Nonlinear Circulations in a Symmetrically Unstable Flow
Abstract The time solution of a transverse inviscid circulation in a basic flow possessing either symmetric instability (SI) or conditional symmetric instability (CSI) is studied. By making the assumption that the circulation pattern is arbitrary but invariable with times, it can be proven that (i) the time evolution of a SI circulation integral is periodic and similar to that of a large amplitude pendulum started from the unstable equilibrium position, (ii) the same feature exists for a CSI circulation integral only when the mass center of the circulation loop is just at the mean (latent) heating level, (iii) a CSI circulation will spin up like a forced large amplitude pendulum (or oscillate like a damping pendulum) if its mass center is above (or below) the mean heating level.
The paper examines the nature and extent of integration of Indian market with the rest of the world. On various counts, Indian market is considered as one of the most active market of the world. Instead of relying on the concept of constant correlation we have measured the correlation for segmented periods and observed the correlation asymmetry in different periods under study which results into the rejection of the null hypothesis of a normal distribution. This ultimately refutes the relevance of widely accepted classical mean-variance theory. It is also revealed that asymmetries in correlation generally cause greater downward moves. The study suggests further, the investors should try to reshuffle asset mix along with the regime shift. Diversification without constant rebalance and switchover may cause sub optimal solution.