arXiv subjects

Raj Saha

Publications and source records attributed to Raj Saha.

3 recordsLinked to original sources

arXiv2016

Relaxation oscillations in an idealized ocean circulation model

This work is motivated by a desire to understand transitions between stable equilibria observed in Stommel's 1961 thermohaline circulation model. We adapt the model, including a forcing parameter as a dynamic slow variable. The resulting model is a piecewise-smooth, three time-scale system. The model is analyzed using geometric singular perturbation theory to demonstrate the existence of attracting periodic orbits. The system is capable of producing classical relaxation oscillations as expected, but there is also a parameter regime in which the model exhibits small amplitude oscillations known as canard cycles. Forcing the model with obliquity variations from the last 100,000 years produces oscillations that are modulated in amplitude and frequency. The output shows similarities with important features of the climate proxy data of the same period.

math.DS↗

arXiv2015

Millennial-scale stable oscillations between sea ice and convective deep water formation

During the last ice age there were several quasi-periodic abrupt warming events. The climatic effects of the so-called Dansgaard-Oeschger (DO) events were felt globally, although the North Atlantic experienced the largest and most abrupt temperature anomalies. Similar but weaker oscillations also took place during the interglacial period. This paper proposes an auto-oscillatory mechanism between sea ice and convective deep water formation in the north Atlantic as the source of the persistent cycles. A simple dynamical model is constructed by coupling and slightly modifying two existing models of ocean circulation and sea ice. The model exhibits mixed mode oscillations, consisting of decadal scale small amplitude oscillations, and a large amplitude relaxation fluctuation. The decadal oscillations occur due to the insulating effect of sea ice and leads to periodic ventilation of heat from the polar ocean. Gradually an instability builds up in the polar column and results in an abrupt initiation of convection and polar warming. The unstable convective state relaxes back to the small amplitude oscillations from where the process repeats in a self-sustained manner. Freshwater pulses mimicking Heinrich events cause the oscillations to be grouped into packets of progressively weaker fluctuations, as also observed in the proxy records. Modulation of this stable oscillation mechanism by freshwater and insolation variations could account for the distribution and pacing of DO and Bond events. Physical aspects of the system such as sea ice extent and oceanic advective flow rates could determine the characteristic 1,500 year timescale of DO events.

physics.ao-ph↗

arXiv2015

Periodic fluctuations in deep water formation due to sea ice

During the last ice age several quasi-periodic abrupt warming events took place. Known as Dansgaard-Oeschger (DO) events their effects were felt globally, although the North Atlantic experienced the largest temperature anomalies. Paleoclimate data shows that the fluctuations often occurred right after massive glacial meltwater releases in the North Atlantic and in bursts of three or four with progressively decreasing strengths. In this study a simple dynamical model of an overturning circulation and sea ice is developed with the goal of understanding the fundamental mechanisms that could have caused the DO events. Interaction between sea ice and the overturning circulation in the model produces self-sustained oscillations. Analysis and numerical experiments reveal that the insulating effect of sea ice causes the ocean to periodically vent out accumulated heat in the deep ocean into the atmosphere. Subjecting the model to idealized freshwater forcing mimicking Heinrich events causes modulation of the natural periodicity and produces burst patterns very similar to what is observed in temperature proxy data. Numerical experiments with the model also suggests that the characteristic period of 1,500 years is due to the geometry, or the effective heat capacity, of the ocean that comes under sea ice cover.

physics.ao-ph↗