RANSE Modeling of the Oscillatory Flow Over Two‐Dimensional Rigid Ripples

Abstract

In the nearshore region, the hydrodynamics and the sediment transport are highly affected by the interaction of the waves with the sea bottom. Often the sea bed is covered with small-scale undulations, called ripples .In the coastal region, the ripples generated by surface waves are characterized by wavelengths of the order of tens of centimeters and heights of the order of centimeters. Moreover, ripples can be either two-dimensional (long-crested ripples) or three-dimensional.Ripples are relevant from a practical point of view because they influence both the surface wave and the sediment transport. Indeed, ripples dissipate wave energy because of the vortices which are generated each half oscillation cycle at the ripple crest. Such vortices influence also the near-bottom sediment transport, because they are particularly effective in picking up the sediment from the bottom and they influence the spatial and temporal evolution of sediment concentration close to the sea bed.At the early stages of their development, two-dimensional ripples have a small height. These bottom features are called rolling-grain ripples (Sleath, 1984). The mechanism of formation of rolling-grain ripples from a plane bed subject to an oscillatory flow is associated to the formation of steady recirculating cells which form because of the interaction of the bottom profile, which is characterized by a waviness of small amplitude, with the oscillatory flow (Sleath, 1984). The steady velocity components close to the bottom profile are directed from the troughs toward the crests of the waviness, thus dragging the sediment and causing the growth of the ripples. Vittori (1989) showed that the number of steady recirculating cells per ripple wavelength can be two or four, depending on the values of the controlling parameters.Typically rolling-grain ripples evolve into vortex ripples. Stable rolling grain ripples are observed mainly in laboratory experiments.

Selection of vortex ripple dimensions in sinusoidal oscillatory flows. Part 1. Ripple dimensions and fluid kinematics

“…The shape of vortex ripples generated by wave boundary layers could be important in the local hydrodynamics and sediment transport, which is a result of many factors such as the oscillatory flow intensity, wave period, wave nonlinearity, horizontal steady streaming, migration direction and sediment properties (Wang & Yuan 2019; Sishah & Vittori 2022). In order to avoid additional complexity, similar to Önder & Yuan (2019), the bottom profile in all our simulations is defined as the superposition of two harmonics, which reads where is the wavenumber of the ripple waviness, and the relative amplitude of the second harmonic is prescribed to be following Önder & Yuan (2019).…”