arXiv subjects

Ashwin K Seshadri

Publications and source records attributed to Ashwin K Seshadri.

9 recordsLinked to original sources

arXiv2026

Quadratic invariants and Hamiltonian structure in coupled gyrostat low-order model hierarchies

Coupled gyrostat low-order models (GLOMs) are energy-conserving cores of Galerkin-truncated fluid and geophysical systems, including Rayleigh-Benard convection and vorticity dynamics. A single gyrostat always possesses two quadratic invariants; when gyrostats are coupled, the number and geometry of invariants vary sensitively with model configuration, influencing the effective dimension of the dynamics, nonlinear stability, and statistical equilibria. We provide a systematic theory of this dependence. For sparse nested hierarchies of K gyrostats (M=2K+1 modes, no linear feedback), the number of independent quadratic invariants is exactly (M+1)/2; for general GLOMs with all parameters nonzero, energy is the only guaranteed invariant. The standard algebraic approach to finding invariants does not scale with model size. We show instead that many GLOMs admit a non-canonical Hamiltonian structure, with quadratic invariants recoverable as Casimir functions of an explicitly constructible Poisson matrix. The Hamiltonian structure imposes precise, computationally verifiable constraints on the nonlinear coefficients. For Hamiltonian hierarchies, Casimir gradients project consistently across models of increasing complexity, so that invariants are compatible under restriction to subspaces. The clear geometric interpretation of these models enables consistent application of Hamiltonian dynamics across low-order model hierarchies.

math.DS↗

arXiv2026

Emergence of an Advective Boundary Layer in Monsoon Cross-Equatorial Flow: Scaling, Dynamics, and Idealized Models

The conventional Ekman model of the tropical boundary layer neglects nonlinear momentum advection and breaks down near the equator, where Coriolis effects are weak. During South Asian monsoon onset, we identify a dynamical regime transition to an advective boundary layer (ABL). Reanalysis links this transition to a shift in the zonal momentum balance from frictional to meridional-advection control as cross-equatorial flow intensifies, accompanied by increasing local Rossby number and vanishing absolute vorticity, signaling the breakdown of Ekman balance. A scaling analysis shows that this transition occurs when the meridional length scales of geopotential and zonal wind contract such that their product approaches $ϕ/f^2$. In the resulting ABL regime, kinetic energy is governed by a balance between its generation and advection, yielding a linear diagnostic relation between meridional geopotential gradient and meridional wind. A simple theoretical model predicts that the sensitivity of this relation is controlled by an advective timescale that equals the inertial timescale ($1/f$) at the transition latitude, where zonal and meridional wind speeds become comparable. Testing this framework in idealized aquaplanet experiments confirms that stronger cross-equatorial pressure gradients and slower planetary rotation rates amplify advective effects and shift the transition latitude poleward. Across experiments, the sensitivity of meridional winds to the geopotential gradient remains tightly linked to $1/f$ at the transition latitude. Together, these results establish the ABL as a distinct dynamical regime, with important implications for monsoon onset, intraseasonal variability, and the representation of tropical boundary layer processes in climate models.

physics.ao-ph↗

arXiv2023

Minimal chaotic models from the Volterra gyrostat

Low-order models obtained through Galerkin projection of several physically important systems (e.g., Rayleigh-Bénard convection, mid-latitude quasi-geostrophic dynamics, and vorticity dynamics) appear in the form of coupled gyrostats. Forced dissipative chaos is an important phenomenon in these models, and this paper introduces and identifies 'minimal chaotic models' (MCMs), in the sense of having the fewest external forcing and linear dissipation terms, for the class of models arising from an underlying gyrostat core. The identification of MCMs reveals common conditions for chaos across a wide variety of physical systems. It is shown here that a critical distinction is whether the gyrostat core (without forcing or dissipation) conserves energy, depending on whether the sum of the quadratic coefficients is zero. The paper demonstrates that, for the energy-conserving condition of the gyrostat core, the requirement of a characteristic pair of fixed points that repel the chaotic flow dictates placement of forcing and dissipation in the minimal chaotic models. In contrast if the core does not conserve energy, the forcing can be arranged in additional ways for chaos to appear in the subclasses where linear feedbacks render fewer invariants in the gyrostat core. In all cases, the linear mode must experience dissipation for chaos to arise. The Volterra gyrostat presents a clear example where the arrangement of fixed points circumscribes more complex dynamics.

physics.flu-dyn↗

arXiv2023

Invariants and chaos in the Volterra gyrostat without energy conservation

The model of the Volterra gyrostat (VG) has not only played an important role in rigid body dynamics but also served as the foundation of low-order models of many naturally occurring systems. It is well known that VG possesses two invariants, or constants of motion, corresponding to kinetic energy and squared angular momentum, giving oscillatory solutions to its equations of motion. Nine distinct subclasses of the VG have been identified, two of which the Euler gyroscope and Lorenz gyrostat are each known to have two constants. This paper characterizes quadratic invariants of the VG and each of its subclasses, showing how these enjoy two invariants even when rendered in terms of a non-invertible transformation of parameters, leading to a transformed Volterra gyrostat (TVG). If the quadratic coefficients of the TVG sum to zero, as they do for the VG, the system conserves energy. In all of these cases, the flows preserve volume. However, physical models where the quadratic coefficients do not sum to zero are ubiquitous, and characterization of invariants and the resulting dynamics for this more general class of models with volume conservation but without energy conservation is lacking. This paper provides the first such characterization for each of the subclasses of the VG in the absence of energy conservation, showing how the number of invariants depends on the number of linear feedback terms. It is shown that the gyrostat with three linear feedback terms has no invariants. The number of invariants circumscribes the possible dynamics for these three-dimensional flows, and those without any invariants are shown to admit rich dynamics including chaos. This gives rise to a broad class of three-dimensional volume conserving chaotic flows, arising naturally from model reduction techniques.

physics.ao-ph↗

arXiv2023

Convergent estimators of variance of a spatial mean in the presence of missing observations

In the geosciences, a recurring problem is one of estimating spatial means of a physical field using weighted averages of point observations. An important variant is when individual observations are counted with some probability less than one. This can occur in different contexts: from missing data to estimating the statistics across subsamples. In such situations, the spatial mean is a ratio of random variables, whose statistics involve approximate estimators derived through series expansion. The present paper considers truncated estimators of variance of the spatial mean and their general structure in the presence of missing data. To all orders, the variance estimator depends only on the first and second moments of the underlying field, and convergence requires these moments to be finite. Furthermore, convergence occurs if either the probability of counting individual observations is larger than 1/2 or the number of point observations is large. In case the point observations are weighted uniformly, the estimators are easily found using combinatorics and involve Stirling numbers of the second kind.

math.ST↗

arXiv2021

Cumulative emissions accounting of greenhouse gases due to path independence for a sufficiently rapid emissions cycle

Cumulative emissions accounting for carbon-dioxide (CO2) is founded on recognition that global warming in Earth System Models (ESMs) is roughly proportional to cumulative CO2 emissions, regardless of emissions pathway. However, cumulative emissions accounting only requires the graph between global warming and cumulative emissions to be approximately independent of emissions pathway ("path-independence"), regardless of functional relationship between these variables. The concept and mathematics of path-independence are considered for an energy-balance climate model (EBM), giving rise to a closed-form expression of global warming, together with analysis of the atmospheric cycle following emissions. Path-independence depends on the ratio between the period of the emissions cycle and the atmospheric lifetime, being a valid approximation if the emissions cycle has period comparable to or shorter than the atmospheric lifetime. This makes cumulative emissions accounting potentially relevant beyond CO2, to other greenhouse gases (GHGs) with lifetimes of several decades whose emissions have recently begun.

physics.ao-ph↗

arXiv2020

Economics of carbon-dioxide abatement under an exogenous constraint on cumulative emissions

The fossil-fuel induced contribution to further warming over the 21st century will be determined largely by integrated CO2 emissions over time rather than the precise timing of the emissions, with a relation of near-proportionality between global warming and cumulative CO2 emissions. This paper examines optimal abatement pathways under an exogenous constraint on cumulative emissions. Least cost abatement pathways have carbon tax rising at the risk-free interest rate, but if endogenous learning or climate damage costs are included in the analysis, the carbon tax grows more slowly. The inclusion of damage costs in the optimization leads to a higher initial carbon tax, whereas the effect of learning depends on whether it appears as an additive or multiplicative contribution to the marginal cost curve. Multiplicative models are common in the literature and lead to delayed abatement and a smaller initial tax. The required initial carbon tax increases with the cumulative abatement goal and is higher for lower interest rates. Delaying the start of abatement is costly owing to the increasing marginal abatement cost. Lower interest rates lead to higher relative costs of delaying abatement because these induce higher abatement rates early on. The fraction of business-as-usual emissions (BAU) avoided in optimal pathways increases for low interest rates and rapid growth of the abatement cost curve, which allows a lower threshold global warming goal to become attainable without overshoot in temperature. Each year of delay in starting abatement raises this threshold by an increasing amount, because the abatement rate increases exponentially with time.

econ.GN↗

arXiv2017

Statistics of spatial averages and optimal averaging in the presence of missing data

We consider statistics of spatial averages estimated by weighting observations over an arbitrary spatial domain using identical and independent measuring devices, and derive an account of bias and variance in the presence of missing observations. We test the model relative to simulations, and the approximations for bias and variance with missing data are shown to compare well even when the probability of missing data is large. Previous authors have examined optimal averaging strategies for minimizing bias, variance and mean squared error of the spatial average, and we extend the analysis to the case of missing observations. Minimizing variance mainly requires higher weights where local variance and covariance is small, whereas minimizing bias requires higher weights where the field is closer to the true spatial average. Missing data increases variance and contributes to bias, and reducing both effects involves emphasizing locations with mean value nearer to the spatial average. The framework is applied to study spatially averaged rainfall over India. We use our model to estimate standard error in all-India rainfall as the combined effect of measurement uncertainty and bias, when weights are chosen so as to yield minimum mean squared error.

stat.ME↗

arXiv2017

Economics of limiting cumulative CO2 emissions

Global warming from carbon dioxide (CO2) is known to depend on cumulative CO2 emissions. We introduce a model of global expenditures on limiting cumulative CO2 emissions, taking into account effects of decarbonization and rising global income and making an approximation to the marginal abatement costs (MAC) of CO2. Discounted mitigation expenditures are shown to be a convex function of cumulative CO2 emissions. We also consider minimum-expenditure solutions for meeting cumulative emissions goals, using a regularized variational method yielding an initial value problem in the integrated decarbonization rate. A quasi-stationary solution to this problem can be obtained for a special case, yielding decarbonization rate that is proportional to annual CO2 emissions. Minimum-expenditure trajectories in scenarios where CO2 emissions decrease must begin with rapid decarbonization at rate decreasing with time. Due to the shape of global MAC the fraction of global income spent on CO2 mitigation ("burden") generally increases with time, as cheaper avenues for mitigation are exhausted. Therefore failure to rapidly decarbonize early on reduces expenditures by a small fraction (on the order of 0.01 %) of income in the present, but leads to much higher burden to future generations (on the order of 1 % of income).

econ.GN↗