100 yr erosion return period. Unfortunately, a specific probability level may be associated with numerous combinations of storm characteristics. These combinations, despite having the same multivariate probability, may cause very different erosion outcomes. This paper explores this ambiguity problem in the context of copula based multivariate return periods and using a case study at Durban on the east coast of South Africa. Simulations were used to correlate multivariate return periods of historical events to return periods of estimated storm induced erosion volumes. In addition, the relationship of the most-likely design event (Salvadori et al., 2011) to coastal erosion was investigated. It was found that the multivariate return periods for wave height and duration had the highest correlation to erosion return periods. The most-likely design event was found to be an inadequate design method in its current form. We explore the inclusion of conditions based on the physical realizability of wave events and the use of multivariate linear regression to relate storm parameters to erosion computed from a process based model. Establishing a link between storm statistics and erosion consequences can resolve the ambiguity between multivariate storm return periods and associated erosion return periods.

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Recent coastal storms in southern Africa have highlighted the need for more proactive management of the coastline. Within the southern and eastern African region the availability of coastal information is poor. The greatest gap in information is the likely effects of a combination of severe sea storms and future sea level rise (SLR) on the shoreline. This lack of information creates a barrier to informed decision making. This research outlines a practical localized approach to this problem, which can be applied as a first order assessment within the region. In so doing it provides a cost effective and simple decision support tool for the built environment and disaster professionals in development and disaster assessments. In a South African context the newly promulgated Integrated Coastal Management Act requires that all proposed coastal developments take into consideration future SLR, however such information currently does not exist, despite it being vital for informed planning in the coastal zone. This practical approach has been applied to the coastline of Durban, South Africa as a case study. The outputs are presented in a Geographic Information System (GIS) based freeware viewer tool enabling ease of access to both professionals and laypersons. This demonstrates that a simple approach can provide valuable information about the current and future risk of flooding and coastal erosion under climate change to buildings, infrastructure as well as natural features along the coast. OPEN ACCESSWater 2012, 4 238