Dynamics of boundary layer formation in a volcano channel in a cavitating high-viscosity magma flow

Based on the full mathematical model of a viscous magma melt flow ascending in the gravity field behind a decompression wave front, an unsteady two-dimensional axisymmetric problem of the melt state dynamics at the initial stage of an explosive volcanic eruption and specific features of the flow in the vicinity of the channel wall for the cases of stationary and dynamically increasing viscosity are studied. The evolution of the boundary layer is numerically analyzed for a constant melt viscosity equal to $\mu = 10^3,10^5$, and $10^7$ Pa $\cdot$ sec. It is demonstrated that a boundary layer is formed on the wall of the channel with a radius of $100$ m as the melt viscosity is changed in the range of $10^3$–$10^5$ Pa $\cdot$ sec, and the boundary layer thickness increases from $2$ to $15$ m. As the magma viscosity increases to $10^7$ Pa $\cdot$ sec, the boundary layer chokes the major part of the channel, thus, locking the flow in the vicinity of the axis of symmetry of the channel almost over the entire channel length. Substantial changes in the flow structure caused by dynamically increasing viscosity are demonstrated by an example of the melt in the channel with a radius of $10$ m. By the time $t = 1.1$ sec, the boundary layer thickness in the channel cross section at a height of approximately $1000$ m reaches almost $8$ m, the boundary layer acquires the shape similar to a “diaphragm”, penetrates inward the channel by $200$ m (with the mass velocity ranging from $0$ to $15$ m/sec), and locks the flow in a zone with a radius of approximately $2$ m around the axis of symmetry of the channel.