Variation of effective roll number on MHD Rayleigh-Benard convection confined in a small-aspect ratio box

MHD Rayleigh-Benard convection was studied experimentally using a box filled with liquid metal with five in aspect ratio and square horizontal cross section. Applying horizontal magnetic field organizes the convection motion into quasi-two dimensional rolls arranged parallel to the magnetic field. The number of rolls has tendency, decreases with increasing Rayleigh number $Ra$ and increases with increasing Chandrasekhar number $Q$. To fit the box with relatively smaller aspect ratio, the convection rolls take regime transition accompanying variation of the roll number against variations of $Ra$ and $Q$. We explored convection regimes in a ranges, $2 \times 10^3 < Q < 10^4$ and $5 \times 10^3 < Ra < 3 \times 10^5$ using ultrasonic velocity profiling that can capture time variations of instantaneous velocity profile. In a range $Ra/Q \sim 10$, we found periodic flow reversals in which five rolls periodically change the direction of their circulation with gradual skew of rolls. We performed POD analysis on the spatio-temporal velocity distribution obtained by UVP and indicated that that the periodic flow reversals consist of periodic emergence of 4-rolls mode in dominant 5-rolls mode. POD analysis also provided evaluation of effective number of rolls as a more objective approach.