Guidance on Setup, Calibration, and Validation of Hydrodynamic, Wave, and Sediment Models for Shelf Seas and Estuaries

© 2017 Jon J. Williams and Luciana S. Esteves. The paper is motivated by a present lack of clear model performance guidelines for shelf sea and estuarine modellers seeking to demonstrate to clients and end users that a model is fit for purpose. It addresses the common problems associated with data availability, errors, and uncertainty and examines the model build process, including calibration and validation. It also looks at common assumptions, data input requirements, and statistical analyses that can be applied to assess the performance of models of estuaries and shelf seas. Specifically, it takes account of inherent modelling uncertainties and defines metrics of performance based on practical experience. It is intended as a reference point both for numerical modellers and for specialists tasked with interpreting the accuracy and validity of results from hydrodynamic, wave, and sediment models

The Erpenbeck high frequency instability theorem for ZND detonations

The rigorous study of spectral stability for strong detonations was begun by J.J. Erpenbeck in [Er1]. Working with the Zeldovitch-von Neumann-D\"oring (ZND) model, which assumes a finite reaction rate but ignores effects like viscosity corresponding to second order derivatives, he used a normal mode analysis to define a stability function V(\tau,\eps) whose zeros in $\Re \tau>0$ correspond to multidimensional perturbations of a steady detonation profile that grow exponentially in time. Later in a remarkable paper [Er3] he provided strong evidence, by a combination of formal and rigorous arguments, that for certain classes of steady ZND profiles, unstable zeros of $V$ exist for perturbations of sufficiently large transverse wavenumber \eps, even when the von Neumann shock, regarded as a gas dynamical shock, is uniformly stable in the sense defined (nearly twenty years later) by Majda. In spite of a great deal of later numerical work devoted to computing the zeros of V(\tau,\eps), the paper \cite{Er3} remains the only work we know of that presents a detailed and convincing theoretical argument for detecting them. The analysis in [Er3] points the way toward, but does not constitute, a mathematical proof that such unstable zeros exist. In this paper we identify the mathematical issues left unresolved in [Er3] and provide proofs, together with certain simplifications and extensions, of the main conclusions about stability and instability of detonations contained in that paper. The main mathematical problem, and our principal focus here, is to determine the precise asymptotic behavior as \eps\to \infty of solutions to a linear system of ODEs in $x$, depending on \eps and a complex frequency $\tau$ as parameters, with turning points $x_*$ on the half-line $[0,\infty)$

X-band radar system to support coastal management decisions

The difficulties and costs associated with the acquisition of hydrodynamic and bathymetry data in the nearshore is widely recognised. While technological advances have enabled in situ measurements at increased precision, the limited spatial and temporal resolution of data continues to hinder evidence-based coastal management. This paper presents selected results from the ‘X-Band radar as a coastal monitoring tool’ (X-Com) project which tests the suitability of a land-based X-Band radar system to provide data required for practical coastal management applications. Results are shown from a radar installation at Thorpeness (Suffolk, eastern England) from August 2015 to October 2016. At this location, coastal erosion threatens clifftop and beach front properties, and the lack of understanding about the local nearshore-shore-cliff interactions has been identified as a key factor limiting the development of a sustainable coastal strategy. A model is used in a preliminary examination of surface current data from the radar. X-Com results indicate that X-Band radar systems have an unrealised potential and could become a cost-effective tool for coastal management applications pending improvements in the automation of data processing, assessment of data accuracy and end user-friendly output formats

Heat flux effects on magnetic field dynamics in solid density plasmas traversed by relativistic electron beams

Relativistic electron beam propagation through solid density plasma is a rich area for magnetic field dynamics. It is well known that Ohmic heating of the background plasma caused by the beam significantly affects magnetic field generation, primarily through changes in the resistivity. In particular, temperature changes in the background plasma leads to the generation of a magnetic field that acts to deflect relativistic electrons from the beam axis. This 'beam hollowing' field could have disastrous implications for the fast ignitor scheme. In this paper, the effects of background heat flow on magnetic field generation are considered, first with a simple analytic investigation, and then with 1D Vlasov Fokker–Planck and classical transport simulations using a rigid beam for the fast electrons. It is shown that the thermal conduction of the background plasma acts to diffuse the temperature, reducing both the temperature gradients and the beam hollowing field. This gives rise to the re-emergence of a collimating magnetic field. The influence of the background heat flux is also investigated in the context of solids with imposed resistivity gradients, and is shown to significantly enhance the magnetic field present. More exotic transport effects, such as an enhanced Nernst velocity (due to non-local heat flux) and double peaked temperature profiles (due to distortion of the heating and heat-flow profiles by the magnetic field), are also reported