We investigate the scaling properties of the primary flow modes and their sensitivity to aspect ratio in a liquid gallium (Prandtl number $Pr = 0.02$ ) convection system through combined laboratory experiments and numerical simulations. We survey cylindrical aspect ratios $1.4 \le \varGamma \le 3$ and Rayleigh numbers $10^{4} \lesssim Ra \lesssim 10^{6}$ . In this range the flow is dominated by a large-scale circulation (LSC) subject to low-frequency oscillations. In line with previous studies, we show robust scaling of the Reynolds number $Re$ with $Ra$ and we confirm that the LSC flow is dominated by a jump-rope vortex (JRV) mode whose signature frequency is present in velocity and temperature measurements. We further show that both $Re$ and JRV frequency scaling trends are relatively insensitive to container geometry. The temperature and velocity spectra consistently show peaks at the JRV frequency, its harmonic and a secondary mode. The relative strength of these peaks changes and the presence of the secondary peak depend highly on aspect ratio, indicating that, despite having a minimal effect on typical velocities and frequencies, the aspect ratio has a significant effect on the underlying dynamics. Applying a bandpass filter at the secondary frequency to velocity measurements reveals that a clockwise twist in the upper half of the fluid layer coincides with a counterclockwise twist in the bottom half, indicating a torsional mode. For aspect ratio $\varGamma = 3$ , the unified LSC structure breaks down into multiple rolls in both simulation and experiment.

Background: Flow of cerebrospinal fluid (CSF) through brain perivascular spaces (PVSs) is essential for the clearance of interstitial metabolic waste products whose accumulation and aggregation is a key mechanism of pathogenesis in many diseases. The PVS geometry has important implications for CSF flow as it affects CSF and solute transport rates. Thus, the size and shape of the perivascular spaces are essential parameters for models of CSF transport in the brain and require accurate quantification. Methods: We segmented two-photon images of pial (surface) PVSs and the adjacent arteries and characterized their sizes and shapes of thousands of cross sections from 14 PVS segments in 9 mice. Based on the analysis, we propose an idealized model that approximates the cross-sectional size and shape of pial PVSs, closely matching their area ratios and hydraulic resistances. Results: PVS size only approximately scales with vessel size, and the ratio of PVS-to-vessel area varies widely across the thousands of cross sections analyzed. The hydraulic resistance per unit length of the PVS scales with the PVS cross-sectional area, and we found a power-law fit that predicts resistance as a function of the area. Three idealized geometric models were compared to PVSs imaged in vivo, and their accuracy in reproducing hydraulic resistances and PVS-to-vessel area ratios were evaluated. The area ratio was obtained across thousands of different cross sections, and we found that the distribution peaks for the original PVS and its closest idealized fit (polynomial fit) were 1.12 and 1.21, respectively. The peak of the hydraulic resistance distribution is 1.73 x 1015 Pa-s/m5 and 1.44 x 1015 Pa-s/m5 for the segmentation and its closest idealized fit, respectively. Conclusions: Brief summary and potential implicationsPVS hydraulic resistance can be reasonably predicted as a function of the PVS area. The proposed polynomial-based fit most closely captures the shape of the PVS with respect to area ratio and hydraulic resistance. Idealized PVS shapes are convenient for modeling, which can be used to better understand how anatomical variations affect clearance and drug delivery transport.

Background Flow of cerebrospinal fluid (CSF) through brain perivascular spaces (PVSs) is essential for the clearance of interstitial metabolic waste products whose accumulation and aggregation is a key mechanism of pathogenesis in many diseases. The PVS geometry has important implications for CSF flow as it affects CSF and solute transport rates. Thus, the size and shape of the perivascular spaces are essential parameters for models of CSF transport in the brain and require accurate quantification. Methods We segmented two-photon images of pial (surface) PVSs and the adjacent arteries and characterized their sizes and shapes of cross sections from 14 PVS segments in 9 mice. Based on the analysis, we propose an idealized model that approximates the cross-sectional size and shape of pial PVSs, closely matching their area ratios and hydraulic resistances. Results The ratio of PVS-to-vessel area varies widely across the cross sections analyzed. The hydraulic resistance per unit length of the PVS scales with the PVS cross-sectional area, and we found a power-law fit that predicts resistance as a function of the area. Three idealized geometric models were compared to PVSs imaged in vivo, and their accuracy in reproducing hydraulic resistances and PVS-to-vessel area ratios were evaluated. The area ratio was obtained across different cross sections, and we found that the distribution peaks for the original PVS and its closest idealized fit (polynomial fit) were 1.12 and 1.21, respectively. The peak of the hydraulic resistance distribution is $$1.73\times 10^{15}$$ 1.73 × 10 15  Pa  s/m$$^{5}$$ 5 and $$1.44\times 10^{15}$$ 1.44 × 10 15  Pa s/m$$^{5}$$ 5 for the segmentation and its closest idealized fit, respectively. Conclusions PVS hydraulic resistance can be reasonably predicted as a function of the PVS area. The proposed polynomial-based fit most closely captures the shape of the PVS with respect to area ratio and hydraulic resistance. Idealized PVS shapes are convenient for modeling, which can be used to better understand how anatomical variations affect clearance and drug transport.

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