scholarly journals Pullback Attractor for Nonautonomous Primitive Equations of Large-Scale Ocean and Atmosphere Dynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Kun Li ◽  
Fang Li
Keyword(s):  
Large Scale ◽  
Primitive Equations ◽  
Pullback Attractor

scholarly journals Convergence Results on the Boundary Conditions for 2D Large-Scale Primitive Equations in Oceanic Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Yuanfei Li
Keyword(s):  
Boundary Conditions ◽  
Large Scale ◽  
Weather Prediction ◽  
A Priori ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Convergence Result ◽  
Primitive Equations ◽  
Convergence Results ◽  
Initial Boundary Value

In this paper, the initial boundary value problem for the two-dimensional large-scale primitive equations of large-scale oceanic motion in geophysics is considered, which are fundamental models for weather prediction. By establishing rigorous a priori bounds with coefficients and deriving some useful inequalities, the convergence result for the boundary conditions is obtained.

scholarly journals Strong Solvability of a Variational Data Assimilation Problem for the Primitive Equations of Large-Scale Atmosphere and Ocean Dynamics

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Peter Korn
Keyword(s):  
Data Assimilation ◽  
Large Scale ◽  
Initial Conditions ◽  
Strong Solutions ◽  
Variational Data Assimilation ◽  
Ocean Dynamics ◽  
Primitive Equations ◽  
Cost Functional ◽  
Strong Solvability ◽  
Gradient Based

AbstractFor the primitive equations of large-scale atmosphere and ocean dynamics, we study the problem of determining by means of a variational data assimilation algorithm initial conditions that generate strong solutions which minimize the distance to a given set of time-distributed observations. We suggest a modification of the adjoint algorithm whose novel elements is to use norms in the variational cost functional that reflects the $$H^1$$ H 1 -regularity of strong solutions of the primitive equations. For such a cost functional, we prove the existence of minima and a first-order adjoint condition for strong solutions that provides the basis for computing these minima. We prove the local convergence of a gradient-based descent algorithm to optimal initial conditions using the second-order adjoint primitive equations. The algorithmic modifications due to the $$H^1$$ H 1 -norms are straightforwardly to implement into a variational algorithm that employs the standard $$L^2$$ L 2 -metrics.

scholarly journals Nonlinear interactions of nearly non-dispersive equatorial shallow-water waves

2020 ◽  
Vol 85 (3) ◽  
pp. 365-384
Author(s):  
Mian Wang ◽  
Zhan Wang ◽  
Hennes Hajduk
Keyword(s):  
Water Waves ◽  
Large Scale ◽  
Multiple Scales ◽  
Wave Interaction ◽  
Finite Element Approximation ◽  
Galerkin Projection ◽  
Primitive Equations ◽  
Element Approximation ◽  
Nonlinear Interactions ◽  
Simplified Models

Abstract This paper is concerned with nonlinear interactions of fundamental equatorial modes. In order to understand the mechanism of large-scale atmospheric motions in the near equator regime—especially the observed wavenumber-frequency spectrum—we develop novel models describing interactions among Kelvin, Yanai and Poincaré waves. Based on the methods of multiple scales and Galerkin projection, the primitive equations can be simplified to model equations which reduce the complexity and cost of computation significantly. Subsequently, the detailed numerical results indicate that wave interactions between the aforementioned modes in the non-dispersive regime depends on initial amplitude and relative phase and that the eastward Yanai wave can be generated from the second Poincaré mode. We also compare the simplified models to an advanced finite element approximation for the primitive equations. The fact that results of the latter are in good agreement, at least qualitatively, with those of the simplified models, indicates that reduced models capture most of the wave interaction mechanisms in the nearly non-dispersive regime.

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