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How to cope with uncertainty monsters in flood risk management?
- Martin Knotters, Onno Bokhove, Rob Lamb, P.M. Poortvliet
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- Journal:
- Cambridge Prisms: Water / Volume 2 / 2024
- Published online by Cambridge University Press:
- 24 January 2024, e6
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- Article
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Strategies are proposed to cope with uncertainties in a way that all possible kinds of uncertainty are named, recognized, statistically quantified as far as possible and utilized in efficient decision-making in flood risk management (FRM). We elaborated on the metaphor of uncertainty as a monster. We recommend two strategies to cope with the uncertainty monster to support efficient decision-making in FRM: monster adaptation and monster assimilation. We present three cases to illustrate these strategies. We argue that these strategies benefit from improving the structure and reducing the complexity of decision problems. We discuss ways to involve decision-makers in FRM, and how communication strategies can be responsive to their informational needs.
11 - Variational Water Wave Modelling: from Continuum to Experiment
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- By Onno Bokhove, University of Leeds, Leeds, Anna Kalogirou, University of Leeds, Leeds
- Edited by Thomas J. Bridges, University of Surrey, Mark D. Groves, Universität des Saarlandes, Saarbrücken, Germany, David P. Nicholls, University of Illinois, Chicago
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- Book:
- Lectures on the Theory of Water Waves
- Published online:
- 05 February 2016
- Print publication:
- 04 February 2016, pp 226-260
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Summary
Abstract
Variational methods are investigated asymptotically and numerically to model water waves in tanks with wave generators. As a validation, our modelling results using (dis)continuous Galerkin finite element methods will be compared to a soliton splash event resulting after a sluice gate is removed during a finite time in a long water channel with a contraction at its end.
Introduction
A popular approach in the modelling of nonlinear water waves is to make the approximations that the three-dimensional fluid velocity u is irrotational and divergent free, such that u = ∇ϕ and ∇ · u = ∇2ϕ = 0, and that the dynamics is inviscid, such that the dynamics is governed by variational and Hamiltonian dynamics [1, 2]. At least symbolically one can invert this Laplace equation for the interior potential ϕ and reduce the dynamics to the free surface, expressed in terms of the potential ϕs at the free surface and the position of this free surface. For non-overturning waves, this free surface dynamics can be expressed in terms of the water depth h = h(x, y, t) and ϕs(x, y, t) = ϕ(x, y, z = b + h, t) with horizontal coordinates x and y as well as time t. Here the fixed topography is denoted by b = b(x, y). The free surface thus lies at the vertical level z = b(x, y)+h(x, y, t), parametrised by x and y.
One then often considers the initial value problem governed by autonomous Hamiltonian dynamics for h and ϕs with initial conditions h(x, y,0) and ϕs(x, y,0) without any forcing or dissipation. In practical situations, however, waves are generated continuously by wave makers or temporarily by opening a sluice gate, both involving time dependent internal or boundary conditions. This implies that the dynamics is non-autonomous, including explicit dependence of the equations on time. Sometimes, these non-autonomous aspects can be included in the variational principles governing the wave dynamics.
We will therefore start to formulate finite-dimensional variational dynamics in which the variational principle indeed depends explicitly on time. The forced-dissipative nonlinear pendulum with the harmonic oscillator as linearisation is a first example of such a non-autonomous variational principle.
On hydrostatic flows in isentropic coordinates
- ONNO BOKHOVE
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- Journal:
- Journal of Fluid Mechanics / Volume 402 / 10 January 2000
- Published online by Cambridge University Press:
- 10 January 2000, pp. 291-310
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The hydrostatic primitive equations of motion which have been used in large-scale weather prediction and climate modelling over the last few decades are analysed with variational methods in an isentropic Eulerian framework. The use of material isentropic coordinates for the Eulerian hydrostatic equations is known to have distinct conceptual advantages since fluid motion is, under inviscid and statically stable circumstances, confined to take place on quasi-horizontal isentropic surfaces. First, an Eulerian isentropic Hamilton's principle, expressed in terms of fluid parcel variables, is therefore derived by transformation of a Lagrangian Hamilton's principle to an Eulerian one. This Eulerian principle explicitly describes the boundary dynamics of the time-dependent domain in terms of advection of boundary isentropes sB; these are the values the isentropes have at their intersection with the (lower) boundary. A partial Legendre transform for only the interior variables yields an Eulerian ‘action’ principle. Secondly, Noether's theorem is used to derive energy and potential vorticity conservation from the Eulerian Hamilton's principle. Thirdly, these conservation laws are used to derive a wave-activity invariant which is second-order in terms of small-amplitude disturbances relative to a resting or moving basic state. Linear stability criteria are derived but only for resting basic states. In mid-latitudes a time- scale separation between gravity and vortical modes occurs. Finally, this time-scale separation suggests that conservative geostrophic and ageostrophic approximations can be made to the Eulerian action principle for hydrostatic flows. Approximations to Eulerian variational principles may be more advantageous than approximations to Lagrangian ones because non-dimensionalization and scaling tend to be based on Eulerian estimates of the characteristic scales involved. These approximations to the stratified hydrostatic formulation extend previous approximations to the shallow- water equations. An explicit variational derivation is given of an isentropic version of Hoskins & Bretherton's model for atmospheric fronts.