Cooling-induced Vortex Decay in Keplerian Disks

Vortices are readily produced by hydrodynamical instabilities, such as the Rossby wave instability, in protoplanetary disks. However, large-scale asymmetries indicative of dust-trapping vortices are uncommon in submillimeter continuum observations. One possible explanation is that vortices have short lifetimes. In this paper, we explore how radiative cooling can lead to vortex decay. Elliptical vortices in Keplerian disks go through adiabatic heating and cooling cycles. Radiative cooling modifies these cycles and generates baroclinicity that changes the potential vorticity of the vortex. We show that the net effect is typically a spin down, or decay, of the vortex for a subadiabatic radial stratification. We perform a series of two-dimensional shearing box simulations, varying the gas cooling (or relaxation) time, t cool, and initial vortex strength. We measure the vortex decay half-life, t half, and find that it can be roughly predicted by the timescale ratio t cool/t turn, where t turn is the vortex turnaround time. Decay is slow in both the isothermal (t cool ≪ t turn) and adiabatic (t cool ≫ t turn) limits; it is fastest when t cool ∼ 0.1 t turn, where t half is as short as ∼300 orbits. At tens of astronomical units where disk rings are typically found, t turn is likely much longer than t cool, potentially placing vortices in the fast decay regime.

PENGARUH JARAK ALUR TERHADAP KESTABILAN ALIRAN FLUIDA BERDENYUT DALAM SALURAN BERPENAMPANG SEGIEMPAT

The pulsatile fluid flow in a transverse grooved channel would become self-sustained oscillatory flow at a certain critical Reynold number. The critical Reynold number where laminar unsteady flow changed to unsteady transitional one depends on grooves distances. The objective of this research is to analyze the effect of grooves distances toward the vortex strength and the stability of the fluid flow. This research was done by implementing a closed square cross-section channel, where the bottom surface of the channel was semicircle grooved. The frequency of flow oscillation measurement was done by setting up a resistance manometer and measurement was done at several Reynold numbers. From the research result, it is seen that the largest vortex strength occurs at the smallest groove distance. The flows become instability in all of the grooves distances by seen Phase Plane.

Stretching and shearing contamination analysis for Liutex and other vortex identification methods

The newly developed vortex-identification method, Liutex, has provided a new systematic description of the local fluid rotation, which includes scalar, vector, and tensor forms. However, the advantages of Liutex over the other widely used vortex-identification methods such as Q, ∆, λ2, and λci have not been realized. These traditional methods count on shearing and stretching as a part of vortex strength. But, in the real flow, shearing and stretching do not contribute to fluid rotation. In this paper, the decomposition of the velocity gradient tensor is conducted in the Principal Coordinate for uniqueness. Then the contamination effects of stretching and shearing of the traditional methods are investigated and compared with the Liutex method in terms of mathematical analysis and numerical calculations. The results show that the Liutex method is the only method that is not affected by either stretching or shear, as it represents only the local fluid rigid rotation. These results provide supporting evidence that Liutex is the superior method over others.

Effect of Ground Boundary Condition on Near-Field Wingtip Vortex Flow and Lift-Induced Drag

The ground proximity is known to induce an outboard movement and suppression of the wingtip vortices, leading to a reduced lift-induced drag. Depending on the ground boundary condition, a large scatter exists in the published lift-induced drag and vortex trajectory. In this experiment, the ground boundary condition-produced disparity in the vortex strength and induced drag were evaluated. No significant discrepancy appeared for a ground distance or clearance larger than 30% chord. As the stationary ground was further approached, there was the appearance of a corotating ground vortex (GV), originated from the downstream progression of a spanwise ground vortex filament, which added vorticity to the tip vortex, leading to a stronger tip vortex and a larger lift-induced drag compared to the moving ground. For the moving ground, the ground vortex was absent. In close ground proximity, the rollup of the high-pressure fluid flow escaped from the wing's tip always caused the formation of a counter-rotating secondary vortex, which dramatically weakened the tip vortex strength and produced a large induced-drag reduction. The moving ground effect, however, induced a stronger secondary vortex, leading to a smaller lift-induced drag and a larger outboard movement of the tip vortex as compared to the stationary ground effect.

Extending the Modular Earth Submodel System (MESSy v2.54) model hierarchy: the ECHAM/MESSy IdeaLized (EMIL) model setup

As models of the Earth system grow in complexity, a need emerges to connect them with simplified systems through model hierarchies in order to improve process understanding. The Modular Earth Submodel System (MESSy) was developed to incorporate chemical processes into an Earth System model. It provides an environment to allow for model configurations and setups of varying complexity, and as of now the hierarchy ranges from a chemical box model to a fully coupled chemistry–climate model. Here, we present a newly implemented dry dynamical core model setup within the MESSy framework, denoted as ECHAM/MESSy IdeaLized (EMIL) model setup. EMIL is developed with the aim to provide an easily accessible idealized model setup that is consistently integrated in the MESSy model hierarchy. The implementation in MESSy further enables the utilization of diagnostic chemical tracers. The setup is achieved by the implementation of a new submodel for relaxation of temperature and horizontal winds to given background values, which replaces all other “physics” submodels in the EMIL setup. The submodel incorporates options to set the needed parameters (e.g., equilibrium temperature, relaxation time and damping coefficient) to functions used frequently in the past. This study consists of three parts. In the first part, test simulations with the EMIL model setup are shown to reproduce benchmarks provided by earlier dry dynamical core studies. In the second part, the sensitivity of the coupled troposphere–stratosphere dynamics to various modifications of the setup is studied. We find a non-linear response of the polar vortex strength to the prescribed meridional temperature gradient in the extratropical stratosphere that is indicative of a regime transition. In agreement with earlier studies, we find that the tropospheric jet moves poleward in response to the increase in the polar vortex strength but at a rate that strongly depends on the specifics of the setup. When replacing the idealized topography to generate planetary waves by mid-tropospheric wave-like heating, the response of the tropospheric jet to changes in the polar vortex is strongly damped in the free troposphere. However, near the surface, the jet shifts poleward at a higher rate than in the topographically forced simulations. Those results indicate that the wave-like heating might have to be used with care when studying troposphere–stratosphere coupling. In the third part, examples for possible applications of the model system are presented. The first example involves simulations with simplified chemistry to study the impact of dynamical variability and idealized changes on tracer transport, and the second example involves simulations of idealized monsoon circulations forced by localized heating. The ability to incorporate passive and chemically active tracers in the EMIL setup demonstrates the potential for future studies of tracer transport in the idealized dynamical model.

Stretching and Shearing Contamination Analysis for Liutex and Other Vortex Identification Methods

The newly developed vortex-identification method, Liutex, has provided a new systematic description of the local fluid rotation, which includes scalar, vector, and tensor forms. However, the advantages of Liutex over the other widely used vortex-identification methods such as Q, Δ, λ2 , and λci have not been realized. These traditional methods count on shearing and stretching as a part of vortex strength. But, in the real flow, shearing and stretching do not contribute to fluid rotation. In this paper, the decomposition of the velocity gradient tensor is conducted in the Principal Coordinate for uniqueness. Then the contamination effects of stretching and shearing of the traditional methods are investigated and compared with the Liutex method in terms of mathematical analysis and numerical calculations. The results show that the Liutex method is the only method that is not affected by either stretching or shear, as it represents only the local fluid rigid rotation. These results provide supporting evidence that Liutex is the superior method over others.