Conservative Semi-Lagrangian Scheme Applied to One-Dimensional Shallow Water Equations

2022

Asia-Pac J Atmos Sci

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An inviscid, nonlinear shallow water model is applied to study the formation of filaments and merging of potential vorticity (PV, π). We confirm that misalignment of vorticity with the streamlines is crucial to merger. Flow creates positive PV tendency (πt) on the lee side of π ridge, which increases the angle between streamlines and PV contours and the efficiency of vorticity transport along the parallel but oppositive direction in the positive quadrants of πt. So, the vortices move closer while rotating around each other. Filamentation starts as weak vorticity shatters from the outer edge of vortex core. The filament grows and rotates around the cores, but shows little effects to positive PV advection or vortex merging in the inner core, evidenced by the steady core area integrated PV trends. Consecutive PV transfer from lower to higher interval levels are observed during merger process while elongated filamentation is dissolving into the lower level PV regime. The vortices never merge when negative πt prevails between two vortices. Distance between the vortex cores show direct correspondence to positive πt between them. Hence, the advance of positive πt provides a simple mechanism of merging. The Rossby radius of deformation (LD) is confirmed to be another strong indicator for vortex pair merger where LD comparable or smaller than the initial vortex core separation length scale makes merger more likely due to geostrophic adjustment. The Rossby number (Ro) affected the overall flow interaction speed speed when LD is fixed.

Section: Introductionsupporting

confidence: 58%

Vortex Merger in Shallow Water Model

2022

Asia-Pac J Atmos Sci

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“…4b). Because the size of vortex is much less than the radius of deformation, the height field changes drastically to adjust to the velocity field, as discussed in Sun (2007).…”

Section: Initial Vortex From Gradient Wind Equationmentioning

confidence: 99%

The vortex moving toward Taiwan and the influence of the central mountain range

2016

Geosci. Lett.

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Surface friction is important to a vortex moving toward Taiwan but was ignored in several previous studies. The change of the potential vorticity comes from friction in the shallow-water equation, hence, it was applied to study the westbound vortex influenced by the central mountain range (CMR) blocking and surface friction, which is defined as friction coefficient multiplied by the square root of topographic elevation. Without surface friction, the movement of vortex is not affected by the CMR due to the conservation of potential vorticity. With small surface friction, the simulated vortex first deflects southward slightly, then rebounds gently north due to the effect of channel flow, as the previous studies. With moderate or large surface friction, when the vortex approaching Taiwan, it deforms and creates two wind maxima; one due to effect of channel flow and the other on the east of the vortex, because the slowdown vortex is pushed by the mean easterly flow behind. Meanwhile, the vortex and two wind maxima rotate cyclonically. Hence, the vortex can deflect north or south, or form a loop, that depends on the strength and location of the wind maxima. If the circulation of the vortex moves around the northern tip of Taiwan, it can induce a significant secondary vortex on the lee side. On the other hand, the secondary vortex, triggered by the flow passing over the CMR, is rather weak. This paper may provide the formation of asymmetric inner flow and the deflection of the vortex, which may be difficult to define in a more complicated atmospheric model.

“…This resulted in a change of temperature, pressure, wind, cloud, and precipitation over that area. The disturbances caused by the dusts introduced a geostrophic adjustment and secondary circulations (Sun, 2007). Hence, the influence of the dust spreads from the polluted area.…”

Section: Effect Of Dust On Regional Weather/climatementioning

confidence: 99%

Numerical Simulations of Asian Dust-Aerosols and Regional Impact on Weather and Climate- Part II: PRCM-Dust Model Simulation

Yang

Lin

2013

Aerosol Air Qual. Res.

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The Purdue Regional Climate Model (PRCM)-Dust, an on-line coupled regional climate-dust model, has been developed to study the dust life cycle and radiative effect of dust on regional weather and climate in Asia in April 1998. The dust model is built on the PRCM discussed in Part I. The dust module includes the major phases of the mineral dust cycle, such as emission, advection, diffusion, and deposition. Furthermore, the optical properties of the dust aerosols are included in the radiation calculation of the PRCM, so that the feedback of radiative forcing of dust-aerosols can be considered in the PRCM modeling. The PRCM-Dust successfully simulated the uplifted dusts to reached around 500-800 hPa over the source regions and remained at 3-5 km or higher to be transported further eastward. The spatial and temporal distributions of the dust aerosols were consistent with the satellite images, the TOMS Aerosol Index maps, lidar observations, and the surface network reports. The regional climatic impacts due to radiative effect of dust aerosols include warming over the high concentration regions in North Asia and cooling in dust-free South Asia. Since there is no nudging, restart, or other artificial forcing in the PRCM-Dust model, the simulated dust concentrations, size distribution, as well as meteorological and soil environments follow the conservation laws of physics. They are suitable to study the interactions among dusts, soil, and regional weather/climate.