Laminar-turbulent transition in debris flow: measurement of basal pore fluid pressure in an open channel flow experiment

The fluidity of a debris flow varies by grain size. Flows containing principally coarse grains are considered to be laminar and those featuring largely incohesive fine grains turbulent. The transition from laminar to turbulent flow depends on the ratio of flow depth to grain size (i.e., the relative flow depth). Debris flows with relative flow depths of approximately 10 are entirely laminar; those with relative flow depths over approximately 20 exhibit transitional flow behavior from entirely laminar to partially turbulent. This transitional flow has been investigated in the laboratory using the resistance law and the vertical distribution of streamwise velocity. The flow exhibits a two-layer structure; the lower layer remains laminar but the upper layer becomes turbulent. However, transition modeling remains incomplete given the lack of data on the internal stresses associated with transitional flow. Here, we studied the laminar-turbulent transitions of debris flows by measuring basal pore fluid pressures using flume tests.

We flowed saturated monodisperse granular materials over an open-channel rigid bed; we used sediment particles of diameters 2.9, 2.2, 1.3, 0.8, 0.5, and 0.2 mm. When the debris flow attained the steady state, the flow depth and basal pore fluid pressure were measured using an ultrasonic sensor and pressure gages respectively, and the basal total normal stress estimated using the bulk density of the debris flow assessed at the downstream end.

The relative flow depths ranged from 5 to 130. Comparisons among the measured pore fluid pressures and the hydrostatic and total normal stresses indicated that a pore fluid pressure of 0.2 mm differed greatly from the hydrostatic pressure, equaling, in fact, the total normal stress, and indicating fully turbulent flow. In contrast, pore fluid pressures of 2.9, 2.2, and 1.3 mm were slightly higher than the hydrostatic pressures, indicating that the Reynolds stresses of the pore fluid due to the strong shears imparted by the sediment particles were in play; flow was entirely laminar. Pore fluid pressures of 0.8 and 0.5 mm were intermediate between the hydrostatic and total normal stresses, indicating the transition from fully laminar to partially turbulent flow.

By analogy with the Reynolds number for Newtonian fluid, we investigated the transition based on the non-dimensional number for debris flows (thus, the ratios of inertial to dynamic stresses caused by interparticle collisions and the Reynolds stresses of the debris flow pore fluid). This identified the critical Reynolds number in terms of transition commencement. We describe the transitional flow behavior of monodisperse granular debris flows using a two-layered model in which the position of the between-layer interface is estimated based on that critical Reynolds number.