In this paper we develop a theoretical framework to study the hydrodynamic interactions in the presence of a nonflat and no-slip boundary. We calculate the influence of a small amplitude and sinusoidal deformations of a boundary wall in the self-mobility and the two-body hydrodynamic interactions for spherical particles. We show that the surface roughness enhances the self-mobility of a sphere in a way that, for motion in front of a local hump of the surface, the mobility strength decreases while it increases for the motion above a local deep of the rough surface. The influence of the surface roughness in the two-body hydrodynamic interactions is also analyzed numerically.

The several-million-degree, low-density quiet solar corona requires a total energy-loss flux of about 3 × 105 erg cm−2 s−1. Solar coronal bright points (CBPs) are ubiquitous in the quiet Sun. They may release magnetic energy to heat the solar corona, but their contribution to the energy flux has not been determined yet. We used an automatic identification and tracking method for CBPs, which was developed based on the support vector machine classifier and Zernike moments of extreme ultraviolet (EUV) observations from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory. We applied a spatial synthesis differential emission measure method and a Vertical-Current Approximation Nonlinear Force-Free Field technique to extract the thermal and magnetic energetics of the CBPs, respectively. By analyzing 7.5 yr (within the solar cycle 24) of AIA observations, we show that the average thermal energy and magnetic free energy of 140,000 CBPs are positively correlated with sunspots. However, the number of CBPs and sunspots are highly anti-correlated. We calculate a total energy-loss flux (sum of the radiative and conductive loss flux) of about (4.84 ± 1.60) × 103 erg cm−2 s−1 for the system of CBPs. Therefore, it is about 1.61% ± 0.53% of the total energy-loss flux of quiet corona. By extending the distribution of the magnetic Poynting flux and energy-loss flux for CBPs to nanoflares, the total magnetic Poynting flux and total energy-loss flux are obtained to be in the range of 1.48 × 105 to 1.57 × 106 and 3.86 × 104 to 2.35 × 105 erg cm−2 s−1, respectively.