The paper addresses the prediction of roll-waves occurrence in mud-flows. The spatial growth of a point-wise disturbance is analytically described, based on the linearized flow model of a Herschel and Bulkley fluid, in the neighborhood of an initial uniform base condition. The theoretical achievements allow to generalize to mud-flows the minimum channel criterion commonly used for the prediction of roll-waves in clear-water. The applicability of the criterion is discussed through the comparison with literature laboratory data concerning unstable flows without rollwaves.
Floristic composition, morphological functional types, and altitudinal distribution pattern for C4 species were studied in Yunnan province, South-western China. 159 species, in 6 families and 60 genera, were identified with C4 photosynthesis. 93 % of these C4 species were found in Monocotyledoneae, e.g. Cyperaceae (18 species), Gramineae (129 species), and Commelinaceae (1 species), the other 7 % was in Dicotyledoneae, e.g. Amaranthaceae (5 species), Portulacaceae (4 species), and Chenopodiaceae (2 species). Hence C4 plants mainly occurred in very few families in the tropical region. Compared with those in semi-arid grasslands and arid deserts in North China, more C4 grasses and much less Chenopodiaceae C4 species occurred in the tropical region. This indicates the physiological responses of C4 plants from the two families are very different. Chenopodiaceae C4 species may be more fit semi-arid and arid environments, while C4 grasses are more fit the moist tropical conditions. There was a strong relationship between C4 distribution and altitude in the tropical region. Altitudinal distribution pattern for C4 species in the region was consistent with altitude, climate, and habitats.