Paolo Blondeaux

A unified bar–bend theory of river meanders

A two-dimensional model of flow and bed topography in sinuous channels with erodible boundaries is developed and applied in order to investigate the mechanism of meander initiation. By reexamining the problem recently tackled by Ikeda, Parker & Sawai (1981), a previously undiscovered ‘resonance’ phenomenon is detected which occurs when the values of the relevant parameters fall within a neighbourhood of certain critical values. It is suggested that the above resonance controls the bend growth, and it is shown that it is connected in some sense with bar instability. In fact, by performing a linear stability analysis of flow in straight erodible channels, resonant flow in sinuous channels is shown to occur when curvature ‘forces’ a ‘natural’ solution represented by approximately steady perturbations of the alternate bar type. A comparison with experimental observations appears to support the idea that resonance is associated with meander formation.

Numerical experiments on flapping foils mimicking fish-like locomotion

The results of numerical experiments aimed at investigating the topology of the vortex structures shed by an oscillating foil of finite span are described. The motion of the foil and its geometry are chosen to mimic the tail of a fish using the carangiform swimming. The numerical results have been compared with the flow visualizations of Freymuth [J. Fluids Eng. 111, 217 (1989)] and those of von Ellenrieder et al. [J. Fluid Mech.490, 129 (2003)]. The results show that a vortex ring is shed by the oscillating foil every half a cycle. The dynamics of the vortex rings depends on the Strouhal number St. For relatively small values of St, the interaction between adjacent rings is weak and they are mainly convected downstream by the free stream. On the other hand, for relatively large values of St, a strong interaction among adjacent rings takes place and the present results suggest the existence of reconnection phenomena, which create pairs of longitudinal counter-rotating vortices.

Coherent structures in oscillatory boundary layers

The dynamics of the vortex structures appearing in an oscillatory boundary layer (Stokes boundary layer), when the flow departs from the laminar regime, is investigated by means of flow visualizations and a quantitative analysis of the velocity and vorticity fields. The data are obtained by means of direct numerical simulations of the Navier–Stokes and continuity equations. The wall is flat but characterized by small imperfections. The analysis is aimed at identifying points in common and differences between wall turbulence in unsteady flows and the well-investigated turbulence structure in the steady case. As in Jimenez & Moin (1991), the goal is to isolate the basic flow unit and to study its morphology and dynamics. Therefore, the computational domain is kept as small as possible. The elementary process which maintains turbulence in oscillatory boundary layers is found to be similar to that of steady flows. Indeed, when turbulence is generated, a sequence of events similar to those observed in steady boundary layers is observed. However, these events do not occur randomly in time but with a repetition time scale which is about half the period of fluid oscillations. At the end of the accelerating phases of the cycle, low-speed streaks appear close to the wall. During the early part of the decelerating phases the strength of the low-speed streaks grows. Then the streaks twist, oscillate and eventually break, originating small-scale vortices. Far from the wall, the analysis of the vorticity field has revealed the existence of a sequence of streamwise vortices of alternating circulation pumping low-speed fluid far from the wall as suggested by Sendstad & Moin (1992) for steady flows. The vortex structures observed far from the wall disappear when too small a computational domain is used, even though turbulence is self-sustaining. The present results suggest that the streak instability mechanism is the dominant mechanism generating and maintaining turbulence; no evidence of the well-known parent vortex structures spawning offspring vortices is found. Although wall imperfections are necessary to trigger transition to turbulence, the characteristics of the coherent vortex structures, for example the spacing of the low-speed streaks, are found to be independent of wall imperfections.

River, coastal and estuarine morphodynamics

1 Perspectives in Morphodynamics.- 2 Sediment Entrainment and Transport in Complex Flows.- 3 Alluvial Roughness in Streams with Dunes: A Boundary-Layer Approach.- 4 The Use of Numerical Models in Coastal Hydrodynamics and Morphology.- 5 Process of Occurrence, Flow and Deposition of Viscous Debris Flow.- 6 Transverse Slope of Bed and Turbid-Clear Water Interface of Channelized Turbidity Currents Flowing around Bends.- 7 Pattern Formation in the Nearshore.- 8 Long-Term Morphological Prediction.- 9 River and Tidal Networks.

On the formation of sand waves and sand banks

A fully three-dimensional model is proposed for the generation of tidal sand waves and sand banks from small bottom perturbations of a flat seabed subject to tidal currents. The model predicts the conditions leading to the appearance of both tidal sand waves and sand banks and determines their main geometrical characteristics. A finite wavelength of both sand waves and sand banks is found around the critical conditions, thus opening the possibility of performing a weakly nonlinear stability analysis able to predict the equilibrium amplitude of the bottom forms. As shown by previous works on the subject, the sand wave crests turn out to be orthogonal to the direction of the main tidal current. The present results also show that in the Northern Hemisphere sand bank crests are clockwise or counter-clockwise rotated with respect to the main tidal current depending on the counter-clockwise or clockwise rotation of the velocity vector induced by the tide. Only for unidirectional or quasi-unidirectional tidal currents are sand banks always counter-clockwise rotated. The predictions of the model are supported by comparisons with field data. Finally, the mechanisms leading to the appearance of sand waves and sand banks are discussed in the light of the model findings. In particular, it is shown that the growth of sand banks is not only induced by the depth-averaged residual circulation which is present around the bedforms and is parallel to the crests of the bottom forms: a steady drift of the sediment from the troughs towards the crests is also driven by the steady velocity component orthogonal to the crests which is present close to the bottom and can be quantified only by a three-dimensional model. While the former mechanism appears to trigger the formation of counter-clockwise sand banks only, the latter mechanism can give rise to both counter-clockwise and clockwise rotated sand banks.

A note on tidally generated sand waves

The process leading to the formation of sand waves in tide dominated coastal areas is investigated by means of the linear stability analysis of a flat sandy bottom subject to oscillatory tidal currents. The conditions for the decay or amplification of small bottom perturbations are determined for arbitrary values of the parameters of the problem. According to field observations, the initial growth of sand waves requires a minimum amplitude of the tidal current, even when the critical bed shear stress for the initial motion of sediment is set equal to zero. Moreover the minimum amplitude depends on sediment characteristics. In particular, the analysis shows that sand waves appear only for a sandy bottom and their growth does not take place when a coarse sediment covers the sea bed. The solution procedure extends the truncation method which is often used to describe the flow generated by the interaction of bottom perturbations with the oscillatory tidal current. The obtained results show that the truncation method describes the mechanism inducing the growth of sand waves, but values of the parameters exist for which its results are not quantitatively accurate. Finally, the asymptotic approach for large values of both r ,w hich isthe ratio between the amplitude of the horizontal tidal excursion and the wavelength of the bottom perturbations, and of the stress parameter s is modified in the bottom boundary layer to describe cases characterized by values of s of order one, which is the order of magnitude suggested by an analysis of field data.

Sand ripples under sea waves Part 3. Brick-pattern ripple formation

An oscillatory flow over a cohesionless bottom can produce regular three-dimensional bedforms known as brick-pattern ripples characterized by crests perpendicular to the direction of fluid oscillations joined by equally spaced bridges shifted by half a wavelength between adjacent sequences (a photo of brick-pattern ripples is shown in Sleath 1984, p. 141). In the present paper brick-pattern ripple formation is explained on the basis of a weakly nonlinear stability analysis of a flat cohesionless bottom subject to an oscillatory flow in which three-dimensional perturbations are considered.

Sea ripple formation: the heterogeneous sediment case

Abstract Ripple formation beneath sea waves is analyzed both by experimental and analytical means when the bottom is made up of a mixture of sands. An oscillatory flow is obtained in a closed duct by the oscillations of two rigidly connected pistons located at the ends of the duct. The amplitude and period of the oscillations can be continuously varied. A fixed tray, located at the bottom of the duct and filled with different types of sediments, allows ripple formation to be observed. The presence of graded sediments is found to have a stabilizing effect and causes longer ripples to appear. Moreover a selective sediment transport is observed and quantified which tends to pile up the coarse grains at ripple crests leaving the fine ones in the troughs. As in the companion paper, the theory is based on a linear stability analysis of a flat sandy bottom subject to an oscillatory flow. Because of the presence of a mixture, a modified version of Exner equation is used and an “hiding” factor should be inserted in the sediment transport rate formula. The flow regime in the bottom boundary layer is assumed to be turbulent. The conditions for ripple appearance are determined along with their wavelengths as they form. Good agreement is found between experimental data and theoretical findings.

Turbulent boundary layer under a solitary wave

The boundary layer generated by the propagation of a solitary wave is investigated by means of direct numerical simulations of continuity and Navier-Stokes equations. The obtained results show that, for small wave amplitudes, the flow regime is laminar. Turbulence appears when the wave amplitude becomes larger than a critical value which depends on the ratio between the boundary-layer thickness and the water depth. Moreover, turbulence is generated only during the decelerating phase, or conversely, turbulence is present only behind the wave crest. Even though the horizontal velocity component far from the bed always moves in the direction of wave propagation, the fluid particle velocity near the bottom reverses direction as the irrotational velocity decelerates. The strength and length of time of flow reversal are affected by turbulence appearance. Also the bed shear stress feels the effects of turbulence presence.

Migrating sea ripples

Ripple formation under sea waves is investigated by means of a linear stability analysis of a flat sandy bottom subject to the viscous flow which is present in the boundary layer at the bottom of propagating sea waves. Nonlinear terms in the momentum equation are retained to account for the presence of a steady drift. Hence the work by Blondeaux is extended by considering steeper waves and/or less deep waters. Second order effects in the sea wave steepness are found to cause neither destabilizing nor stabilizing effects on the process of ripple formation. However, because of the presence of a steady velocity component in the direction of wave propagation, ripples are found to migrate at a constant rate which is predicted as function of sediment and wave characteristics. The analysis assumes the flow regime in the bottom boundary layer to be laminar and the results are significant for ripples at the initial stage of their formation or for mature ripples of small amplitude (rolling-grain ripples). A comparison of the theoretical findings with laboratory experiments supports the reliability of the approach and of the theoretical results.