  In this research article we study the wake formation behind 3-Dimensional
Multi-scale Porous Obstacles (3DMPOs). Particle Imaging Velocimetry (PIV) is
used in a non-shallow ($B/h =1.5$) water flume, with measurements carried out
across the $x$ - $y$ plane (at $z$ = 130 mm) and with $Re=70,000$ based on the
free-stream velocity ($U_{\infty}$). To characterise the downstream wake
characteristics of 3DMPOs the obstacles are split into 3 regimes; (1)
non-porous, (2) porous with a single internal scale and (3) porous fractals
(based on the Sierpinski carpet). The void fraction ($\phi=0.7$) and external
dimensions ($D$) of the obstacles remained constant, whilst the internal
geometrical parameters such as fractal dimension ($D_f$), lacunarity
($\Lambda$) and succolarity ($\sigma$) were varied. We are able to identify a
relationship between these topological parameters characterising the 3DMPOs and
the resultant wake characteristics. The fractal dimension ($D_f$) and
lacunarity ($\Lambda$) are found to be responsible for the formation of the
downstream steady wake region, whilst the succolarity ($\sigma$) affects the
position of the detached low velocity recirculation region. The power spectral
energy densities (PSDs) of the 3DMPOs are also seen to be affected by the
succolarity ($\sigma$) in case (3), and indicate movement away from
Kolomogorov's -5/3 power law.
