Author Posting. © Annual Reviews, 2007. This is the author's version of the work. It is posted here by permission of Annual Reviews for personal use, not for redistribution. The definitive version was published in Annual Review of Earth and Planetary Sciences 36 (2008): 601-647, doi:10.1146/annurev.earth.35.031306.140139.

/pdf/coastal-impacts-due-to-sea-level-rise-3e2h8eh3jm.pdf

Coastal Impacts Due to Sea-Level Rise

Approximate layer-averaged equations describing the mechanics of turbid underflows are derived. Closure of the equations describing the balance of fluid mass, sediment mass, and mean flow momentum provides for the delineation of a three-equation model. A description of sediment exchange with the bed allows for the possibility of a self-accelerating turbidity current in which sediment entrainment from the bed is linked to flow velocity. A consideration of the balance of the mean energy of the turbulence yields a constraint on physically realistic solutions to the three-equation model. It is shown that the self-acceleration predicted by the three-equation model is so strong that the energy constraint fails to be satisfied. In particular, the turbulent energy consumed in entraining new bed sediment exceeds the supply of energy to the turbulence, so that the turbulence, and thus the turbidity current, must die. The problem is rectified by the formulation of a four-equation model, in which an explicit accounting is made of the mean energy of the turbulence. Sediment entrainment from the bed is linked to the level of turbulence in the four-equation model. Self-acceleration is again predicted, although it is somewhat subdued compared with that predicted by the three-equation model. The predictions of both models are summarized over a wide range of conditions.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112086001404

Self-accelerating turbidity currents

Summary
The literature on the structure and behaviour of gravity currents is reviewed, with emphasis on some recent studies, and with particular attention to turbidity currents, though reference is also made to comparable behaviour in pyroclastic flows. Questions of definition are discussed, in particular the distinction between dense currents, which may deposit en masse, and more dilute currents. High-density dispersions may exist as a discrete, independently moving layer beneath a more dilute flow, as the basal part of a continuous density distribution or possibly as a transient depositional layer. Existing theory appears inadequate to explain the behaviour of some high-density dispersions. Surge-type currents are contrasted with quasi-steady currents, which may be generated by a variety of mechanisms including direct feed by rivers in flood. Such fluvially generated currents provide one means of generating currents with reversing buoyancy. Geologically significant turbidity currents are impractical for direct study owing to their large scale and (often) destructive nature. Small-scale laboratory currents offer a wealth of insights into turbidity current behaviour. This paper summarizes recent experimental studies that focus on the physical structure of gravity currents, with emphasis on the velocity and turbulence structure, the vertical density distribution and the stability of stratification. Preliminary quantification of the turbulence structure (including controls on turbulent entrainment, turbulent kinetic energy, Reynolds stresses and turbulence production) has been facilitated by recent technological developments that have allowed the measurement of instantaneous fluctuations in both velocity and concentration. Laboratory models, however, generally involve substantial simplification, and require compromises in some parameters to achieve adequate scaling of the parameters of most interest. Mathematical modelling also provides important insights into turbidity current behaviour. We discuss various approaches to modelling, ranging from simple hydraulic equations to systems of partial differential equations that explicitly treat conservation of momentum, fluid and sediment mass, and turbulent kinetic energy. The application for which the model is designed (i.e. to calculate mean head velocity or to create an instantaneous two-dimensional contour plot of downstream velocity in a current) determines the complexity of the mathematical model required. The behaviour of suspension currents around topography is complex and depends upon the relative height of the topography, and upon the density and velocity structure of the current. Many interactions with topography are well described by the internal Froude number, Fri. Both reflection and deflection of currents may occur on the upstream side of topography, depending upon Fri. On the downstream side of topography, flow separation, lee waves or hydraulic jumps may occur.

The structure and fluid mechanics of turbidity currents: a review of some recent studies and their geological implications

In the face of a global rise in sea level, understanding the response of the shoreline to changes in sea level is a critical scientific goal to inform policy makers and managers. A body of scientific information exists that illustrates both the complexity of the linkages between sea-level rise and shoreline response, and the comparative lack of understanding of these linkages. In spite of the lack of understanding, many appraisals have been undertaken that employ a concept known as the “Bruun Rule”. This is a simple two-dimensional model of shoreline response to rising sea level. The model has seen near global application since its original formulation in 1954. The concept provided an advance in understanding of the coastal system at the time of its first publication. It has, however, been superseded by numerous subsequent findings and is now invalid. Several assumptions behind the Bruun Rule are known to be false and nowhere has the Bruun Rule been adequately proven; on the contrary several studies disprove it in the field. No universally applicable model of shoreline retreat under sea-level rise has yet been developed. Despite this, the Bruun Rule is in widespread contemporary use at a global scale both as a management tool and as a scientific concept. The persistence of this concept beyond its original assumption base is attributed to the following factors: 1. Appeal of a simple, easy to use analytical model that is in widespread use. 2. Difficulty of determining the relative validity of ‘proofs’ and ‘disproofs’. 3. Ease of application. 4. Positive advocacy by some scientists. 5. Application by other scientists without critical appraisal. 6. The simple numerical expression of the model. 7. Lack of easy alternatives. The Bruun Rule has no power for predicting shoreline behaviour under rising sea level and should be abandoned. It is a concept whose time has passed. The belief by policy makers that it offers a prediction of future shoreline position may well have stifled much-needed research into the coastal response to sea-level rise.

Sea-level rise and shoreline retreat: time to abandon the Bruun Rule

Controls on coastal dune morphology, shoreline erosion and barrier island response to extreme storms

The concept of shoreface profile of equilibrium is the basis for most models used to quantitatively describe and predict profile response on beaches. We question the validity of the concept as used in coastal engineering. The equilibrium shoreface profile concept is based on the following assumptions: (1) underfying geology does not play a role in determining the profile shape; (2) shoreface sediment is moved only by the interaction of wave orbitals with the sea floor, unidirectional current flow is not accounted for; (3) there is no significant net movement of sediment seaward of a so called "closure depth." The equilibrium shoreface profile equation implies: (1) offshore bars do not play an important role in shoreface sediment transport; (2) grain size is the only variable determining shoreface profile shape variability; (3) the shoreface transport system is two-dimentional; and (4) all shorefaces in the world can be described by a single equation with sediment grain size as the only variable. To varying degrees, all of these assumptions fail to be met in real world situations in light of well documented oceanographic and geologic phenomena. A fundamental reexamination of the engineering methods of determining nearshore shoreface evolution is needed. As currently practiced such methods are based on poor oceanographic assumptions.

/pdf/the-concept-of-shoreface-profile-of-equilibrium-a-critical-2074lk7b9y.pdf

Walter D. Pilkey

Papers

The Concept of Shoreface Profile of Equilibrium: A Critical Review

An analytical study of turbidity current steady flow

Mechanics of Solids