arXiv subjects

J. S. Wettlaufer

Publications and source records attributed to J. S. Wettlaufer.

At least 19 recordsLinked to original sources

arXiv2026

Stochastic coupling of climate variables and ice volume over the Late Pleistocene glacial cycles

Understanding the interactions between ice sheets and global climate forcings over geological timescales is essential for projecting their future. Previous studies have highlighted the role of ice dynamics and climate interactions in establishing the 100,000-year glacial cycles, particularly regarding the growth of the North American ice sheet. Researchers have reconstructed consistent time series for ice volume, temperature, and carbon dioxide by applying inverse forward modeling to benthic oxygen isotope records. Here we model the stochastic behavior of paleoclimate time series to evaluate the coupling between climate variables during the Pleistocene glacial cycles. We quantify the behavior of these time series using multifractal time-weighted detrended fluctuation analysis, which differentiates between near-red-noise and white-noise behavior below and above the 100,000-year glacial cycle, respectively, in all records. This study builds upon the work of Keyes et al. [Chaos vol. 33, 093132 (2023)] by incorporating ice volume into a five-variable model that includes carbon dioxide, methane, nitrous oxide, and temperature, along with intervariable coupling terms to capture potential relationships among these variables. Our analysis shows that ice volume, carbon dioxide, and temperature have a stabilizing effect upon each other. To test our model, we compute response functions for each pair of variables and compare these with empirical data, confirming our predictions regarding intervariable stability and coupling. This study provides a comprehensive overview of glacial-interglacial dynamics and highlights the role of cryosphere-climate feedbacks in shaping Earth's climate evolution.

physics.ao-ph↗

arXiv2026

Stochastic Lorenz dynamics and wind reversals in Rayleigh-Bénard Convection

The Lorenz equations [1] are a severe Galerkin-truncation of the Oberbeck-Boussinesq (OB) equations describing Rayleigh-Bénard convection (RBC). Here we examine the mathematical connections between the chaotic lobe-switching behavior of a stochastic form of the Lorenz equations, that model the interaction between the thermal boundary layers and the core circulation, and the mean wind reversals in the experiments of Sreenivasan et al. [2]. Long-time numerical simulations of these stochastic equations, not easily accessible with the OB equations, yield a probability distribution for lobe inter-switch timings that exhibits non-Gaussian, multifractal behavior. In the Gaussian frequency range the simulations mirror the laboratory measurements and the classical Hurst exponent and quadratic variation show Brownian second-moment statistics. Further scrutiny reveals a non-linear cumulant generating function, or moment-exponent function, and thus multifractality. A simple generalized two-scale Cantor-cascade analysis reproduces these properties, showing that multiplicative intermittency, characteristic of turbulence, strongly influences the statistics. This demonstrates that this stochastic Lorenz system is a faithful, low-dimensional surrogate for mean-wind reversals in RBC.

physics.flu-dyn↗

arXiv2025

Electric field effects on the collision efficiency of uncharged water droplets in a linear flow

We study the dynamics of collisions between a pair of uncharged conducting droplets under the influence of a uniaxial compressional flow and an external electric field. The near-field asymptotic expression for the electric-field-induced attractive force demonstrate that surface-to-surface contact in finite time is facilitated by overcoming lubrication resistance. We demonstrate the significant role of the external electric field on the relative trajectories of two droplets in a compressional flow and provide estimates of the correlation between collision efficiency and the forces induced by the electric field. For droplet collisions in clouds, continuum lubrication approximations become inadequate to capture collision dynamics, and thus we incorporate non-continuum lubrication interactions into our analysis to address this complexity. Our findings reveal the dependence of collision efficiency on the strength of the electric field, geometry of the two interacting droplets, non-continuum effects, and van der Waals forces.

physics.flu-dyn↗

arXiv2025

Mid-latitude interactions expand the Hadley circulation

The Hadley circulation describes a planetary-scale tropical atmospheric flow, which has a major influence on climate. Contemporary theoretical understanding is based upon angular momentum conservation, the basic dynamical constraint governing the state of the flow pattern. However, despite the degree of success in representing the Hadley circulation, the canonical theoretical model does not treat interactions with other regions, particularly the mid-latitudes. Here, we extend the original model of Held and Hou (1980) to include the influence of mid-latitude large-scale atmospheric dynamics, which we treat using the planetary-scale heat equation with a parameterized poleward heat flux driven by synoptic eddies. The energy flux balance within the Hadley cell includes the poleward heat flux at the poleward edge of the cell, which is controlled by the baroclinic instability of the sub-tropical jet. We find that an increase (decrease) in the poleward heat flux leads to a strengthening (weakening) tropical convection, driving an equatorward (poleward) shift of the edge of the Hadley cell. Thus, our theoretical solutions suggest that global warming, which can reduce the baroclinicity of the subtropical jet, can lead to the poleward expansion of the Hadley cell due to the change in energy flux balance within it.

physics.ao-ph↗

arXiv2024

Prograde and meandering wall modes in rotating Rayleigh-Bénard convection with conducting walls

We use direct numerical simulations to study convection in rotating Rayleigh-Bénard convection in horizontally confined geometries of a given aspect ratio, with the walls held at fixed temperatures. We show that this arrangement is unconditionally unstable to flow that takes the form of wall-adjacent convection rolls. For wall temperatures close to the temperatures of the upper or lower boundaries, we show that the base state undergoes a Hopf bifurcation to a state comprised of spatio-temporal oscillations--`wall modes'--precessing in a retrograde direction. We study the saturated nonlinear state of these modes, and show that the velocity boundary conditions at the upper and lower boundaries are crucial to the formation and propagation of the wall modes: asymmetric velocity boundary conditions at the upper and lower boundaries can lead to prograde wall modes, while stress-free boundary conditions at both walls can lead to wall modes that have no preferred direction of propagation.

physics.flu-dyn↗

arXiv2024

Analytical Survival Analysis of the Non-autonomous Ornstein-Uhlenbeck Process

The survival probability for a periodic non-autonomous Ornstein-Uhlenbeck process is calculated analytically using two different methods. The first uses an asymptotic approach. We treat the associated Kolmogorov Backward Equation with an absorbing boundary by dividing the domain into an interior region, centered around the origin, and a "boundary layer" near the absorbing boundary. In each region we determine the leading-order analytical solutions, and construct a uniformly valid solution over the entire domain using asymptotic matching. In the second method we examine the integral relationship between the probability density function and the mean first passage time probability density function. These allow us to determine approximate analytical forms for the exit rate. The validity of the solutions derived from both methods is assessed numerically, and we find the asymptotic method to be superior.

cond-mat.stat-mech↗

arXiv2023

Wrinkling composite sheets

We examine the buckling shape and critical compression of confined inhomogeneous composite sheets lying on a liquid foundation. The buckling modes are controlled by the bending stiffness of the sheet, the density of the substrate, and the size and the spatially dependent elastic coefficients of the sheet. We solve the (linearized) Föppl-von Kármán equations describing the mechanical equilibrium of a sheet when its bending stiffness varies parallel to the direction of confinement. The case of a homogeneous bending stiffness exhibits a degeneracy of wrinkled states for certain sizes of the confined sheet. This degeneracy disappears for spatially dependent elastic coefficients. Medium length sheets buckle similarly to their homogeneous counterparts, whereas the wrinkled states in large length sheets localize the bending energy towards the soft regions of the sheet.

cond-mat.soft↗

arXiv2023

Flow driven interfacial waves: an inviscid asymptotic study

Motivated by wind blowing over water, we use asymptotic methods to study the evolution of short wavelength interfacial waves driven by the combined action of these flows. We solve the Rayleigh equation for the stability of the shear flow, and construct a uniformly valid approximation for the perturbed streamfunction, or eigenfunction. We then expand the real part of the eigenvalue, the phase speed, in a power series of the inverse wavenumber and show that the imaginary part is exponentially small. We give expressions for the growth rates of the Miles (1957) and rippling (e.g., Young & Wolfe 2013) instabilities that are valid for an arbitrary shear flow. The accuracy of the results is demonstrated by a comparison with the exact solution of the eigenvalue problem in the case when both the wind and the current have an exponential profile.

physics.flu-dyn↗

arXiv2023

Stochastic Paleoclimatology: Modeling the EPICA Ice Core Climate Records

We analyze and model the stochastic behavior of paleoclimate time series and assess the implications for the coupling of climate variables during the Pleistocene glacial cycles. We examine 800 kyr of carbon dioxide, methane, nitrous oxide, and temperature proxy data from the EPICA Dome-C ice core, which are characterized by 100~kyr glacial cycles overlain by fluctuations across a wide range of time scales. We quantify this behavior through multifractal time-weighted detrended fluctuation analysis, which distinguishes near red-noise and white-noise behavior below and above the 100~kyr glacial cycle respectively in all records. This allows us to model each time series as a one-dimensional periodic non-autonomous stochastic dynamical system, and assess the stability of physical processes and the fidelity of model-simulated time series. We extend this approach to a four-variable model with linear coupling terms, which we interpret in terms of the interrelationships between the time series. Methane and nitrous oxide are found to have significant destabilizing influences, while carbon dioxide and temperature have smaller stabilizing influences. We draw conclusions about causal relationships in glacial transitions and the climate processes that may have facilitated these couplings, and highlight opportunities to further develop stochastic modeling approaches.

cond-mat.soft↗

arXiv2023

The Thermodynamic Cost of Erasing Information in Finite-time

The Landauer principle sets a fundamental thermodynamic constraint on the minimum amount of heat that must be dissipated to erase one logical bit of information through a quasi-statically slow protocol. For finite time information erasure, the thermodynamic costs depend on the specific physical realization of the logical memory and how the information is erased. Here we treat the problem within the paradigm of a Brownian particle in a symmetric double-well potential. The two minima represent the two values of a logical bit, 0 and 1, and the particle's position is the current state of the memory. The erasure protocol is realized by applying an external time-dependent tilting force. We derive analytical tools to evaluate the work required to erase a classical bit of information in finite time via an arbitrary continuous erasure protocol, which is a relevant setting for practical applications. Importantly, our method is not restricted to the average work, but instead gives access to the full work distribution arising from many independent realizations of the erasure process. Using the common example of an erasure protocol that changes linearly with time acting on a double-parabolic potential, we explicitly calculate all relevant quantities and verify them numerically.

cond-mat.stat-mech↗

arXiv2023

Orientation dynamics of two-dimensional concavo-convex bodies

We study the orientation dynamics of two-dimensional concavo-convex solid bodies more dense than the fluid through which they fall under gravity. We show that the orientation dynamics of the body, quantified in terms of the angle $ϕ$ relative to the horizontal, undergoes a transcritical bifurcation at a Reynolds number $Re_{c}^{(1)}$, and a subcritical pitchfork bifurcation at a Reynolds number $Re_{c}^{(2)}$. For $Re Re_{c}^{(2)}$, the concave-downwards orientation of $ϕ=0$ is again unstable, and bodies that start concave-downwards exhibit overstable oscillations about the unstable fixed point, eventually tumbling into the stable $ϕ=π$ orientation. The $Re_{c}^{(2)}\approx15$ at which the subcritical pitchfork bifurcation occurs is distinct from the $Re$ for the onset of vortex shedding, which causes the $ϕ=π$ equilibrium to also become unstable, with bodies fluttering about $ϕ=π$. The complex orientation dynamics of irregularly shaped bodies evidenced here are relevant in a wide range of settings, from the tumbling of hydrometeors to settling of mollusk shells.

physics.flu-dyn↗

arXiv2022

Asymptotic interpretation of the Miles mechanism of wind-wave instability

When wind blows over water, ripples are generated on the water surface. These ripples can be regarded as perturbations of the wind field, which is modelled as a parallel inviscid flow. For a given wavenumber $k$, the perturbed streamfunction of the wind field and the complex phase speed are the eigenfunction and the eigenvalue of the so-called Rayleigh equation in a semi-infinite domain. Because of the small air-water density ratio, $ρ_{\rm{a}}/ρ_{\rm{w}}\equivε<<1$, the wind and the ripples are weakly coupled, and the eigenvalue problem can be solved perturbatively. At the leading order, the eigenvalue is equal to the phase speed $c_0$ of surface waves. At order $ε$, the eigenvalue has a finite imaginary part, which implies growth. Miles (1957) showed that the growth rate is proportional to the square modulus of the leading-order eigenfunction evaluated at the so-called critical level $z=z_c$, where the wind speed is equal to $c_0$ and the waves extract energy from the wind. Here, we construct uniform asymptotic approximations of the leading-order eigenfunction for long waves, which we use to calculate the growth rate as a function of $k$. In the strong wind limit, we find that the fastest growing wave is such that the aerodynamic pressure is in phase with the wave slope. The results are confirmed numerically.

physics.flu-dyn↗

arXiv2022

Biolocomotion and premelting in ice

Biota are found in glaciers, ice sheets and permafrost. Ice bound micro-organisms evolve in a complex mobile environment facilitated or hindered by a range of bulk and surface interactions. When a particle is embedded in a host solid near its bulk melting temperature, a melted film forms at the surface of the particle in a process known as interfacial premelting. Under a temperature gradient, the particle is driven by a thermomolecular pressure gradient toward regions of higher temperatures in a process called thermal regelation. When the host solid is ice and the particles are biota, thriving in their environment requires the development of strategies, such as producing exopolymeric substances (EPS) and antifreeze glycoproteins (AFP) that enhance the interfacial water. Therefore, thermal regelation is enhanced and modified by a process we term {\em bio-enhanced premelting}. Additionally, the motion of bioparticles is influenced by chemical gradients influenced by nutrients within the icy host body. We show how the overall trajectory of bioparticles is controlled by a competition between thermal regelation and directed biolocomotion. By re-casting this class of regelation phenomena in the stochastic framework of active Ornstein-Uhlenbeck dynamics, and using multiple scales analysis, we find that for an attractive (repulsive) nutrient source, that thermal regelation is enhanced (suppressed) by biolocomotion. This phenomena is important in astrobiology, the biosignatures of extremophiles and in terrestrial paleoclimatology.

cond-mat.soft↗

arXiv2022

The combined effects of buoyancy, rotation, and shear on phase boundary evolution

We use well-resolved numerical simulations to study the combined effects of buoyancy, pressure-driven shear and rotation on the melt rate and morphology of a layer of pure solid overlying its liquid phase in three dimensions at a Rayleigh number $Ra = 1.25 \times 10^5$. During thermal convection we find that the rate of melting of the solid phase varies non-monotonically with the strength of the imposed shear flow. In the absence of rotation, depending on whether buoyancy or shear dominates the flow, we observe either domes or ridges aligned in the direction of the shear flow respectively. Furthermore, we show that the geometry of the phase boundary has important effects on the magnitude and evolution of the heat flux in the liquid layer. In the presence of rotation, the strength of which is characterized by the Rossby number, Ro, we observe that for Ro = O(1) the mean flow in the interior is perpendicular to the direction of the constant horizontal applied pressure gradient. As the magnitude of this pressure gradient increases, the geometry of solid-liquid interface evolves from the voids characteristic of melting by rotating convection, to grooves oriented perpendicular or obliquely to the direction of the pressure gradient.

physics.flu-dyn↗

arXiv2022

Analytical solution of stochastic resonance in the nonadiabatic regime

We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability density function that asymptotically connects local solutions in boundary layers near the two minima with those in the region of the maximum that separates them. The validity of the analytical solution is confirmed numerically. Free from the constraints of the adiabatic limit, the approach allows us to predict the escape rate from one stable basin to another for systems experiencing a more complex periodic forcing.

cond-mat.stat-mech↗

arXiv2021

Melting driven by rotating Rayleigh-Bénard convection

We study numerically the melting of a horizontal layer of a pure solid above a convecting layer of its fluid rotating about the vertical axis. In the rotating regime studied here, with Rayleigh numbers of order $10^7$, convection takes the form of columnar vortices, the number and size of which depend upon the Ekman and Prandtl numbers, as well as the geometry -- periodic or confined. As the Ekman and Rayleigh numbers vary, the number and average area of vortices vary in inverse proportion, becoming thinner and more numerous with decreasing Ekman number. The vortices transport heat to the phase boundary thereby controlling its morphology, characterized by the number and size of the voids formed in the solid, and the overall melt rate, which increases when the lower boundary is governed by a no-slip rather than a stress-free velocity boundary condition. Moreover, the number and size of voids formed are relatively insensitive to the Stefan number, here inversely proportional to the latent heat of fusion. For small values of the Stefan number, the convection in the fluid reaches a slowly evolving geostrophic state wherein columnar vortices transport nearly all the heat from the lower boundary to melt the solid at an approximately constant rate. In this quasi-steady state, we find that the Nusselt number, characterizing the heat flux, co-varies with the interfacial roughness, for all the flow parameters and Stefan numbers considered here. This confluence of processes should influence the treatment of moving boundary problems, particularly those in astrophysical and geophysical problems where rotational effects are important.

physics.flu-dyn↗

arXiv2020

A Non-Gaussian Stochastic Model for the El Niño Southern Oscillation

A non-autonomous stochastic dynamical model approach is developed to describe the seasonal to interannual variability of the El Niño-Southern Oscillation (ENSO). We determine the model coefficients by systematic statistical estimations using partial observations involving only sea surface temperature data. Our approach reproduces the observed seasonal phase locking and its uncertainty, as well as the highly non-Gaussian statistics of ENSO. Finally, we recover the intermittent time series of the hidden processes, including the thermocline depth and the wind bursts.

physics.ao-ph↗

arXiv2020

Predicting Critical Transitions in Multiscale Dynamical Systems Using Reservoir Computing

We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and induces critical transitions. By taking advantage of recent advances in reservoir computing, we present a data-driven method to predict the future evolution of the state. We show that our method is capable of predicting a critical transition event at least several numerical time steps in advance. We demonstrate the success as well as the limitations of our method using numerical experiments on three examples of systems, ranging from low dimensional to high dimensional. We discuss the mathematical and broader implications of our results.

physics.comp-ph↗