Multiplicative cascade
The models in multiplicative cascade are a dependence structures between successive scales. As mentioned above, the cascade phenomenology was initialized by the Richardson poem. However, it was until 1960s that explicit multiplicative cascade models were first developed. Even though they almost certainly played a role when Kolmogorov formulated his famous law in 1941 [Kolmogorov, A. N, 1941][1], he did not explicitly mention cascades.
The multiplicative cascade were designed in order to generate conservative fields. The cascade concept is used to reproduce the variability (intermittent) of the measured field (geophysics, biology, finance,...etc).
