IDENTIFICACIÓN DE ESTRATEGIAS ALTERNATIVAS

For more precise estim ation of dune m igration speed, a b e tte r estim ation of sand trap p ing efficiency is necessary, for which wake and turbulence effects on sand- grain trajectories need to be incorporated into the m odel (section 2.4.2). It is also im p o rtan t to bear in m ind th a t wind stru ctu re in th e lee of a dune fluctuates significantly (section 2.4.4).

It is suggested th a t the w ind-directional proflle of a barchan dune can be explained in term s of th e self-adjusting mechanism such th a t a dune is a t equilibrium . W ith the sam e assum ption of equilibrium it may also be possible to explain why the cross-sectional shape th a t is perpendicular to the wind is independent of dune height. To check this, the model should be extended into three dimensions. A possible modelling scheme would be to consider a barchan dune as p a rt of a sinuous transverse dune whose linguoid height is zero (section 4.4).

W hen a dune is far from equilibrium , it is probably difficult to investigate the windward surface profile from th e estim ation of sand trap p in g efficiency. In such a situation, we m ay need to rely on th e iterative calculation models illustrated in Figures 2.3 and 3.2.

7.3.2

D u n e field m odel

This thesis has discussed barchan, transverse, dome and linear dunes in particular relation to th eir form ative environm ents. However some other types of free dune, such as star, network and zibar parabolic dunes, have yet to be sim ulated (sec­ tion 2.2). A n a tu ra l extension of the present study m ight be to sim ulate parabolic dunes, which occur where vegetation is present (Lancaster, 1995, pp76-77). O th ­ ers m ay be sim ulations of climbing and falling dunes, in which existing topography should be incorporated into the model (Lancaster, 1995, pp82-83). Ultimately, the m odel will aim a t a dune field where many types of dunes co-exist (Figure 7.1). Such a model will be hierarchical and distributed, by assigning regionally differ­ ent param eters for each subset of the whole sim ulated area (lattice). The study of coastal dune system s is an example of areas th a t require a d istrib uted model. In de C astro ’s (1995) coastal dune-field model, as th e sim plest approxim ation, param eters are constant throughout th e sim ulated area, b u t different boundary conditions are enforced on th e upwind and downwind edges, each representing sea and inland respectively.

The study of transitions between types of dune may be an intriguing topic th a t could be investigated w ith th e model, especially in respect to p a tte rn form ation in a non-linear system . We have already seen, for exam ple, two types of transition when increasing sand availability in a uni-directional w ind environm ent (section 6.3.1). There was an acute tran sition from no p a tte rn to a p a tte rn of isolated (dome) dunes, where th e system also shows bi-stability depending on initial con­ ditions. G radual transitions from dome to barchan, from barchan to transverse dunes have been modelled. A detailed and comprehensive study in a param eter

L i n e a t e d S a n d S h e e t

S tar D u n es an d T ran sv erse M ega-D unes

Complex D unes

S tar D unes

Linear M ega-D unes / S an d S h e e t T ra n sv erse M ega-D unes

Linear M ega-D unes

Figure 7.1: Various types of dune in the Great W estern Sand Sea in Algeria (transferred from Cooke e t al., 1993, figure 28.5; the original is in Breed e t a!., 1979).

space, for example in sand-availability-wind-complexity space, is im p o rtant {cf.

an example of such an investigation can be seen in the study of Duffing’s equa­ tion which describes a periodically forced oscillator (Ueda, 1980 referred to in Thom pson and Stewart, 1985, figure 1.10).

Because the sim ulation rules are introduced phenomenologically, continuous com­ parison between sim ulated results and observations of n atu ral bedforms is vital to the improvement of the models. Unlike the study of aeolian bedforms, the study of subaqueous bedforms can use the detailed and quantitative d a ta th a t are readily available. For example recent flume experiments show how ripples grow; the ini­ tial fiat surface is destabilised and a two-dimensional transverse p attern appears; as it grows, the ripples change their form in a more three-dim ensional m anner (Baas, 1999; Figure 7.2). This secondary instability, which is the breaking of the sym m etry in the direction at right angles to the current {i.e. the origin of sinu­

trr.•,2 =141 mm ■17 mm) 1 _r 0 0 1 2 ^ . , 2

Figure 7.2 : Current ripples development observed in a flume (transferred from Baas, 1999).

osity), has also been observed in bedforms under oscillatory currents (Lundbek Hansen et a l, 2001). The study of subaqueous bedforms is interesting not only for geomorphology or sedimentology. It provides topics th a t are intriguing for the stu d y of p a tte rn form ation in non-linear and non-equilibrium systems. For exam­ ple, in addition to the above secondary instability, Lundbek Hansen et a l, (2001) also showed how the wavelength of ripples changed, depending on param eters (am plitude and frequency of the oscillation). For these bedforms, well defined experim ents are available. Param eters are easily controllable and recurrent re­ sults are available a t tim e scales of only m inutes to days. These experim ents m ay have th e potential to be prototypes in the study of non-linear dynamics, alongside, or even taking over from, conventional experim ents such as those of B énard convection and in studies of electrically-driven liquid crystal convection (Cross and Hohenberg, 1993).

7.3.3

C ollaboration

The m athem atical modelling of dunes and dune fields is a t th e boundary where m any fields of study, such as geomorphology, geology, meteorology, physics and

m athem atics, m eet. C ollaboration am ongst people from these fields of study is essential for im proved modelling. We have already seen in th e previous section th a t insights based on non-linear dynam ics can play a significant role (section 7.2.1) in th e investigation of dune-field m orphodynam ics. A nother successful example of collaboration was in the a tte m p t to m odel a single dune. The au th o r was fam iliar w ith th e idea of self-consistent m odelling, th ro u g h th e knowledge of phase tra n sitio n and m agnetic recording. T he suggestion th a t m odel results m ight be applicable to dune-to-plane-bed tran sitio n in subaqueous bedform s was m ade by A ndrew W arren^, who had a wide range of knowledge of dunes. To revise each m odel fu rth er, fluid dynam ic, meteorological, clim atological and geological knowledge will be necessary.