A unified model for bedform development and equilibrium under unidirectional, oscillatory and combined‐flows

Abstract

The development of bedforms under unidirectional, oscillatory and combined-flows results from temporal changes in sediment transport, flow and morphological response. In such flows, the bedform characteristics (for example, height, wavelength and shape) change over time, from their initiation to equilibrium with the imposed conditions, even if the flow conditions remain unchanged. These variations in bedform morphology during development are reflected in the sedimentary structures preserved in the rock record. Hence, understanding the time and morphological development in which bedforms evolve to an equilibrium stage is critical for informed reconstruction of the ancient sedimentary record. This article presents results from a laboratory flume study on bedform development and equilibrium development time conducted under purely unidirectional, purely oscillatory and combined-flow conditions, which aimed to test and extend an empirical model developed in past work solely for unidirectional ripples. The present results yield a unified model for bedform development and equilibrium under unidirectional, oscillatory and combined-flows. The experimental results show that the processes of bedform genesis and growth are common to all types of flows, and can be characterized into four stages: (i) incipient bedforms; (ii) growing bedforms; (iii) stabilizing bedforms; and (iv) fully developed bedforms. Furthermore, the development path of bedform; growth exhibits the same general trend for different flow types (for example, unidirectional, oscillatory and combined-flows), bedform size (for example, small versus large ripples), bedform shape (for example, symmetrical or rounded), bedform planform geometry (for example, two-dimensional versus three-dimensional), flow velocities and sediment grain sizes. The equilibrium time for a wide range of bed configurations was determined and found to be inversely proportional to the sediment transport flux occurring for that flow condition.

Predicting bedforms and primary current stratification in cohesive mixtures of mud and sand

“…In reality, however, changes in bedform size and shape often lag behind changes in flow strength. This so-called bedform hysteresis effect has been studied in detail by, for example, Muller (1941), Raudkivi (1963), Alexander (1980), Tsujimoto & Nakagawa (1982), Lam Lau (1988, Raudkivi & Witte (1990), Baas (1994Baas ( , 1999, Oost & Baas (1994), Betat et al (2002), Coleman et al (2003), Rauen et al (2009), Soulsby et al (2012, Nabi et al (2013) and Perillo et al (2014c) for current ripples, by Gee (1975), Allen (1976aAllen ( -d, 1978; Allen & Friend (1976a,b), Fredsoe (1979), Wijbenga (1990), Gabel (1993), Coleman et al (2003), Venditti et al (2005), Martin & Jerolmack (2013) and Nabi et al (2013) for current-generated dunes, and by Faraci & Foti (2002), Austin et al (2007), Lacy et al (2007), Chou & Fringer (2010), Soulsby et al (2012), Calantoni et al (2013) and Perillo et al (2014c) for wave-generated bedforms and combined flow bedforms. The adaptation time of bedforms to a change in flow forcing increases with increasing equilibrium size of the bedforms, increasing sediment size and decreasing flow strength (e.g.…”

“…The adaptation time of bedforms to a change in flow forcing increases with increasing equilibrium size of the bedforms, increasing sediment size and decreasing flow strength (e.g. van Rijn 1993;Baas 1994Baas , 1999Soulsby et al 2012;Perillo et al 2014c). Because flow velocities in nature are prone to rapid temporal variations, many natural bedforms continuously try to adapt to changes in flow velocity without reaching a state of equilibrium, or at best maintain equilibrium for a short period of time.…”

“…Equation (4) is also applicable to wave ripples and combined flow bedforms (Perillo et al 2014c); yet Baas et al (2014) inferred from flume experiments that wave ripples develop at a faster rate than current ripples.…”

Simple stochastic cellular automaton model for starved beds and implications about formation of sand topographic features in terms of sand flux

“…If the sand discharge is quantified by bulk volume (including both sand and intergrain voids) per unit time, the dimensions of sand flux are the square of length over time (L 2 /T), because the volume per width is measured in units of L 2 . It is known that when a bedform develops from a flat bed, the migration velocity decreases, but the size of the bedform increases asymptotically (Baas 1994;Coleman et al 2003;Perillo et al 2014). However, the actual time dependence of the sand flux has rarely been measured; this is probably due to the difficulty of doing so.…”

“…Bedforms, including both subaerial and subaqueous ones, have been studied for more than half a century, mainly starting with the pioneering field observations of Bagnold (1941) and the laboratory studies of Allen (1968) and continuing to recent comprehensive experiments (e.g., Perillo et al 2014). Theoretical studies also have been conducted, employing various approaches, such as linear and nonlinear stability analyses (e.g., Melo et al 2012;Andreotti et al 2012); first-principle calculations for fluids and/or grains (e.g., Wippermann and Gross 1986;Schwämmle and Herrmann 2003;Duran et al 2014); simulations with simplified continuous models, such as a defect-crest line dynamics model (Werner and Kocurek 1999), a skeleton model (Niiya et al 2010), and a single-dune-based particle model (Parteli and Herrmann 2003;Diniega et al 2010); and simulations with various cellular automaton (CA) models (e.g., Nishimori and Ouchi 1993;Werner 1995;Momiji et al 2000;Katsuki et al 2005).…”