Narrow Results

We model an elastic beam subject to a contact load which displaces under a chaotic external forcing, motivated by application of a ship carrying either a crane, or fluids in internal tanks. This model not only has rich dynamics and relevance in its own right, it gives rise to a Partial Differential Equation (PDE) whose solutions are chaotic, with an attractor whose points lie "near" a low-dimensional curve. This form identifies a data-driven dimensionality reduction which encapsulates a Cartesian product, approximately, of a principal manifold, corresponding to spatial regularity, against a temporal complex dynamics of the intrinsic variable of the manifold. The principal manifold element serves to translate the complex information at one site to all other sites on the beam. Although points of the attractor do not lie on the principal manifold, they lie sufficiently close that we describe that manifold as a "backbone" running through the attractor, allowing the manifold to serve as a suitable space to approximate behaviors.

The upper ocean mixing in the Bay of Bengal (BoB) gets substantial influence from the local winds, huge fresh water influx and tidal forcing that makes the mixing more complex and dynamic. This study aims to understand the role of tidal forcing on upper ocean mixing in the BoB and how this mixing process changes in presence of river fresh water. Moreover, it is also seen that how this tidal forcing modulates the air-sea interactions in the region. The analysis includes three high resolution (1/12°) Regional Ocean Modelling System (ROMS) simulations, a control run, a tide run and a river-tide run. In the tide forcing simulations, the tidal components included are M2, S2, N2, K2, K1, O1, P1, Q1, Mf and Mm. Again, the river-tide simulation additionally has the discharge from the major rivers (Ganges, Brahmaputra, Irrawaddy, Godavari, Krishna, Mahanadi and Subarnarekha) in the region. The analyses show that the tidal buoyancy deepens the mixed layer increasing the integrated upper ocean temperature, while the surface temperature reduces. The upper ocean temperature profile further reduces in the tidal vertical mixing process in presence of river fresh water. The tidal mixing increases the surface salinity, whereas the addition of low saline river discharge largely reduces the surface and subsurface salinity. The warmer upper ocean layers in the tidal forcing simulation radiates more surface longwave, sensible and latent surface heat fluxes over the region. Therefore, the study shows that the tidal forcing has major influence in the upper ocean mixing as well as the air-sea fluxes over the BoB.