Turbulent Properties of Stationary Flows in Porous Media

In this study, we investigate the flow dynamics in a fixed bed of hydrogel beads using particle tracking velocimetry to compute the velocity field in the middle of the bed for moderate Reynolds numbers (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>Re</a:mi><a:mo stretchy="false">=</a:mo><a:mo stretchy="false">[</a:mo><a:mn>124</a:mn><a:mo>,</a:mo><a:mn>169</a:mn><a:mo>,</a:mo><a:mn>203</a:mn><a:mo>,</a:mo><a:mn>211</a:mn><a:mo stretchy="false">]</a:mo></a:mrow></a:math>). We discover that even though the flow is stationary at the larger scales, it exhibits complex multiscale spatial dynamics reminiscent of those observed in classical turbulence. We find evidence of the presence of an inertial range and a direct energy cascade, and are able to obtain a value for a “porous” Kolmogorov constant of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi>C</f:mi><f:mn>2</f:mn></f:msub><f:mo>=</f:mo><f:mn>3.1</f:mn><f:mo>±</f:mo><f:mn>0.3</f:mn></f:math>. This analogy with turbulence opens up new possibilities for understanding mixing and global transport properties in porous media.