arXiv subjects

Joseph A. Biello

Publications and source records attributed to Joseph A. Biello.

6 recordsLinked to original sources

arXiv2025

Idealized Cumulus Cloud-Scale Motions and the Dynamics of Isolated and Coupled Flows

Developing an understandable theory for the dynamic evolution of the morphology of clouds remains intractable. To break this deadlock, we introduce a new conceptual model for cloud-scale motions named the Kinematics Representation of Non-rotating Updraft Tori (KRoNUT) model, where non-rotating reflects the absence of motion in the azimuthal direction. Using this model, we conduct a series of relaxation experiments whereby we ``turn off'' the baroclinic term associated with a pre-existing cloud-scale circulation. We then implement a moment reduction technique to generate a system of differential equations named the Dynamics of Non-rotating Updraft Tori (DoNUT) equations, which describe the temporal evolution of a cloudy circulation under various combinations of forcings, namely turbulent diffusion, self-advection, and cross-advection from a neighboring cloud-scale flow. The solutions of the DoNUT equations show that all single KRoNUT configurations either start at or evolve toward a specific steady state circulation. The cloud-scale motions represented by the current KRoNUT model always grow vertically but may narrow, due to advection, or widen, due to diffusion. Meanwhile, invigoration or enervation of the vertical velocity may result from advection or diffusion processes, with short, wide KRoNUTs more likely to invigorate and tall, narrow KRoNUTs likely to enervate. Our study of the coupled KRoNUTs provides insight into clouds' tendencies to attract or repel one another. Important results of the coupled KRoNUT analysis include a scaled metric for interaction, ranges of specific height ratios that induce the most meaningful interaction, and circulation parameters that alter the location and stability of a steady KRoNUT.

physics.flu-dyn↗

arXiv2025

Numerical Assessment of Advective and Diffusive Dynamics of Interacting and Isolated Prototypical Convectively Initiated Circulations

The bulk circulation associated with convective clouds includes not only a region of updraft and cloudy air but also a region of compensating descent and cloud-free air and horizontal motions coupling these regions. The Kinematic Representation of Non-rotating Updraft Tori (KRoNUT) model is a simple representation of this entire flow. First, the skill of the KRoNUT in representing flows from a high resolution full-physics simulation of marine tropical convection is compared to various plume representations of convection. Then the KRoNUT is used to construct bulk descriptions of the dry dynamics of isolated and interacting convective circulations under the influence of advection and diffusion (only). Cross sections of advective and diffusive tendencies show that while vertical advection of the vertical wind is the most important advective tendency in clouds, the horizontal component of the convective circulation and advection thereof plays a crucial role in the evolution of circulations in the absence of buoyancy. Strong curvature of the flow near the surface and near the updraft core results in locally strong diffusive tendencies that depend on scale. Cross sections of tendencies from the KRoNUT compare favourably to results from the simulation. Interacting circulations are shown to exhibit a wide range of dynamics with some cases of interactions leading to unique stability of geometric properties of otherwise evolving flows and some leading to geometric clustering of circulation centers.

physics.ao-ph↗

arXiv2016

Multiple-scale analysis on the radiation within the coupled KdV equations

A multiple scale model of the nonlinearly coupled KdV equations is established to predict mechanism of interaction of equatorial Rossby waves and barotropic waves in certain case. Analytically, predicted precursor radiation is a centrosymmetric object and is shown in excellent quantitative agreement with numerical simulations; furthermore, the multiple scale model elucidates the salient mechanisms of the interaction of solitary waves and the mechanism for radiation. While the atmosphere-ocean science community is very interested in theoretical studies of tropical wave interactions and in developing reduced dynamical models that can explain some key features of equatorial phenomena, our analytic predictions quantitively explain formation of radiation during interaction in Biello's model beyond qualitative level.

nlin.PS↗

arXiv2016

Equilibrium circulation and stress distribution in viscoelastic creeping flow

An analytic, asymptotic approximation of the nonlinear steady-state equations for viscoelastic creeping flow, modeled by the Oldroyd-B equations with polymer stress diffusion, is derived. Near the extensional stagnation point the flow stretches and aligns polymers along the outgoing streamlines of the stagnation point resulting in a stress-island, or birefringent strand. The polymer stress diffusion coefficient is used, both, as an asymptotic parameter and a regularization parameter. The structure of the singular part of polymer stress tensor is a Gaussian aligned with the incoming streamline of the stagnation point; a smoothed $δ$-distribution whose width is proportional to the square-root of the diffusion coefficient. The amplitude of the stress island scales with the Wiessenberg number and, although singular in the limit of vanishing diffusion, it is integrable in the cross stream direction due to its vanishing width; this yields a convergent secondary flow. The leading order velocity response to this stress island is constructed and shown to be {\em independent} of the diffusion coefficient in the limit. The secondary circulation counteracts the forced flow and has a vorticity jump at the location of the stress islands, essentially expelling the background vorticity from the location of the birefringent strands. The analytic solutions are shown to be in excellent quantitative agreement with full numerical simulations and, therefore, the analytic solutions elucidate the salient mechanisms of the flow response to viscoelasticity and the mechanism for instability.

physics.flu-dyn↗

arXiv2002

Stages of Energy Transfer in the FPU Model

The Alpha version of the Fermi-Pasta-Ulam problem is revisited through direct numerical simulations and an application of weak turbulence theory. The energy spectrum, initialized with a large scale excitation, is traced through a series of distinct qualitative phases en route to eventual equipartition. Weak turbulence theory is applied in an attempt to provide and effective quantitative description of the evolution of the energy spectrum. Some scaling predictions are well-confirmed byt the numerical simulations.

nlin.CD↗

arXiv2001

Layer Formation in Semiconvection

Layer formation in a thermally destabilized fluid with stable density gradient has been observed in laboratory experiments and has been proposed as a mechanism for mixing molecular weight in late stages of stellar evolution in regions which are unstable to semiconvection. It is not yet known whether such layers can exist in a very low viscosity fluid: this work undertakes to address that question. Layering is simulated numerically both at high Prandtl number (relevant to the laboratory) in order to describe the onset of layering intability, and the astrophysically important case of low Prandtl number. It is argued that the critical stability parameter for interfaces between layers, the Richardson number, increases with decreasing Prandtl number. Throughout the simulations the fluid has a tendency to form large scale flows in the first convecting layer, but only at low Prandtl number do such structures have dramatic consequences for layering. These flows are shown to drive large interfacial waves whose breaking contributes to significant mixing across the interface. An effective diffusion coefficient is determined from the simulation and is shown to be much greater than the predictions of both an enhanced diffusion model and one which specifically incorporates wave breaking. The results further suggest that molecular weight gradient interfaces are ineffective barriers to mixing even when specified as initial conditions, such as would arise when a compositional gradient is redistributed by another mechanism than buoyancy, such as rotation or internal waves.

astro-ph↗