Elsevier

Continental Shelf Research

Volume 112, 1 January 2016, Pages 31-45
Continental Shelf Research

Research papers
A model to predict the migration of sand waves in shallow tidal seas

https://doi.org/10.1016/j.csr.2015.11.011Get rights and content

Highlights

  • The geometrical characteristics of sand waves are predicted using an idealized model.

  • The predictions of the model are compared with field observations.

  • The migration speed of the bedforms is evaluated as function of tide characteristics.

Abstract

A model is presented to determine the wavelength, the height and, more importantly, the migration speed of sand waves (also named tidal dunes) in shallow tidal seas. The model is based on a linear stability analysis and predicts the growth and migration of the fastest growing mode of a random perturbation of the flat sea bed forced by tidal current and wind waves. The growth of the fastest growing mode is assumed to generate the sand waves and to have the same geometrical and kinematical characteristics of these bottom forms. The characteristics of the sand waves predicted by the stability analysis are found to be in fair agreement with field observations, even though the number of accurate quantitative and simultaneous measurements of sand waves and forcing tidal currents is small and does not allow an exhaustive comparison between theoretical results and field data.

Introduction

The sandy bottom of shelf seas is often characterised by the presence of periodic morphological patterns generated by either tidal currents or sea waves. The characteristic wavelength of these bottom forms ranges from a few centimetres to hundred of kilometres, i.e. from the scale of ripples to that of sand banks. Even though sand banks are the largest bedforms observed in the continental shelves, they do not pose significant engineering problems, since they are nearly static. On the other hand sand waves, which have wavelengths of hundreds of metres and heights up to tens of metres, may interact with human activities because of their significant migration speed which is O(10)m/year. The migration of sand waves may cause the exposure and buckling of pipelines and/or cables. Moreover, migrating sand waves may reduce the local water depth to the minimum depth for shipping and may require frequent dredging activities which should be carefully planned. Finally, migrating sand waves are a risk for the stability of oil platforms and wind farms.

Field surveys show the existence of sand waves all around the world (Allen, 1984; Stride, 1982). In the Atlantic and the Pacific coasts of North America, these bottom forms were studied by many authors (Bokuniewicz et al., 1977, Perillo and Ludwick, 1984, Xu et al., 2008, Sterlini et al., 2009). Sand waves were also observed along the coasts of Argentina (Aliotta and Perillo, 1987), in Asian waters (Boggs Jr., 1974, Reeder et al., 2011, Ozasa, 1974, Ikehara and Kinoshita, 1994, Knaapen and Hulscher, 2002) and last but not least in the North Sea. Van Veen (1935) was one of the first to observe sand waves in the North Sea and his observations were later followed by those of Stride (1970) and McCave (1971) and more recently by Reynaud et al. (1999), Le Bot et al. (2000), Knaapen (2009), Van Landeghem et al., 2009, Van Landeghem et al., 2012. However, the available field data do not allow us to have accurate estimates of the geometrical characteristics of sand waves as a function of the local tide and sediment characteristics and, in particular, no attempt has been made to estimate the migration speed of these bedforms on the basis of field measurements. Attempts to predict the wavelength, the height and the migration speed of sand waves have been made by theoretical models and numerical simulations. As described in the following the results obtained so far are not entirely satisfactory. In the following, an improvement of the model of Besio et al. (2006) is described which seems to lead to reliable predictions of the sand waves characteristics and in particular of their migration speed.

Section snippets

The mechanism of sand wave formation and its modelling

Hulscher (1996) showed that sand waves arise as free instabilities of the morphodynamic system describing the interaction between tidal currents and the sea bottom. In particular, Hulscher (1996) showed that sand waves are originated by a mechanism similar to that which leads to the appearance of ripples under sea waves (Blondeaux, 1990, Vittori and Blondeaux, 1990, Foti and Blondeaux, 1995a, Foti and Blondeaux, 1995b, Roos and Blondeaux, 2001). In fact, an oscillatory tidal current,

A model to predict of the characteristics (wavelength, height and migration speed) of sand waves (tidal dunes)

As pointed out in the introduction, field data collected by different authors show a correlation between the wavelength of sand waves and the local water depth as well as between the height of the bottom forms and their wavelength (see figure 11.25 (I) of the book of Allen, 1984). However, the scatter of the data is large and it does not allow us to determine reliable and accurate predictive formulae. As discussed in Blondeaux and Vittori (2010), even though the length and the height of sand

The modelling of sand wave formation and migration in the North Sea

Even though the present model is largely based on that of Besio et al. (2006), significant differences are present. Hence, to give the reader some confidence on the predictive capability of the model, we describe the application of the model to the two field observations considered also by Besio et al. (2006). First, the model has been applied to the bathymetric data measured at 52°21N and 3°9E by SNAM PROGETTI S.p.A.. The average water depth is about 40 m and the sand waves are characterized

Remarks

The theoretical approach described in Section 3 allows us to consider also a diurnal constituent (e.g. O1) of the tide and, hence, the presence of the spring-neap cycle which is originated by the small mismatch between the period of the diurnal constituent and twice that of the semidiural constituent. Unfortunately, the data described in Menninga (2012) do provide information only on the M2, M4 and Z0 constituents. Hence, it is not possible to compare the prediction of the model with field

Conclusions

In the previous sections, we describe the model results and their comparison with field data. Let us point out that the model has no parameter to be tuned to fit the field measurements. Therefore, it appears that the idealized model contains the main ingredients which are necessary to provide a reliable description of the process which leads to the formation of sand waves. However, let us point out that laboratory and field measurements show that some of the parameters of the model assume

Acknowledgements

This study was funded by the ‘Ministero dell'Istruzione, dell'Universitá e della Ricerca’ under research project 2012BYTPR5 (Hydro-morphodynamic modelling of coastal processes for engineering purposes' and by the University of Genoa under Contract PRA2014.

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