rium dune field
6.3 T h e effects o f sand availability and w ind vari ability
W ind variability and sand availability are tho u g h t to be th e two m ost im p o rtan t controls of dune type (see section 2.3). In this section, th e effects of these two controls are investigated. The first two subsections (6.3.1 and 6.3.2) discuss uni directional w ind regimes, and the last subsection (6.3.3) deals w ith bi-directional wind regimes. In th e model, sand availability is defined as th e average num ber of slabs per site (havg) taken over all sites. T he effects of sand availability are inves tig ated w ith the concept of the reference num ber of slabs, which was introduced in section 5.6. W ind variability is sim ulated w ith th e lattice ro ta tio n introduced in section 5.7.
6.3.1 D u n e ty p es in a uni-directional w ind regime: p at
tern and sand availability
In Figure 6.9 we show th e results of a sim ulation of t = 1500 beginning w ith an alm ost fiat surface. As havg increases, the dune field changes from no p a tte rn (havg < 1.1) to barchan dunes shown in Figure 6.9(a) for havg = 2.0, th en to laterally connected barchan dunes (Figure 6.9(b), havg = 7.0), and finally to transverse dunes (Figure 6.9(c), havg = 20.0). T he laterally connected barchan dunes are more sinuous th a n th e transverse dunes form ed in an infinitely deep sand field. T he change from barchan dunes to transverse dunes in response to th e increase of sand availability coincides w ith field observations (Livingstone and W arren, 1996, figure 5.22; reproduced in Figure 2.2).
C haracteristics of each p a tte rn can be extracted th ro u g h th e Fourier transform
(h{i,j) —>• h{ i,j )) . The Fourier com ponents which are n o t th o u g h t to contribute to the p a tte rn (h(0, j ) and h(i, 0)) are all excluded. As sand availability increases, th e wavelength in the i direction decreases. For an infinitely deep sand field, the
(a)
(b)
(c)
Figure 6.9: Different types of dune simulated with various sand avail abilities (/iavg): (a) 2.0, (b) 7.0 and (c) 20.0. All simulations started with an almost flat surface. The wind blows from left to right. The contour interval \s h = b.
first peak is 78.8, and the second is 102.4. Transverse dune system s formed in an infinitely deep sand field are more regular th a n one w ith inter-dune bare surfaces. The intensity ratio of the first peak to the second peak is higher when havg ^ 20.0 th a n when havg = 10.0.
There is a sudden transition from no p a tte rn to a p a tte rn of isolated dunes w ithout d istinct asym m etry or slip face, nam ely dome dunes. T his tran sitio n was checked by using 15 different sets of sim ulations. Table 6.2 shows th e resulting m axim um num ber of slabs (hmax), for sand availability (havg) values of 1.1 and 1.2. In all sim ulations w ith an average num ber of slabs per site (havg) of 1.1, no p a tte rn was formed, whereas for havg of 1.2, isolated dunes form ed in all sim ulations. The threshold thus lies between havg of 1.1 and 1.2. As sand availability increases further to havg = 2.0, these dome dunes gradually change to barchan dunes. If, ra th e r th a n startin g w ith an alm ost flat surface, we s ta rt w ith an initial sur face consisting of barchan dunes, they rem ain as features even when th e sand availability is less th a n the previously determ ined threshold.
In th e following numerical experim ents, the sim ulation tim e (t) is 3000, th e first half {t < 1500) of this tim e being for th e in itial barchan dunes creation. At
t = 1500 half of th e slabs a t every site were removed, and then simulations were resumed. T h a t is a t t = 1500 we reduced th e barchan dunes to half their height, w ith a corresponding reduction in the steepness of th e windward surfaces.
sim ulation 1 2 3 4 5 6 7 8 9 10 ^majc(^avg — IT ) 5 5 5 4 5 5 4 5 5 4 ^raax(^avg “ 1.2) 23 25 22 24 25 25 21 22 23 24 sim ulation 11 12 13 14 15 ^max(^avg ~ IT ) 4 4 4 4 5 ^majc(^avg — 1.2) 24 26 25 24 22
T able 6.2: Maximum dune height when sand availabilities are below and above the threshold.
The initial sand availability (havg(^ < 1500)) was varied from 1.2 to 2.0. Ta ble 6.3 shows the sand availabilities (havg) for t < 1500 and for t > 1500, the resulting m axim um num ber of slabs {hmax) and th e p a tte rn s a t t = 3000. ‘N ’ and ‘D ’ represent no p a tte rn and th e p a tte rn w ith (barchan) dunes, respectively. Dunes did no t disappear completely, even w ith th e sand availability less th a n th e threshold. However, m any of these dunes are not strongly asym m etric in th eir w ind-directional shape, and do not have distinct slip faces. In th e region below th e threshold, the system can be said to be bistable, i.e. b o th no p a tte rn and th e p a tte rn w ith isolated (dom e/barchan) dunes can exist, depending on the initial surface morphology. To check if there is another threshold in sand avail ability, below which initially placed barchan dunes disappear, m ore sim ulations are necessary.