Dynamic Transitions of Quasi-Geostrophic Channel Flow

The main aim of this paper is to describe the dynamic transitions in flows described by the two-dimensional, barotropic vorticity equation in a periodic zonal channel. In \cite{CGSW03}, the existence of a Hopf bifurcation in this model as the Reynolds number crosses a critical value was proven. In this paper, we extend the results in \cite{CGSW03} by addressing the stability problem of the bifurcated periodic solutions. Our main result is the explicit expression of a non-dimensional number $\gamma$ which controls the transition behavior. We prove that depending on $\gamma$, the modeled flow exhibits either a continuous (Type I) or catastrophic (Type II) transition. Numerical evaluation of $\gamma$ for a physically realistic region of parameter space suggest that a catastrophic transition is preferred in this flow

ON THE SPECTRAL INSTABILITY AND BIFURCATION OF 2D-QUASI-GEOSTROPHIC POTENTIAL VORTICITY EQUATION

The analysis on hydrodynamic stability of shear flows is an active research direction in fluid dynamics. In this article, the spectral instability and bifurcation of forced shear flows governed by the 2D quasi-geostrophic equation with a generalized Kolmogorov forcing are investigated. We prove that the corresponding eigenvalue problem can be transferred into a family of algebraic equations with infinity number of variables, and the nontrivial solutions to the algebraic equations are expressed in form of continuous fractions. After obtaining the asymptotic estimate for the ratio of the imaginary parts of eigenvalues to a control parameter R as it approaches to infinity, we show that there exists a critical value Rc above which, the forced shear flows become unstable, where the control parameter R is the product of Reynolds number Re and the intensity of the curl of the forcing. To shed light on the bifurcation involved in the losing stability of the forced shear flows, a natural method used to reduce the quasi-geostrophic equation to ODEs is introduced. Based on numerical experiments on the coefficients in the ODEs, we show that both supercritical and subcritical Hopf bifurcations occur in the forced shear flows, which only depend on the type of generalized Kolmogorov forcing

Dynamic Transitions for Quasilinear Systems and Cahn-Hilliard equation with Onsager mobility

The main objectives of this article are two-fold. First, we study the effect of the nonlinear Onsager mobility on the phase transition and on the well-posedness of the Cahn-Hilliard equation modeling a binary system. It is shown in particular that the dynamic transition is essentially independent of the nonlinearity of the Onsager mobility. However, the nonlinearity of the mobility does cause substantial technical difficulty for the well-posedness and for carrying out the dynamic transition analysis. For this reason, as a second objective, we introduce a systematic approach to deal with phase transition problems modeled by quasilinear partial differential equation, following the ideas of the dynamic transition theory developed recently by Ma and Wang

Acute alcohol consumption is associated with increased interatrial electromechanical delay in healthy men

Background: Acute alcohol consumption can cause atrial fibrillation in patients with, and without, heart disease. Increased atrial electromechanical delay (EMD) has been associated with atrial fibrillation. We evaluated the atrial conduction properties by tissue Doppler imaging (TDI) echocardiography in healthy men following acute alcohol intake. Methods: Thirty healthy male volunteers were included in this study. Baseline ECG, heart rate, blood pressure, and TDI echocardiographic findings were compared to readings taken one hour after drinking six 12-oz cans of beer (76.8 g of ethanol). Results: Although the blood pressure and heart rate remained similar before and one hour after alcohol intake, Pmax and Pd values were significantly prolonged (114.2 &#177; 10.4 vs 100.8 &#177; 10.6, p = 0.002; 50.6 &#177; 9.6 vs 34.5 &#177; 8.8, p < 0.0001). Interatrial EMD was significantly increased after drinking alcohol compared to the baseline (19.8 &#177; 9.2 vs 14.0 &#177; 5.5 ms, p < 0.0002). Conclusions: Acute moderate alcohol intake was associated with an increased interatrial EMD obtained by TDI echocardiography. This finding may help explain how these patients express increased susceptibility to atrial fibrillation. (Cardiol J 2011; 18, 6: 682&#8211;686