The logistic equation with nonlinear advection term

2022 ◽  
Vol 65 ◽  
pp. 103503
Author(s):  
Willian Cintra ◽  
Marcelo Montenegro ◽  
Antonio Suárez
Keyword(s):  
Logistic Equation ◽  
Advection Term ◽  
Nonlinear Advection

scholarly journals Influence of Advective Accelerations on Estuarine Exchange at a Chesapeake Bay Tributary

2012 ◽  
Vol 42 (10) ◽  
pp. 1617-1634 ◽  
Author(s):  
Nuvit B. Basdurak ◽  
Arnoldo Valle-Levinson
Keyword(s):  
Spatial Distribution ◽  
Chesapeake Bay ◽  
Momentum Balance ◽  
Exchange Flow ◽  
Hampton Roads ◽  
Relative Contribution ◽  
Advection Term ◽  
Nonlinear Advection ◽  
Order Of Magnitude ◽  
Estuarine Exchange

Abstract The influence of nonlinear advection on estuarine exchange flow was investigated with observations at the transition between the James River and Chesapeake Bay, Hampton Roads, Virginia. Data were collected under different tidal forcing, wind forcing, and river discharge in 2004 and 2005. The relative contribution of nonlinear advective terms to the along-channel momentum balance had the same order of magnitude as pressure gradient and friction, verifying recent analytical and numerical model results. Both the magnitude and the spatial distribution of nonlinear advection showed fortnightly variability. Nonlinear advection was more influential on along-channel flow at spring tides than at neap tides because of increased tidal velocities, in a cross-sectionally averaged sense. The flow structures induced by each nonlinear advective process were investigated for the first time with observations. The lateral advection term υuy was found to enhance laterally sheared exchange acting along with Coriolis forcing at spring tides and opposing it at neap tides. Vertical advection wuz showed similar spatial distribution as υuy at spring tides but was vertically sheared (landward at middepth and seaward in the rest of the water column) at neaps. Longitudinal advection uux augmented landward flow in the channel.

scholarly journals The effects of mesoscale regions of precipitation on the ionospheric dynamics, electrodynamics and electron density in the presence of strong ambient electric fields

2010 ◽  
Vol 28 (6) ◽  
pp. 1345-1360 ◽  
Author(s):  
J. D. de Boer ◽  
J.-M. A. Noël ◽  
J.-P. St.-Maurice
Keyword(s):  
Electron Density ◽  
Electric Fields ◽  
Current Density Distribution ◽  
Electron Density Profile ◽  
Particle Precipitation ◽  
Advection Term ◽  
Nonlinear Advection ◽  
High Latitude Ionosphere ◽  
E Region ◽  
Current Densities

Abstract. We have developed a new high resolution two-dimensional model of the high latitude ionosphere in which nonlinear advection terms are closely coupled with the electrodynamics. The model provides a self-consistent description of the ionospheric feedback on the electrodynamical perturbations produced by auroral arc-related particle precipitation in regions with strong ambient electric fields. We find in particular that a heretofore neglected ion Pedersen advection term can introduce considerable changes in the electron density profile, the current density distribution, the conductivities and the electron temperatures. We find that the convective effects can carry the ionisation more than 150 km outside the precipitation region in a few minutes, with attendant large changes in the current distribution and E-region densities that become enhanced outside the region of particle precipitation. The production of a tongue of ionisation that slowly decays outside the auroral boundaries contrasts with the sharp geometric cut-off and associated stronger current densities found in previous studies.

An analytical model of gravity currents in a stable atmosphere

2000 ◽  
Vol 420 ◽  
pp. 27-46 ◽  
Author(s):  
YIZHAK FELIKS
Keyword(s):  
Froude Number ◽  
Gravity Waves ◽  
Cold Front ◽  
Gravity Current ◽  
Gravity Currents ◽  
Structure Functions ◽  
Synoptic Wind ◽  
Advection Term ◽  
Nonlinear Advection ◽  
Nonlinear Gravity

An analytical solution to the nonlinear equations of motion and thermodynamic energy for gravity currents propagating in stable atmosphere is found. This solution differs from the previous analytical studies in several aspects. In our solution the head of the gravity current is a strong vortex and the dynamics are non-hydrostatic. The solution has two regimes: (i) a supercritical regime when the Froude number Fr = (c – U)/Na is larger than 1 – in this case the cold front is local; (ii) a subcritical regime when Fr is smaller than 1. Here, ahead of the front there is a disturbance of nonlinear gravity waves. The scale of the wave and its amplitude increase as the Froude number decreases.We found that the square of the speed of the gravity current (relative to the synoptic wind) is proportional to the mean drop of potential temperature over the front area times the front height a. The constant of proportionality is function of the environmental conditions. The thermal, velocity and vorticity fields can be described by non-dimensional structure functions of two numbers: pa = 1/Fr and ka. The amplitude of the structure functions is proportional to (c – U) 2/a for the thermal field, to (c – U) for the velocity field, and to (c – U)/a for the vorticity field.The propagation is studied in terms of the vorticity equation. The horizontal gradient of the buoyancy term always tends to propagate the cold front. The nonlinear advection term in most of the cases investigated here tends to slow the propagation of the gravity current. The propagation of the disturbance of nonlinear gravity waves ahead of the front in regime (ii) in most of the cases is due to the buoyancy term. The nonlinear advection term tends to slow the propagation when the synoptic wind blows in the direction opposite to that of the front propagation, and increase the propagation when the synoptic wind blows in the direction of propagation.

scholarly journals Conditions for the Existence of Global Solutions to Doubly Nonlinear Advection-diffusion Equations

2020 ◽  
Vol 21 (1) ◽  
pp. 83
Author(s):  
Jocemar Q. Chagas ◽  
Patrícia L. Guidolin ◽  
Paulo R. Zingano
Keyword(s):  
Initial Data ◽  
Initial Value Problem ◽  
Global Solutions ◽  
Critical Value ◽  
Initial Value ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Advection Term ◽  
Nonlinear Advection ◽  
Doubly Nonlinear

 In this work, we consider a initial-value problem for an doubly non linear advection-diffusion equation, and we present a critical value of κ up to wich the initial-value problem has global solution independent of the initial data u0, and from which global solutions may still exists, but from initial data u0 satisfying certain conditions. For this, we suppose that the function f(x,t,u) in the advection term, writted in the divergent form, satisfies certain conditions about your variation in Rn, and we also use the decrease of the norm L1(Rn) and an control for the norm L∞(Rn) of solution u(·,t). 

scholarly journals Novel numerical analysis for nonlinear advection–reaction–diffusion systems

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 112-125
Author(s):  
Naveed Shahid ◽  
Nauman Ahmed ◽  
Dumitru Baleanu ◽  
Ali Saleh Alshomrani ◽  
Muhammad Sajid Iqbal ◽  
...  
Keyword(s):  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Continuous System ◽  
Reaction Diffusion ◽  
Uniqueness Of Solutions ◽  
Reaction Diffusion Systems ◽  
System A ◽  
Diffusion Systems ◽  
Advection Term ◽  
Nonlinear Advection

AbstractIn this article, a numerical model for a Brusselator advection–reaction–diffusion (BARD) system by using an elegant numerical scheme is developed. The consistency and stability of the proposed scheme is demonstrated. Positivity preserving property of the proposed scheme is also verified. The designed scheme is compared with the two well-known existing classical schemes to validate the certain physical properties of the continuous system. A test problem is also furnished for simulations to support our claim. Prior to computations, the existence and uniqueness of solutions for more generic problems is investigated. In the underlying system, the nonlinearities depend not only on the desired solution but also on the advection term that reflects the pivotal importance of the study.

scholarly journals Parameter Optimization for Real-World ENSO Forecast in an Intermediate Coupled Model

2019 ◽  
Vol 147 (5) ◽  
pp. 1429-1445 ◽  
Author(s):  
Yuchu Zhao ◽  
Zhengyu Liu ◽  
Fei Zheng ◽  
Yishuai Jin
Keyword(s):  
Data Assimilation ◽  
Parameter Optimization ◽  
Real World ◽  
Climate Models ◽  
Coupled Model ◽  
Prediction Skill ◽  
Model Parameters ◽  
Real World Data ◽  
The Real ◽  
Advection Term

Abstract We performed parameter estimation in the Zebiak–Cane model for the real-world scenario using the approach of ensemble Kalman filter (EnKF) data assimilation and the observational data of sea surface temperature and wind stress analyses. With real-world data assimilation in the coupled model, our study shows that model parameters converge toward stable values. Furthermore, the new parameters improve the real-world ENSO prediction skill, with the skill improved most by the parameter of the highest climate sensitivity (gam2), which controls the strength of anomalous upwelling advection term in the SST equation. The improved prediction skill is found to be contributed mainly by the improvement in the model dynamics, and second by the improvement in the initial field. Finally, geographic-dependent parameter optimization further improves the prediction skill across all the regions. Our study suggests that parameter optimization using ensemble data assimilation may provide an effective strategy to improve climate models and their real-world climate predictions in the future.

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