Response of largescale coastal basins to wind for

Authors: Wen L Chen Pieter C Roos Henk M Schuttelaars Mohit Kumar Tjerk J Zitman Suzanne J M H Hulscher

Publish Date: 2016/02/27

Volume: 66, Issue: 4, Pages: 549-565

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Abstract

Because wind is one of the main forcings in storm surge we present an idealised processbased model to study the influence of topographic variations on the frequency response of largescale coastal basins subject to timeperiodic wind forcing Coastal basins are represented by a semienclosed rectangular inner region forced by wind It is connected to an outer region represented as an infinitely long channel without wind forcing which allows waves to freely propagate outward The model solves the threedimensional linearised shallow water equations on the f plane forced by a spatially uniform wind field that has an arbitrary angle with respect to the alongbasin direction Turbulence is represented using a spatially uniform vertical eddy viscosity combined with a partial slip condition at the bed The surface elevation amplitudes and hence the vertical profiles of the velocity are obtained using the finite element method FEM extended to account for the connection to the outer region The results are then evaluated in terms of the elevation amplitude averaged over the basin’s landward end as a function of the wind forcing frequency In general the results point out that adding topographic elements in the inner region such as a topographic step a linearly sloping bed or a parabolic crossbasin profile causes the resonance peaks to shift in the frequency domain through their effect on local wave speed The Coriolis effect causes the resonance peaks associated with crossbasin modes which without rotation only appear in the response to crossbasin wind to emerge also in the response to alongbasin wind and vice versaWinddriven setup is the main contribution to extreme high water events which may threaten coastal safety This is particularly so when the combined characteristics of the wind forcing and the basin trigger resonance Abraham 1960 A typical example is typhoon Winnie at the Korean coast of the Yellow Sea in 1997 The unusually strong and extensive coastal flooding was partly caused by resonant coupling of the Yellow Sea and the predominant period of the forcing Moon et al 2003Importantly the resonance properties of coastal basins can be affected by largescale topographic elements For example shoals may protect the coast Hanley et al 2013 Alternatively the water body between a longshore bar and the coast may display strong oscillations depending on the frequency of the incoming wave and local bathymetry Büsching 2003 Moreover wind blowing in different directions in a semienclosed basin may lead to significantly different responses Breaker et al 2010 For coastal safety an overall practical goal is to be able to predict the winddriven water levels at any location in basins of arbitrary shape and size This requires physical insight in the influence of largescale topography on resonance properties of largescale coastal basins Below we will review the literature on this topicThe influence of topography on surge response has been investigated in various sitespecific studies using numerical models For example Chen et al 2008 suggested that the recordhigh storm surge of Hurricane Katrina New Orleans Louisiana was caused by the interaction of the surge with the extremely shallow ancient deltaic lobe of the Mississippi river For the surge caused by Hurricane Katrina Irish et al 2008 found that a milder shelf slope would have led to a higher surge Alternatively Weaver and Slinn 2010 found that smallscale variations in nearshore bathymetry of about 20 produce smaller variations in storm surge at the shoreline less than 5 Using a onedimensional numerical model Libicki and Bedford 1990 showed how westward travelling storms over Lake Erie approaching shallower regions produce higher surge levels than eastward travelling storms approaching deeper regions Since these studies produce sitespecific results it is difficult to draw generic conclusionsThe goal of the present study is to investigate the influence of largescale topography on the winddriven frequency response of largescale coastal basins measured in terms of the setup at the coast and paying particular attention to the role of the Coriolis effect and wind angle Here largescale means that we consider topographic elements with horizontal length scales of the scale of the basin and that the basin is large enough for Coriolis effect to be important for phenomena with a time scale of the order of hours to daysTo achieve this goal we have developed an idealised threedimensional processbased model of a semienclosed rectangular rotating coastal basin subject to periodic wind forcing The validity of linearization is debatable for very shallow regions Therefore we have made sure that the water depth is sufficiently large 10 m or more in our examples Furthermore by considering topographic elements with horizontal length scales of the scale of the basin we may safely ignore the associated nonlinearities eg Csanady1968 Mathieu et al2002 Winant2004 The vertical profile of the flow field is resolved fully analytically and expressed in terms of the free surface elevation In turn the spatial pattern of free surface elevation amplitudes follows from solving an elliptic problem using the finite element method FEM extended to account for the connection of the coastal basin to the outer sea

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