A research on initial formation process of intermittent debris flow
Authors: Arai Muneyuki 
Published: March 2020

&lt;p&gt;&lt;br&gt;&lt;html&gt;&lt;/p&gt;&lt;p&gt;&lt;head&gt;&lt;br&gt;&lt;title&gt; &amp;#160; &amp;#160;A research on initial formation process of intermittent debris flow &amp;#160; &lt;/title&gt;&lt;br&gt;&lt;/head&gt;&lt;/p&gt;&lt;p&gt;&lt;body&gt;&lt;br&gt;Some debris flows are intermittent surges flows with discontinuous changes in water depth.&lt;br&gt;These phenomena are considered to be a kind of nonlinear wave phenomena based on flow instability.&lt;br&gt;The authors show a KdV-Burgers equation as an equation representing the change in water depth.&lt;br&gt;When the phase velocity in the equation is long wave velocity, the equation becomes a Burgers equation.&lt;br&gt;The characteristic of the roll wave is that it has a discontinuous change in water depth and flows down intermittently as many surges.&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;br&gt;&lt;br&gt;Roll wave experiments were performed using a straight channel with a length of 56m, a width of 10cm, a depth of 15cm and a channel gradient of &amp;theta;=2.5 deg.&lt;br&gt;The experimental conditions are by a plane water and a flow containing 42% (C=0.42) solid particles.&lt;br&gt;The particles are cylindrical particles with a typical particle size of d = 3 mm and a density of &amp;sigma;=1.04 g/cm&lt;sup&gt;3&lt;/sup&gt; made of polystyrene.&amp;#160;&lt;br&gt;The flow conditions of the plane water are as follows: mean discharge Q = 1112cm&lt;sup&gt;3&lt;/sup&gt;/s,&amp;#160;&lt;br&gt;mean depth h&lt;sub&gt;0&lt;/sub&gt; = 1.23cm at the downstream end of the channel,&amp;#160;&lt;br&gt;mean flow velocity u&lt;sub&gt;0&lt;/sub&gt; = 90.2cm/s,&amp;#160;&lt;br&gt;and the flow conditions with solid particles Q=1193cm&lt;sup&gt;3&lt;/sup&gt;/s, h&lt;sub&gt;0&lt;/sub&gt; = 1.35cm, u&lt;sub&gt;0&lt;/sub&gt; = 88.4cm/s.&amp;#160;&lt;br&gt;To supply water to the flume, a water tank storing 0.5m&lt;sup&gt;3&lt;/sup&gt; is placed on the upstream side of the flume,&amp;#160;&lt;br&gt;and water or a mixture of water and particles is supplied from the upstream end of the flume.&lt;br&gt;The water tank is closed and the inside is kept at a constant pressure according to the Marriott bottle principle. As a result, the water supply is constant.&lt;/p&gt;&lt;p&gt;&lt;br&gt;&lt;br&gt;In the case of plane water, the period is T = 1.12sec at x = 14m from the upstream end of the flume,&amp;#160;&lt;br&gt;and at the downstream end x = 56m T = 2.25sec.&amp;#160;&lt;br&gt;In the flow including solid particles, T = 1.78sec and T = 3.06sec at the same position.&lt;br&gt;In each case, the surge period becomes longer as the flow goes down.&amp;#160;&lt;br&gt;The wave velocity of the surge here in the experimental results is different.&amp;#160;&lt;br&gt;Looking at the details of the waveform, the subsequent surge may catch up.&lt;br&gt;Therefore, it is considered that the period of the surge becomes longer as it flows down and combines with other surges.&amp;#160;&lt;br&gt;In the Burgers equation, the initial condition waveform is integrated into a waveform with wave number k = 1 by the initial condition of a non-integer multiple waveform and non-fixed boundary conditions at both ends.&lt;br&gt;From the above, it is considered that the initial waveform formation of the roll wave is contributed by the weak shock wave equation such as the Burgers equation.&lt;br&gt;In this Burgers equation, when the waveform is integrated into a waveform with wavenumber k = 1, the analytical solution shows that the phase velocity v&lt;sub&gt;p0&lt;/sub&gt; is no longer c&lt;sub&gt;0&lt;/sub&gt;.&lt;br&gt;Therefore, the governing equation returns to the KdV-Burgers equation.&lt;/p&gt;&lt;p&gt;&lt;br&gt;&lt;/body&gt;&lt;/p&gt;&lt;p&gt;&lt;/html&gt;&lt;/p&gt;