Time-dependent linearisation of bottom friction for storm surge modelling in the Wadden Sea

The nonlinear nature of bottom friction in shallow flow complicates its analysis, particularly in idealised models. For tidal flows, Lorentz’ linearisation has been widely applied, using an energy criterion to specify the friction coefficient. Here we propose an extension of this approach to storm surges, leading to a friction coefficient that may gradually vary over a storm event. The derivation is provided along with first results for a single channel

Unsteady linearisation of bed shear stress for idealised storm surge modelling

The modelling of time-varying shallow flows, such as tides and storm surges, is complicated by the nonlinear dependency of bed shear stress on flow speed. For tidal flows, Lorentz’s linearisation circumvents nonlinearity by specifying a (steady) friction coefficient r based on a tide-averaged criterion of energy equivalence. However, this approach is not suitable for phenomena with episodic and irregular forcings such as storm surges Here, we studied the implications of applying Lorentz’s energy criterion in an instantaneous sense, so that an unsteady friction coefficient r(t) adjusts to the temporal development of natural wind-driven flows. This new bed-stress parametrisation was implemented in an idealised model of a single channel, forced by time-varying signals of wind stress (acting over the entire domain) and surface elevation (at the channel mouth). The solution method combines analytical solutions of the cross-sectionally averaged linearised shallow-water equations, obtained in the frequency domain, with an iterative procedure to determine r(t) Model results, compared with a reference finite-difference solution retaining the quadratic bed shear stress, show that this new approach accurately captures the qualitative and quantitative aspects of the surge dynamics (height and timing of surge peaks, sloshing, friction-induced tide-surge interaction) for both synthetic and realistic wind forcing

Storm surges in an idealized tidal channel:A power criterion for the unsteady bed shear stress

Research content This poster presents selected findings from the article Unsteady linearisation of bed shear stress for idealised storm surge modelling of 2021 for the participants in the NCK Days 2022, the yearly get-together of the Netherlands Centre for Coastal Research. This poster is open-access under a Creative Commons Attribution 4.0 International. The summary underlying the poster is available from the event's Book of Abstracts both as web page and as PDF document (p.91). Document design: structure and styling The conference organisers required the production of a paper-based poster in A0 format with portrait orientation. The document has been designed in A4 format, as available from the copy shared in this website. A resolution of 1200 dpi produced sharp enough images when printing a document in PDF format in A0 size. The whole document has been composed as a three-column table of a Google Doc document, using row-wise column merges to produce a well-marked layout consisting of stacked rows. In order to favour speed-reading, two font types and sizes contrast headings and narrative. Likewise, the text blocks are made of short and clearly spaced paragraphs, easy to point to and scan. The font size in the text body was readable when printed in A0 and, in retrospect for the specific venue the poster has been presented in, could still have been reduced to the same effect. Finally, test prints confirmed that an additional margin would have been present around the page. The poster promotes a study published in a journal article, whereby the methods and results on display are already established. The audience is assumed to have been attracted by the poster title, thus to have been moved by an affinity for the topical area and to nurse a potential curiosity about reading the article in depth. As a result, the slant of this poster is intendedly descriptive, if not unimaginative; visuals are not especially meant or positioned to catch the eye. Document design: narrative and presentation The findings of the article selected for the poster are those encapsulating the novelties most compactly. This content selection provides maximum integration between narrative and scientific advances, given the limited space of the document and of the interactions in a poster session. The table cells organise information progressively more detailed in the reading direction, broadly following a general-to-specific or abstraction-to-implementation order. During a poster session, the poster presenter could illustrate the content either in a bottom-up fashion starting from the results, supported by cartoons and graphs; or top-down, starting from the generalities presented as textual narrative. Outside the poster session, interested passers-by may find essential guidance into the topic scanning the poster in normal reading direction. Document design: on-line dissemination Hyperlinks to further resources, aimed at the digital poster version, are in blue. The DOI of this document has been reserved upon creating an unpublished Zenodo entry while drafting the poster. The DOI is shown in the poster so as to inform the viewers of the possibility to download the document after the conference. The poster has been uploaded ahead of the event and embargoed until the planned day of the off-line presentation. The publication date is the date of the poster session. Description authored by Giordano Lipar