International Journal of Sediment Research 23 (2008) 1-12 Transition from wavelets to ripples in a laboratory flume with a diverging channel William B. RAUEN 1 , Binliang LIN 2 , and Roger A. FALCONER 3 Abstract An experimental investigation on the initiation and development of bed forms on a bed of fine silica sand was conducted under alluvial flow conditions in a laboratory flume with a diverging channel. The main aims of the study were to assess: i) the steepness of bed forms in the transition stage of development; and ii) the threshold height of wavelets (η t ) that triggered the start of ripple development. Detailed bed profile measurements were carried out using an acoustic Doppler probe, traversed longitudinally over the sediment bed at various experimentation times. The bed form dimensions were extracted from such bed profile records and analysed for the wavelet, transition and equilibrium stages. It was found that the steepness of ripples in the transition and equilibrium stages were similar, confirming predictions of previous mathematical model simulations. A lognormal distribution fitted the wavelet length data. The wavelet threshold height was estimated as η t ≈ 7 mm, or y + ≈ 80 in wall units. Such a height magnitude suggested that ripple development could be triggered by the wavelets reaching the outer flow zone of a turbulent boundary layer. The η t value obtained corresponded generally to the intersection point between two predictive equations for bed form dimensions. A formulation was developed to predict η t as a function of the sediment grain size, which was confirmed for the fine sand used in this study. Key Words: Bed form, Bed ripple, Doppler sonar, Scale model, Wave height, Wavelength 1 Introduction Previous studies of the mechanics of bed form initiation and growth have shown that the current-induced development of bed forms on an initially flat sediment bed of uniform quartz sand can typically be divided into three stages, including: i) wavelet stage; ii) transition stage; and iii) the equilibrium stage. During each of these stages the time variation of the height (η) and the length (λ) occurs generally according to the schematic representation illustrated in Fig. 1a, where η and λ are depicted in Fig. (1b). As shown by Coleman and Melville (1996), wavelets are incipient 2-D cross-flow bed forms from which both ripples and dunes can develop. The wavelet stage can be generally characterised by these incipient bed forms showing a preferred and almost constant spacing, i.e. λ w , as depicted in Fig. (1a). Zhou and Mendoza (2005) suggested a possible cause for the occurrence of this phenomenon based on the assumption that the incipient bed forms separated by such an interval would receive the maximum energy transfer from the flow field. This effect would guarantee the fastest growth rate for such bed forms, making them the dominant features locally. The wavelet stage is triggered when the height of random pileups of sediment on the bed reaches a certain critical value, i.e. η w , at time t w , as depicted in Fig. (1a). Such a threshold height has been related 1 Dr., 3 Prof., Hydro-environmental Research Centre, School of Engineering, Cardiff University, The Parade, Cardiff CF24 3AA, UK 2 Prof., Hydro-environmental Research Centre, School of Engineering, Cardiff University, The Parade, Cardiff CF24 3AA, UK, E-mail: LinBL@cf.ac.uk Note: The original manuscript of this paper was received in Sept. 2007. The revised version was received in Dec. 2007. Discussion open until March 2009. International Journal of Sediment Research, Vol. 23, No. 1, 2008, pp. 1-12 - 1 -