A model study of tidal distributions in the Celtic and Irish Sea regions determined with finite volume and finite element models

Abstract

An unstructured mesh tidal model of the west coast of Britain, covering the Celtic Sea and Irish Sea is used to compare tidal distributions computed with finite element (F.E.) and finite volume (F.V.) models. Both models cover an identical region, use the same mesh, and have topography and tidal boundary forcing from a finite difference model that can reproduce the tides in the region. By this means solutions from both models can be compared without any bias towards one model or another. Two dimensional calculations show that for a given friction coefficient there is more damping in the F.V. model than the F.E. model. As bottom friction coefficient is reduced the two models show comparable changes in tidal distributions. In terms of mesh resolution, calculations show that for the M2 tide the mesh is sufficiently fine to yield an accurate solution over the whole domain. However in terms of higher harmonics of the tide, in particular the M6 component, its small scale variability in near shore regions which is comparable to the mesh of the model, suggests that the mesh resolution is insufficient in the near coastal regions. Even with a finer mesh in these areas, without detailed bottom topography and a spatial varying friction depending on bed types and bed forms, which is not available, model skill would probably not be improved. In addition in the near shore region, as shown in the literature, the solution is sensitive to the form of the wetting/drying algorithm used in the model. Calculations with a three dimensional version of the F.V. model show that for a given value of k, damping is reduced compared to the two dimensional version due to the differences in bed stress formulation, with the three dimensional model yielding an accurate tidal distribution over the region. (1) Description of models slightly enhanced. As a detailed description is given in published papers, these are cited, as we do not wish to repeat information. In addition since a functional form of the solution is given over each finite element or finite volume this can be used to interpolate solutions (e.g. water elevations) to any location. This point made in text. (2) It is made clear that the staircase representation of the coastline only relates to a certain class of finite difference model. (3) The k-0.003 calculations are mentioned "early on". (4) Possibility of lack of mesh resolution influencing solution of higher harmonics is discussed in context of the fact that this could also be influenced by "wetting and drying". Additional references added. (5) Abstract rephrased to suggest this, rather than claim that it has been shown. Similar in text. (6) Elaborated to show that in the near short region the amplitude of the higher harmonics changes very rapidly from one mesh element to another. A sure sign of a lack of spatial convergence. The confusion between temporal convergence, where iteration ensures that a converged solution does occur and spatial convergence is now clarified. (7) The realistic nature of these coefficients is c...

Modelling tide–surge interaction effects using finite volume and finite element models of the Irish Sea

“…Since this is underestimated in the FV model, compared with observations, the surge is less damped in the FV model compared with the FE model. This is consistent with earlier tidal calculations in which Davies et al (2010) found that M 2 tidal elevations in the eastern Irish Sea computed with the FV model tended to be about 25 cm less than those computed with the FE model (see Tables 1, 2 and 3).…”

“…This amplification gives rise to the appreciable differences shown in Table 1. A consequence of these differences in the M 2 solution is that the FV model tends to underpredict the amplitude of the higher harmonics compared with the FE model which is in good agreement with observations (see Davies et al 2010; see Tables 2 and 3).…”

“…The M 2 tidal distribution found in the FV model is comparable with that found in a solution derived with the ADCIRC (FE) code (Jones et al 2009) and appears to be due to slightly enhanced damping that moves the amphidromic point off the east coast of Ireland and slightly farther north. In addition, there is a reduction in M 2 tidal amplitudes in the eastern Irish Sea (see Davies et al 2010 for a fuller discussion of tidal results from the FV model). As a full discussion of results from both the FE and FV model together with the influence of bottom friction and threedimensional effects is given in Davies et al (2010), together with references describing model formulation (see also Jones and Davies 2010 and references therein), they will not be repeated here.…”

“…In addition, there is a reduction in M 2 tidal amplitudes in the eastern Irish Sea (see Davies et al 2010 for a fuller discussion of tidal results from the FV model). As a full discussion of results from both the FE and FV model together with the influence of bottom friction and threedimensional effects is given in Davies et al (2010), together with references describing model formulation (see also Jones and Davies 2010 and references therein), they will not be repeated here. Some values for the M 2 tide and its higher harmonics computed with the FE and FV models at representative shallow water gauges are given in Tables 1, 2 and 3.…”

“…As discussed previously and clearly shown in the tide only calculation in Table 1, due to slight differences in the M 2 tidal distribution computed over the Celtic and western Irish Sea, with the FE and FV models, these lead to significant differences in the M 2 tidal amplitudes at coastal gauges (Table 1, tide only calculation). Although there are only small differences of order 5 cm in tidal amplitudes between the FE and FV models in the Celtic and western Irish Sea, due to slight differences in location of the amphidromic point (see Davies et al 2010 for detail), these differences are amplified as tidal amplitudes increase in the eastern Irish Sea. This amplification gives rise to the appreciable differences shown in Table 1.…”