A comment on the continuity equation model of slope profile development and its boundary conditions

2007 ◽  
Vol 7 (3) ◽  
pp. 283-284 ◽  
Author(s):  
Adrian C. Armstrong
Keyword(s):  
Boundary Conditions ◽  
Continuity Equation ◽  
Equation Model ◽  
Profile Development

scholarly journals A Variational Multiple–Doppler Radar Three-Dimensional Wind Synthesis Method and Its Impacts on Thermodynamic Retrieval

2009 ◽  
Vol 137 (11) ◽  
pp. 3992-4010 ◽  
Author(s):  
Yu-Chieng Liou ◽  
Ya-Ju Chang
Keyword(s):  
Boundary Conditions ◽  
Wind Field ◽  
Continuity Equation ◽  
Field Experiments ◽  
Doppler Radar ◽  
Traditional Approach ◽  
Synthesis Method ◽  
Three Dimensional ◽  
Retrieval Algorithm ◽  
Thermodynamic Retrieval

Abstract A multiple–Doppler radar synthesis method is developed to recover the three-dimensional wind field. In this method the solutions are obtained by variationally adjusting the winds to satisfy a series of constraints in weak formats. Among them, the primary ones are multiple-radar radial velocity observations, the anelastic continuity equation, the vertical vorticity equation, the background wind, and spatial smoothness terms. The retrieved wind products are at two time levels, and can be readily applied to deduce the information about the pressure and temperature through the use of the thermodynamic retrieval algorithm, in which the temporal derivatives of the wind fields are required. Experiments using model-simulated data are conducted, from which two major findings are obtained. First, the wind field along and near the radar baseline can still be recovered. This is a major advantage over the traditional approach. Therefore, the proposed method is capable of providing uninterrupted observations of a weather system as it passes the baseline. This allows for more flexibility when designing the radar deployment in field experiments. Second, if the winds are applied to infer the thermodynamic fields using the traditional dynamic retrieval method, and an extra sounding (e.g., radiosonde or dropsonde) is combined in order to specify the horizontal average of the thermodynamic perturbations, the preferable place to release this sounding is within the region of weak, rather than strong, convection. In additional to the aforementioned findings, with this method there is no need to prescribe the top or bottom boundary conditions for the vertical velocities in the traditional sense. Since the computation is performed without explicit vertical integration of the continuity equation, the problem of error accumulation due to inappropriate boundary conditions for the vertical velocities is prevented. These finding are consistent with some previous publications. Furthermore, the instability that occurs during traditional iterative dual-Doppler wind synthesis based on a Cartesian coordinate can also be avoided. Finally, data from any number of radars can be easily added to the computation. This method is also tested using the radar datasets collected during the Southwest Monsoon Experiment/Terrain-Influenced Monsoon Rainfall Experiment (SoWMEX/TiMREX), which was conducted from May to June 2008 in Taiwan, and reasonable results are obtained.

scholarly journals Incompressible Fluid flow through free andporous areas

2021 ◽  
pp. 99-102
Author(s):  
Mohamed Saif AlDien ◽  
Hussam M.Gubara
Keyword(s):  
Fluid Flow ◽  
Boundary Conditions ◽  
Incompressible Fluid ◽  
Continuity Equation ◽  
Flow Problem ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Incompressible Fluid Flow ◽  
Flow Through

In this paper we discussedincompressiblefluid flow problem through free and porous areas by using Darcy's law and continuity equation, by apply the boundary conditions required to specify the solutio

Threshold Voltage and Sub-Threshold Slope Variation with Gate-Length in Al2O3/InAlAs/InGaAs Quantum Well (QW) FET's

2011 ◽  
Vol 495 ◽  
pp. 112-115 ◽  
Author(s):  
I. Tsopelas ◽  
A. Gili ◽  
J.P. Xanthakis
Keyword(s):  
Quantum Well ◽  
Schottky Barrier ◽  
Threshold Voltage ◽  
Continuity Equation ◽  
Equation Model ◽  
Gate Length ◽  
Subthreshold Slope ◽  
Fast Switching ◽  
Ingaas Quantum Well

We have theoretically examined the scaling of the Al2O3/InAlAs/InGaAs QW FET one of the proposed III-V channel MOSFET's designed to replace the conventional SiO2/Si structures. To accomplish this we have used a Schroedinger – Poisson – Continuity equation model that is fully 2-dimentional ie all equations are solved along and perpendicular to the channel. We have found out that for the threshold voltage VT to be around zero volts a Schottky barrier ΦΒ of 3.5 - 4.0eV is necessary. Both Cu or W will suffice. for this. The VT value moves by 0.7 as the device is scaled from 65 nm gate length Lg to 25nm. Furthermore, as the Lg is scaled to the desired 20nm value the subthreshold slope SS increases from 90meV/dec to about 170meV/dec guaranteeing fast switching.

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