Mathematical modeling of mudflow dynamics
More details
Hide details
1 |
Georgian Technical University |
Publication date: 2021-07-05
BoZPE 2021;(1):27–42
KEYWORDS
TOPICS
ABSTRACT
Despite the on-going efforts of scientists, there are still few scientifically justified mathematical
models that give a practical prediction of the origin, dynamics and destructive force of
mudflow. Many problems related to the study of mudflows, and especially their dynamics,
are not extensively studied due to the complexity of the process. The contributions of Gagoshidze
(1949; 1957; 1962; 1970), Natishvili et al. (1976; 1963; 1969), Tevzadze (1971),
Beruchash-vili et al. (1958; 1969; 1979), Muzaev, Sozanow (1996), Gavardashvili (1986),
Fleshman (1978), Vinogradov (1976) towards the study of the hydrology of mudflows
deserves atten-tion. In the scientific works of Voinich-Sianozhensky et al. (1984; 1977) and
Obgadze (2016; 2019), many different mathematical models have been developed that accurately
reflect the dynamics of a mudflow caused by a breaking wave. It should also be noted
that many inter-esting imitation models have been developed by the team of Mikhailov and
Chernomorets (1984). In mountainous districts, the first hit of a mudflow is taken on by
lattice-type struc-tures offered by Kherkheulidze (1984a; 1984b) that release the flow from
fractions of large stones and floating trees. After passing through the lattice-type structures,
the mudflow is re-leased from large fractions and turns into a water-mud flow. In order to
simulate this flow, a mathematical model based on the baro-viscous fluid model offered by
Geniev-Gogoladze (1987; 1985) has been developed, where the averaging formula of
Voynich-Sianozhencki is used for the particle density, and for the concentration of the solid
phase, the diffusion equa-tion is added to the system dynamics equations. In the given article,
for the constructed math-ematical model, the exact solution of the one- dimensional flow in
the mudflow channel is considered. The problem of stratification of the fluid density under
equilibrium conditions is discussed. In the riverbed of the Kurmukhi River, for two-dimensional
currents, the problem of flow around the bridge pier with an elliptical cross-section
is considered. The Rvachev-Obgadze variation method (1982; 1989a; 1989b) is used to solve
the streamlined problem.