More Like this

1. The Influence of Shear on Deep Convection Initiation. Part I: Theory

   https://doi.org/10.1175/JAS-D-21-0145.1  

   Peters, John_M; Morrison, Hugh; Nelson, T_Connor; Marquis, James_N; Mulholland, Jake_P; Nowotarski, Christopher_J (June 2022, Journal of the Atmospheric Sciences)

   Abstract This article introduces a novel hypothesis for the role of vertical wind shear (“shear”) in deep convection initiation (DCI). In this hypothesis, initial moist updrafts that exceed a width and shear threshold will “root” within a progressively deeper steering current with time, increase their low-level cloud-relative flow and inflow, widen, and subsequently reduce their susceptibility to entrainment-driven dilution, evolving toward a quasi-steady self-sustaining state. In contrast, initial updrafts that do not exceed the aforementioned thresholds experience suppressed growth by shear-induced downward pressure gradient accelerations, will not root in a deep-enough steering current to increase their inflow, will narrow with time, and will succumb to entrainment-driven dilution. In the latter case, an externally driven lifting mechanism is required to sustain deep convection, and deep convection will not persist in the absence of such lifting mechanism. A theoretical model is developed from the equations of motion to further explore this hypothesis. The model indicates that shear generally suppresses DCI, raising the initial subcloud updraft width that is necessary for it to occur. However, there is a pronounced bifurcation in updraft growth in the model after the onset of convection. Sufficiently wide initial updrafts grow and eventually achieve a steady state. In contrast, insufficiently wide initial updrafts shrink with time and eventually decay completely without external support. A sharp initial updraft radius threshold discriminates between these two outcomes. Thus, consistent with our hypothesis and observations, shear inhibits DCI in some situations, but facilitates it in others. 

   more » « less
2. Sharp critical thresholds in a hyperbolic system with relaxation

   https://doi.org/10.3934/dcds.2021098  

   Bhatnagar, Manas; Liu, Hailiang (January 2021, Discrete & Continuous Dynamical Systems)

   null (Ed.)

   We propose and study a one-dimensional \begin{document}$$ 2\times 2 $$\end{document} hyperbolic Eulerian system with local relaxation from critical threshold phenomena perspective. The system features dynamic transition between strictly and weakly hyperbolic. For different classes of relaxation we identify intrinsic critical thresholds for initial data that distinguish global regularity and finite time blowup. For relaxation independent of density, we estimate bounds on density in terms of velocity where the system is strictly hyperbolic. 

   more » « less
3. Active Galactic Nucleus Variability in the Age of Rubin

   https://doi.org/10.3847/1538-4357/ac9eb2  

   Creque-Sarbinowski, Cyril; Kamionkowski, Marc; Zhou, Bei (December 2022, The Astrophysical Journal)

   Abstract Over the next 10 years, the Vera C. Rubin Observatory (Rubin) will observe ∼10 million active galactic nuclei (AGNs) with a regular and high cadence. During this time, the intensities of most of these AGNs will fluctuate stochastically. Here, we explore the prospects to quantify precisely these fluctuations with Rubin measurements of AGN light curves. To do so, we suppose that each light curve is described by a damped random walk with a given fluctuation amplitude and correlation time. Theoretical arguments and some current measurements suggest that the correlation timescale and fluctuation amplitude for each AGN may be correlated with other observables. We use an expected-information analysis to calculate the precision with which these parameters will be inferred from the measured light curves. We find that the measurements will be so precise as to allow the AGNs to be separated into up to ∼10 different correlation-timescale bins. We then show that if the correlation time varies as some power of the luminosity, the normalization and power-law index of that relation will be determined to $\mathit{}({10}^{-4}\%)$. These results suggest that with Rubin, precisely measured variability parameters will take their place alongside spectroscopy in the detailed characterization of individual AGNs and in the study of AGN population statistics. Analogous analyses will be enabled by other time-domain projects, such as CMB-S4. 

   more » « less
4. Potential Singularity of the 3D Euler Equations in the Interior Domain

   https://doi.org/10.1007/s10208-022-09585-5  

   Hou, Thomas Y. (September 2022, Foundations of Computational Mathematics)

   Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this paper, we present some new numerical evidence that the 3D axisymmetric incompressible Euler equations with smooth initial data of finite energy develop a potential finite time singularity at the origin. This potential singularity is different from the blow-up scenario revealed by Luo and Hou (111:12968–12973, 2014) and (12:1722–1776, 2014), which occurs on the boundary. Our initial condition has a simple form and shares several attractive features of a more sophisticated initial condition constructed by Hou and Huang in (arXiv:2102.06663, 2021) and (435:133257, 2022). One important difference between these two blow-up scenarios is that the solution for our initial data has a one-scale structure instead of a two-scale structure reported in Hou and Huang (arXiv:2102.06663, 2021) and (435:133257, 2022). More importantly, the solution seems to develop nearly self-similar scaling properties that are compatible with those of the 3D Navier–Stokes equations. We will present numerical evidence that the 3D Euler equations seem to develop a potential finite time singularity. Moreover, the nearly self-similar profile seems to be very stable to the small perturbation of the initial data. 

   more » « less
5. Energy Exchange between Two Sub-systems Coupled with a Nonlinear Elastic Path

   Sen, O.T.; Singh, R. (May 2018, NOVEM 2018 Conference)

   The chief objective of this paper is to explore energy transfer mechanism between the sub-systems that are coupled by a nonlinear elastic path. In the proposed model (via a minimal order, two degree of freedom system), both sub-systems are defined as damped harmonic oscillators with linear springs and dampers. The first sub-system is attached to the ground on one side but connected to the second sub-system on the other side. In addition, linear elastic and dissipative characteristics of both oscillators are assumed to be identical, and a harmonic force excitation is applied only on the mass element of second oscillator. The nonlinear spring (placed in between the two sub-systems) is assumed to exhibit cubic, hardening type nonlinearity. First, the governing equations of the two degree of freedom system with a nonlinear elastic path are obtained. Second, the nonlinear differential equations are solved with a semi-analytical (multi-term harmonic balance) method, and nonlinear frequency responses of the system are calculated for different path coupling cases. As such, the nonlinear path stiffness is gradually increased so that the stiffness ratio of nonlinear element to the linear element is 0.01, 0.05, 0.1, 0.5 and 1.0 while the absolute value of linear spring stiffness is kept intact. In all solutions, it is observed that the frequency response curves at the vicinity of resonant frequencies bend towards higher frequencies as expected due to the hardening effect. However, at moderate or higher levels of path coupling (say 0.1, 0.5 and 1.0), additional branches emerge in the frequency response curves but only at the first resonant frequency. This is due to higher displacement amplitudes at the first resonant frequency as compared to the second one. Even though the oscillators move in-phase around the first natural frequency, high amplitudes increase the contribution of the stored potential energy in the nonlinear spring to the total mechanical energy. The out-of-phase motion around the second natural frequency cannot significantly contribute due to very low motion amplitudes. Finally, the governing equations are numerically solved for the same levels of nonlinearity, and the motion responses of both sub-systems are calculated. Both in-phase and out-of-phase motion responses are successfully shown in numerical solutions, and phase portraits of the system are generated in order to illustrate its nonlinear dynamics. In conclusion, a better understanding of the effect of nonlinear elastic path on two damped harmonic oscillators is gained. 

   more » « less