TURBULENT LAVA FLOWS: NOT AS SIMPLE AS RE > 2000

Lava is a complex, multiphase fluid with properties and behavior dependent on temperature, pressure, composition, local shear stresses, and the presence and strength of a solid crust (either stationary or carried along with the lava stream). Early attempts at modeling lava flows necessarily relied on simplifying assumptions such as: 1) constant Newtonian rheology (e.g., Jeffrey’s equation); 2) constant Bingham rheology and flow dimensions (i.e., models deriving yield strength from flow dimensions); 3) constant eruption rates, temperatures, and flow velocities (e.g., the Graetz equation); fully turbulent or laminar (based on the Reynolds number). With current computational capabilities, we should abandon these simplifications, which can lead to misleading or even wrong results.

The Reynolds number is the ratio of inertial forces to viscous forces within a fluid and is given by: Re = ρ u L / μ in which ρ is fluid density (kg/m³); u is fluid velocity (m/s); L (m) is a characteristic length (such as flow depth, or lava tube diameter); and μ is the dynamic viscosity (Pa s). In volcanology, it is commonly assumed 2000 is the critical Re value: lava flow with Re < 2000 is laminar, and Re > 2000 is turbulent.

There are major, often ignored, difficulties to interpreting a lava flow with Re > 2000 as turbulent. First, this critical Re is valid only for internal pipe flow, neglects transitional flow (where 2000>Re<4000; Re>4000 is fully turbulent), and ignores wall roughness effects. Second, the critical Re is strongly geometry dependent (for example, in a pipe, Re>4000, and for sheet flow Re >10⁶ !). Third, turbulent flows have laminar boundary layers governing wall heat loss. For strongly temperature-dependent materials (i.e., lava), the boundary layer is less predictable, possibly migrating (i.e., wall rock melting), and may extend far into the flow.

Using Re = 2000 as the critical value for fully turbulent lava flow is a simplifying assumption that is incorrect most of the time. With COMSOL multiphysics software, we can solve for the lava velocity field without the simplifying assumptions, and clearly demonstrate that fully turbulent lava flows are rare. We can demonstrate this with a range of gravity-driven pipe (lava tube), channel, and sheet flows over a range of common lava characteristics.