scholarly journals Tornado-type stationary vortex with nonlinear term due to moisture transport

2010 ◽  
Vol 4 (1) ◽  
pp. 77-82 ◽  
Author(s):  
P. B. Rutkevich ◽  
P. P. Rutkevych
Keyword(s):  
Tropical Cyclones ◽  
Shooting Method ◽  
Nonlinear Term ◽  
Numerical Solutions ◽  
Variable Temperature ◽  
Slow Rotation ◽  
Nonlinear Phenomenon ◽  
One Dimensional ◽  
Stationary Vortex ◽  
General Possibility

Abstract. Tornado vortex is believed to be essentially nonlinear phenomenon; and the puzzle to choose the nonlinear term(s) responsible for its formation is still unresolved. In the present work we consider the nonlinear term associated with atmosphere humidity, by introducing variable temperature gradient depending on the vertical velocity of the fluid. Such term is able to yield energy to the system and is very suitable for such a problem. Other nonlinear terms are neglected, assuming slow rotation, or in other words a "weak" tornado approximation. We consider one-dimensional radial boundary problem, and use a modificaiton of shooting method to satisfy boundary conditions at large radii. Obtained numerical solutions of the nonlinear differential equation qualitatively agree with the observed atmosphere vortices (tornados, tropical cyclones). The obtained results show general possibility of existence of unstable motion even in convectively stable atmosphere stratification.

scholarly journals A Hypothesis for the Redevelopment of Warm-Core Cyclones over Northern Australia

2008 ◽  
Vol 136 (10) ◽  
pp. 3863-3872 ◽  
Author(s):  
Kerry Emanuel ◽  
Jeff Callaghan ◽  
Peter Otto
Keyword(s):  
Heat Transfer ◽  
Thermal Diffusivity ◽  
Tropical Cyclones ◽  
Deep Layer ◽  
Heat Fluxes ◽  
Northern Australia ◽  
One Dimensional ◽  
Warm Core ◽  
Vertical Heat ◽  
Underlying Soil

Tropical cyclones moving inland over northern Australia are occasionally observed to reintensify, even in the absence of well-defined extratropical systems. Unlike cases of classical extratropical rejuvenation, such reintensifying storms retain their warm-core structure, often redeveloping such features as eyes. It is here hypothesized that the intensification or reintensification of these systems, christened agukabams, is made possible by large vertical heat fluxes from a deep layer of very hot, sandy soil that has been wetted by the first rains of the approaching systems, significantly increasing its thermal diffusivity. To test this hypothesis, simulations are performed with a simple tropical cyclone model coupled to a one-dimensional soil model. These simulations suggest that warm-core cyclones can indeed intensify when the underlying soil is sufficiently warm and wet and are maintained by heat transfer from the soil. The simulations also suggest that when the storms are sufficiently isolated from their oceanic source of moisture, the rainfall they produce is insufficient to keep the soil wet enough to transfer significant quantities of heat, and the storms then decay rapidly.

Diffusion-Limited Cell Dehydration: Analytical and Numerical Solutions for a Planar Model

1999 ◽  
Author(s):  
Alexander V. Kasharin ◽  
Jens O. M. Karlsson
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Planar System ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Constant Diffusivity ◽  
A Cell ◽  
Cell Dehydration ◽  
The One

Abstract The process of diffusion-limited cell dehydration is modeled for a planar system by writing the one-dimensional diffusion-equation for a cell with moving, semipermeable boundaries. For the simplifying case of isothermal dehydration with constant diffusivity, an approximate analytical solution is obtained by linearizing the governing partial differential equations. The general problem must be solved numerically. The Forward Time Center Space (FTCS) and Crank-Nicholson differencing schemes are implemented, and evaluated by comparison with the analytical solution. Putative stability criteria for the two algorithms are proposed based on numerical experiments, and the Crank-Nicholson method is shown to be accurate for a mesh with as few as six nodes.

scholarly journals Dissociation and recombination in the electrolyte flow model

2021 ◽  
Vol 2090 (1) ◽  
pp. 012076
Author(s):  
A Shobukhov ◽  
H Koibuchi
Keyword(s):  
Flow Model ◽  
Numerical Solutions ◽  
Stable Equilibrium ◽  
Steady State Solution ◽  
System Of Equations ◽  
Constant Flow ◽  
Dimensional Model ◽  
Electrolyte Flow ◽  
One Dimensional ◽  
Dilute Aqueous Solution

Abstract We propose a one-dimensional model for the dilute aqueous solution of NaCl which is treated as an incompressible fluid placed in the external electric field. This model is based on the Poisson-Nernst-Planck system of equations, which also contains the constant flow velocity as a parameter and considers the dissociation and the recombination of ions. We study the steady-state solution analytically and prove that it is a stable equilibrium. Analyzing the numerical solutions, we demonstrate the importance of dissociation and recombination for the physical meaningfulness of the model.

Numerical Solutions of Transients in Pneumatic Networks—Transmission-Line Calculations

1968 ◽  
Vol 35 (3) ◽  
pp. 588-595 ◽  
Author(s):  
S. Tsao
Keyword(s):  
Wave Propagation ◽  
Transmission Lines ◽  
Numerical Solutions ◽  
Navier Stokes ◽  
Damping Factor ◽  
Temperature Profiles ◽  
Hypothetical Case ◽  
One Dimensional ◽  
Simplifying Assumptions ◽  
Energy Equations

Equations governing the damped wave propagation along transmission lines are obtained from the Navier-Stokes and energy equations by making certain simplifying assumptions. The flow considered is essentially one-dimensional. However, radial variations of the velocity and temperature profiles must be considered, because the damping factor is directly dependent on them. The equations are integrated by numerical methods. A hypothetical case is computed as an example.

One-dimensional consolidation of multilayered aquifer systems with viscoelastic properties induced by time-dependent groundwater drawdown

2021 ◽  
pp. qjegh2021-073
Author(s):  
Weitao Yang ◽  
Jin Xu
Keyword(s):  
Viscoelastic Properties ◽  
Numerical Solutions ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Time Dependent ◽  
Analytical Models ◽  
Consolidation Process ◽  
One Dimensional ◽  
Groundwater Drawdown ◽  
Aquifer Systems

Most analytical and semi-analytical models for pumping-induced land subsidence invoke the simplifying assumptions regarding characteristics of geomaterials, as well as the pattern of drawdown response to pumping. This paper presents an analytical solution for one-dimensional consolidation of the multilayered soil due to groundwater drawdown, in which viscoelastic property and time-dependent drawdown are taken into account. The presented solution is developed by using the boundary transformation techniques. The validity of the proposed solution is verified by comparing with a degenerated case for a single layer, as well as with the numerical solutions and experimental results for a two-layer system. The difference between the average consolidation degree Up defined by hydraulic head and that Us defined by total settlement is discussed. The detailed parametric studies are conducted to reveal the effects of viscoelastic properties and drawdown patterns on the consolidation process. It is revealed that while the effect of different drawdown response patterns is significant during the early-intermediate stages of consolidation, the viscoelastic properties may have a more dominant influence on long-term consolidation behavior, depending on the values of the material parameters, which are reflected in both the deformation process of soil layers and the dissipation of excess pore-water pressure.

Numerical Solutions of Boundary Value Problems with So-Called Shooting Method

2021 ◽  
Author(s):  
Sujaul Chowdhury ◽  
Mubin Md. Al Furkan ◽  
Nazmus Sayadat Ifat
Keyword(s):  
Boundary Value Problems ◽  
Shooting Method ◽  
Numerical Solutions ◽  
Boundary Value

scholarly journals Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state

1999 ◽  
Vol 396 ◽  
pp. 223-256 ◽  
Author(s):  
B. S. BROOK ◽  
S. A. E. G. FALLE ◽  
T. J. PEDLEY
Keyword(s):  
Shallow Water ◽  
Numerical Solutions ◽  
Godunov Method ◽  
Test Case ◽  
Interesting Phenomenon ◽  
One Dimensional ◽  
Collapsible Tubes ◽  
Highly Nonlinear ◽  
Pressure Area ◽  
The One

Unsteady flow in collapsible tubes has been widely studied for a number of different physiological applications; the principal motivation for the work of this paper is the study of blood flow in the jugular vein of an upright, long-necked subject (a giraffe). The one-dimensional equations governing gravity- or pressure-driven flow in collapsible tubes have been solved in the past using finite-difference (MacCormack) methods. Such schemes, however, produce numerical artifacts near discontinuities such as elastic jumps. This paper describes a numerical scheme developed to solve the one-dimensional equations using a more accurate upwind finite volume (Godunov) scheme that has been used successfully in gas dynamics and shallow water wave problems. The adapatation of the Godunov method to the present application is non-trivial due to the highly nonlinear nature of the pressure–area relation for collapsible tubes.The code is tested by comparing both unsteady and converged solutions with analytical solutions where available. Further tests include comparison with solutions obtained from MacCormack methods which illustrate the accuracy of the present method.Finally the possibility of roll waves occurring in collapsible tubes is also considered, both as a test case for the scheme and as an interesting phenomenon in its own right, arising out of the similarity of the collapsible tube equations to those governing shallow water flow.

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