Related papers: Dynamic Transition Theory for Thermohaline Circula…
We reconsider the problem of the stability of the thermohaline circulation as described by a two-dimensional Boussinesq model with mixed boundary conditions. We determine how the stability properties of the system depend on the intensity of…
In this article, we aim to study the stability and dynamic transition of an electrically conducting fluid in the presence of an external uniform horizontal magnetic field and rotation based on a Boussinesq approximation model. By analyzing…
The main aim of the paper is to investigate the transitions of the thermohaline circulation in a spherical shell in a parameter regime which only allows transitions to multiple equilibria. We find that the first transition is either…
The main objective of this article is to study the nonlinear stability and dynamic transitions of the basic (zonal) shear flows for the three-dimensional continuously stratified rotating Boussinesq model. The model equations are fundamental…
A thorough analysis of the stability of a coupled version of an inter-hemispheric 3-box model of Thermohaline Circulation (THC) is presented. This study follows a similarly structured analysis on an uncoupled version of the same model…
The Boussinesq system for buoyancy driven fluids couples the momentum equation forced by the buoyancy with the convection-diffusion equation for the temperature. One fundamental issue on the Boussinesq system is the stability problem on…
A thorough analysis of the stability of the uncoupled Rooth interhemispheric 3-box model of thermohaline circulation (THC) is presented. The model consists of a northern high latitudes box, a tropical box, and a southern high latitudes box,…
The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In…
A thermodynamically consistent framework able to model either diffusive and displacive phase transitions is proposed. The first law of thermodynamics, the balance of linear momentum equation and the Cahn-Hilliard equation for solute mass…
A new universal theory for flow instability and turbulent transition is proposed in this study. Flow instability and turbulence transition have been challenging subjects for fluid dynamics for a century. The critical condition of turbulent…
This paper addresses the stability and large-time behavior problem on the perturbations near the hydrostatic balance of the two dimensional Boussinesq system, taking into account vertical dissipation and horizontal thermal diffusion. The…
In the present chapter, we discuss an approach for transition from discrete to continuum description of thermomechanical behavior of solids. The transition is carried out for several anharmonic systems: one-dimensional crystal,…
Main objective of this paper is to describe the dynamic transition of the incompressible MHD equations in a rectangular domain in $\mathbb{R}^{3}$. Our analysis shows that the system undergoes a first dynamic transition either to multiple…
We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…
We consider the governing equations for the motion of the viscous fluids in two moving domains and an evolving surface from both energetic and thermodynamic points of view. We make mathematical models for multiphase flow with surface flow…
The main objective of this article is to study the dynamics of the stratified rotating Boussinesq equations, which are a basic model in geophysical fluid dynamics. First, for the case where the Prandtl number is greater than one, a complete…
The equations of motion describing buoyant fluids are often simplified using a set of approximations proposed by J. Boussinesq one century ago. To resume, they consist in assuming constant fluid properties, incompressibility and…
Buoyancy-induced (Rayleigh-Benard) convection of a fluid between two horizontal plates is a central paradigm for studying the transition to complex spatiotemporal dynamics in sustained nonequilibrium systems. To improve the analysis of…
Equilibrium thermodynamics is grounded in the law of energy conservation, with a specific focus on how systems exchange energy with their environment during transitions between equilibrium states. These transitions are typically…
There is a reasonable possibility that the present-day Atlantic Meridional Overturning Circulation is in a bi-stable regime and hence it is relevant to compute probabilities and pathways of noise-induced transitions between the stable…