Characterization of bedform morphology generated under combined flows and currents using wavelet analysis

https://doi.org/10.1016/j.oceaneng.2009.01.014Get rights and content

Abstract

The wavelet transform (WT) has been successfully implemented in many fields such as signal and image processing, communication theory, optics, numerical analysis, and fluid mechanics. However, the application of WT to describe bedform morphology in coastal areas, oceans, and rivers is rare. The present study demonstrates the capability of WT analysis to fully represent the space–frequency characteristics of signals describing bed topography generated in marine and river environments. In this study WT is used to examine the morphological characteristics of bedforms generated in two separate laboratory facilities: a wave tank and a meandering channel. In the wave tank a set of ripples superimposed upon large wave ripples were generated; while in the meandering channel, 2D and 3D migrating ripples and dunes were observed. The WT proved to be a useful tool in detecting the complex variability of the generated bedform structures. The size distribution of the bottom features such as ripples, large wave ripples and sandbars were first examined along a 2D bed profile. Later analysis studied the variability of features in the transverse direction by using the power Hovmöller. Experiments in the wave tank were conducted for a mobility number of ψ=(10, 28), and a Reynolds wave number of Rew=(17,500, 83,500) which correspond to waves alone (WA) and to combined flow (CF) scenarios, respectively. Experiments in the meandering channel were conducted under a morphological regime that produced mainly migrating sandbars.

Introduction

Morphological bed features, such as ripples, large wave ripples (LWRs), sandwaves (SWs), and sandbars, are commonly found in continental shelves and rivers. The term sandwave commonly denotes large bedforms found on continental shelves formed under the action of tidal currents (Komarova and Newell, 2000; Komarova and Hulscher, 2000; Knaapen and Hulscher, 2002; Morelissen et al., 2003). Large wave ripples are much smaller than SWs and have been identified in both laboratory and field studies (Hanes et al., 2001; Grasmeijer and Kleinhans, 2004; Williams et al., 2005). Ripples have been found in the field in isolation (Masselink et al., 2007). However, bedforms are usually observed in amalgamated form, i.e. ripples superimposed upon SWs, LWRs, mega-ripples and sandbars (Hanes et al., 2001; Grasmeijer and Kleinhans, 2004; Gallagher, 2003; Best, 2005). For the remainder of this paper we will focus on amalgamated bedforms.

Very large mega-ripples have been observed in the continental shelf and in the near shore (Li and Amos, 1999; Gallagher, 2003). Ripples vary in size and shape depending on their relative position with respect to the sandwave they are superimposed upon (García and Maza, 1984; Williams et al., 2005; Cataño-Lopera and García, 2006b). Jan and Lin (1998) and Landry et al. (2007) conducted experiments to study the superimposition of ripples upon sandbars under oblique standing waves, and under totally and partially stationary waves, respectively. Landry et al. (2007) found that sorting of sediments also plays an important role in the sandbar formation. Landry et al. (2007) showed that bar crests (located beneath surface wave nodes) were composed of coarser sand while flat plateaus (located beneath surface wave antinodes) were characterized by finer sands. Similar findings based upon field observations of low-energy sandy beaches generated under long period waves were also reported by Doucette (2002). Observations of small scale ripples superimposed upon sand dunes were described by Venditti et al. (2005).

The study of ripples and larger bedforms are of both scientific and engineering interest, as recognized by Yu and Mei, 2000a, Yu and Mei, 2000b, Williams et al. (2005), Németh et al., 2002, Németh et al., 2006, Morelissen et al. (2003), and Knaapen and Hulscher (2002). The form resistance due to bedforms caused by local flow separation and recirculation can be significant and is dependent on their dimensions, as well as, flow and sediment characteristics (Karim, 1999). Ripple size and geometry play an important role in bottom friction distribution, bottom boundary layer flow, wave attenuation, sediment transport, sediment stratification, and other phenomena in riverine and marine environments. For these reasons, many theoretical, laboratory and field investigations of bedforms generated by the interaction of oscillatory flows and movable beds have been conducted in the past several decades (Miller and Komar, 1980a, Miller and Komar, 1980b; Grant and Madsen, 1982; Foti and Blondeaux, 1995; Li and Davies, 1996; Li and Amos, 1998; Karim, 1999; Blondeaux et al., 2000; O’Donoghue et al., 2006).

Sandwaves and sandbars may represent a hazard to pipelines (Morelissen et al., 2003). The directional shift of these bed features can have a significant impact on pipelines as well as navigational channels, cables, and windmill turbines. Depending on the scale of their dimensions and migration rates, bedforms have the potential to decrease navigable depths thus making frequent dredging activities necessary (Besio et al., 2008).

Prediction of bedform geometry is an essential component for estimating flow resistance and water levels during floods in rivers (Karim, 1999). The importance of bedform study is demonstrated, for example, by the case of a subterranean tunnel built in the Paraná River (Argentina) in 1968. The sand layer thickness above the tunnel was not adequate to stand high flows. Over time, large dunes migrated exposing the tunnel and threatening its structural stability (Amsler and García, 1997; García, 2008).

Most theoretical and numerical models developed thus far are in the early stages of development and their predictive capabilities are limited. For the case of sandwaves formed under tidal influence, several models have been proposed including those by Komarova and Newell (2000), Gerkema (2000), Komarova and Hulscher (2000), Németh et al., 2002, Németh et al., 2006, and Morelissen et al. (2003). For sandbars observed in coastal areas, models by Yu and Mei, 2000a, Yu and Mei, 2000b and Hancock et al. (2007) have been proposed. Giri and Shimizu (2006) developed a numerical model dealing with the migration of sand dunes in rivers. Extensive reviews of recent model developments and experimental and theoretical advances in river dune study are found in Besio et al. (2008) and Best (2005), respectively. Most of these models are based upon the assumption that nonlinear effects are weak, which is often not the case in nature. It is also worth noting that currently all models developed for ocean-like or river-like flow conditions are not able to reproduce the coexistence of smaller scale ripples formed upon the larger scale features. Thus, further research on the interaction of multiple size bedforms and how this interaction defines the dominant bedform modes observed in both coastal and river systems is needed.

In cases of ocean-like flows, the typical dimensions of bedforms created in laboratory flumes are approximately 2 cm in height and 5–30 cm in length for ripples and tens of centimeters in height and several meters in length for LWR (García and Maza, 1984; Williams et al., 2005; Cataño-Lopera and García, 2006a, Cataño-Lopera and García, 2006b). Typical sandwaves observed in the field are several meters high and hundreds of meters long (Morelissen et al., 2003; Komarova and Newell, 2000; Németh et al., 2002, Németh et al., 2006, Németh et al., 2007). Field investigations describing the hydrodynamics over sandwaves through velocity measurements in the coastal shelf can be found in Perillo and Ludwick (1984) and Li and Amos (1999). Using state of the art acoustic equipment, Goff et al. (1999) reported detailed bathymetry of offshore environments.

In the case of river-like flows, the typical dimensions of bedforms in laboratory experiments are tens of centimeters in height and one meter in length (Abad and García, 2009b). On the other hand, in the field, typical progressive dunes in the Paraná River are 3 m high and 50 m long (Parsons et al., 2005).

Spectral analysis techniques, such as wavelet analysis, are increasingly becoming useful tools for analyzing localized variations of power within a time series. Unlike Fourier transformation which requires signal resolution into sine functions and cannot be regarded as a typical spectral tool, wavelets do not assume stationarity and periodicity. Wavelet analysis only assumes finite variance of the processed signal. These assumptions allow wavelets to capture both the dominant modes of variability and how those modes vary in time (Torrence and Compo, 1998). Spectral analysis techniques have been used in the case of SWs formed under unidirectional flows (Nordin and Algert, 1966; Nikora et al., 1997; Nikora and Hicks, 1997). However, little work has applied spectral analysis techniques to bedforms generated under oscillatory flows and highly meandering channels. Cataño-Lopera and García, 2006a, Cataño-Lopera and García, 2006b studied the wavelength distribution of ripples superimposed upon sandwaves by using fast Fourier transform (FFT) under waves alone (WA) and combined flow (CF) scenarios. However, the localization of the dominant modes could not be determined through the FFT technique. Smith and Sleath (2005) also used the FFT of bed profile records to help determine the time evolution of transient ripples generated under oscillatory flow conditions in the laboratory.

Wavelet analysis has been used in numerous studies in areas such as geophysics (Farge, 1992; Meyers et al., 1993; Weng and Lau, 1994; Liu, 1994; Gu and Philander, 1995; Massel, 2001), biology and medicine (Dettori and Semler, 2007), and acoustics (Lardies, 2007). However, this technique has still not been extensively applied to the analysis of bedforms generated either under oscillatory or unidirectional flows. In this paper we propose the application of the wavelet transform (WT) technique in the space domain rather than in the time domain, as conventionally used. Our purpose is to characterize the spatial distribution of coexisting bedforms of multiple dimensions generated under different flow field scenarios, WA, CF, and unidirectional flows.

This paper intends to demonstrate the applicability of wavelet transform analysis in the description of bedforms frequently found in coastal and river environments. An improved description of bed features and their interactions will certainly contribute to a more complete understanding of theories describing bedform formation and evolution. Due to the variability of ripple sizes generated under real wave forcing situations (e.g. the ocean) the use of the semi-empirical model by Traykovski (2007), along with the wavelet analysis could be used to study the dominant modes or ripple wavelength. Traykovski (2007) presented a time-dependent model capable of reproducing variable bi-modal ripple spectra due to the different timescales associated with small and large ripples. Since the size and shape of bedforms strongly influence the flow field and shear stress distribution, the overall understanding of small- and large-scale features is of utmost importance, especially because of their strong implications for the associated patterns of sediment transport. Herein, the intent is not to describe the hydrodynamic interaction of multiple-sized bedforms, but rather to describe the bed morphology given averaged hydrodynamic parameters; this could be used to develop and validate numerical approaches that will allow detailed examination of associated hydrodynamic structures.

Section snippets

Experimental setup and test conditions

Bedforms examined in the present study were generated in two experimental facilities: a wave tank, and a highly meandering channel. Application of the WT to characterize bedform morphology is divided in two cases.

The fast Fourier transform

Before discussing some of the WT characteristics, the widely used FFT is explained briefly. The Fourier transform (FT) is a technique that decomposes a wave form or function into sinusoids, covering a wide range of frequencies, which add up to the original wave form (Torrence and Compo, 1998). The discrete Fourier transform (DFT) of a discrete sequence xn is given byx^k=1Nn=0N-1xne-2πikn/Nwhere k is the frequency index. The discrete sequence xn can be in time or space. This technique suffers

Waves alone

Bed morphology is characterized by a regular pattern of ripples superimposed upon a set of regularly spaced LWRs (Fig. 2).

The longitudinal bed profile at y=0 cm (Figs. 2 and 6a) shows that ripples vary in size and shape along the bed depending on their relative position upon the larger bed features (LWRs). In particular, it is noticeable that (i) smaller ripples align with zones between the crest and the trough of the LWR; (ii) larger ripples align with the crests; and (iii) intermediate sized

Discussion

Geometric characteristics and migration rates of both types of bedforms (ripples and LWRs) for a wide range of experimental conditions, were presented and analyzed by Cataño-Lopera and García, 2006a, Cataño-Lopera and García, 2006b. The authors used FFT to study the characteristics, wavelengths, of both LWRs and ripples. The analysis was based solely on FFT considerations and performed over a single longitudinal profile, at y=0 cm (Fig. 2). Through the FFT, the dominant harmonics associated with

Conclusions

In this study, the wavelet transform was introduced to analyze coexisting bed features generated under two main cases: (1) waves alone and combined flows, and (2) flow in a highly meandering channel.

Experimental evidence shows that ripples superimposed upon LWRs can present two-dimensional (2D) and three-dimensional (3D) patterns depending on their relative location upon the larger bedform. Usually, 3D ripples form in between the trough and the crest, although they form preferably near the

Acknowledgements

The authors thank the support of the Coastal Geophysics Program of the US Office of Naval Research through Grants N00014-01-1-0337 and N00014-05-1-0083. Also the financial support of the Civil and Environmental Engineering department at the University of Illinois at Urbana-Champaign is gratefully acknowledged. Thanks are also due to Dr. J. Paul Smith and Nils Oberg for their valuable comments and suggestions. Reviews by three anonymous reviewers were very helpful and substantially improved the

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