Bifurcating steady-state solutions of the dissipative quasi-geostrophic equation in Lagrangian formulation

Chen, Zhimin

doi:10.1088/0951-7715/29/10/3132

Cited by 5 publications

(4 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the mathematical formulation of [2], the energy dissipation controlled by the fractional Laplacian κ(−∆) α is applied to a quasi-geostrophic flow [3,4]. Mathematical theory of the dissipative quasi-geostrophic equation has been extensively studied (see, for example, [3,[5][6][7][8][9][10]). In the present study, we are interested in a quasi-geostrophic flow, which is from the understanding of blocks in atmosphere and involves the weak energy dissipation κ(−∆) α with α = 0.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium states of the Charney-DeVore quasi-geostrophic equation in mid-latitude atmosphere

Chen

Xiong

2016

Journal of Mathematical Analysis and Applications

Self Cite

View full text Add to dashboard Cite

Abstract. On the predictability of atmospheric blocking in the mid-latitude atmosphere, a quasi-geostrophic beta-plane channel model equation was introduced in a pioneering work by Charney and DeVore in 1979 based on the understanding of quasi-stationary weather patterns. The equation is driven by a zonal thermal flow representing a mid-latitude westerly jet and a wave function representing an ocean land topography. They truncated the equation into a three spectral mode model, which gives rise to the existence of multiple equilibrium states showing a blocking mechanism profile. Moreover, they predicted numerically the absence of the multiple equilibrium states with respect to the flat topography situation. In the present paper, this absence observation is discussed from rigorous analysis and the coexistence of two stable equilibrium states, similar to the three mode model equilibrium states accounting for atmospheric blocking, is investigated numerically with the increment of topographic amplitude. keyword beta-plane channel model equation, Charney-DeVore equation, multiple equilibrium states, stability of equilibrium state, zonal flow, topography disturbance

show abstract

Section: Introductionmentioning

confidence: 99%

Equilibrium states of the Charney-DeVore quasi-geostrophic equation in mid-latitude atmosphere

Chen

Xiong

2016

Journal of Mathematical Analysis and Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…which is linearized from (3). The eigenfunctions will be studied in the following three linear orthogonal subspaces of H 4 :…”

Section: Introductionmentioning

confidence: 99%

Bifurcating steady-state flows involving energy dissipation over a Hartmann boundary layer

Chen

2021

Preprint

Self Cite

View full text Add to dashboard Cite

A plane non-parallel vortex flow in a square fluid domain is examined. The energy dissipation of the flow is dominated by viscosity and linear friction effect of a Hartmann layer. This is a traditional Navier-Stokes flow when the linear friction effect is not involved, whereas it is a magnetohydrodynamic flow when the energy dissipation is fundamentally dominated by the friction. It is proved that the critical values of the viscosity and friction with respect to its linearized spectral problem are nonlinear thresholds leading to the onset of secondary steady-state flows, the nonlinear phenomenon observed in laboratory experiments.

show abstract

“…However, it is unknown for the existence of global regular solutions in the supercritical case. If the motion (1) is additionally driven by an external force, the existence of bifurcating stationary flows was studied by Chen and Price [5] and the author [3].…”

Section: Introductionmentioning

confidence: 99%

Quasi-stationary solutions of the surface quasi-geostrophic equation

Chen

2021

Preprint

Self Cite

View full text Add to dashboard Cite

In the present study, we find that the surface quasi-geostrophic equation admits exact solutions, which evolve with time in quasi-stationary states. The solutions presented are available for any dissipation effect κ(−∆) α (κ > 0, 0 ≤ α < 1), involved in the equation. When the equation is supercritical (0 ≤ α < 12 ), the problem on the existence of large global regular solutions remains open. This study, however, provides explicit sample solutions for the understanding of the uncertain problem.

show abstract

Bifurcating steady-state solutions of the dissipative quasi-geostrophic equation in Lagrangian formulation

Abstract: Abstract. It is shown that the non-homogeneous dissipative quasi-geostrophic equationwith α = 0 and β > 1 losses stability at a critical value κc > 0 and this instability gives rise to a circle of steady-state solutions.

Cited by 5 publications

References 35 publications

Equilibrium states of the Charney-DeVore quasi-geostrophic equation in mid-latitude atmosphere

Equilibrium states of the Charney-DeVore quasi-geostrophic equation in mid-latitude atmosphere

Bifurcating steady-state flows involving energy dissipation over a Hartmann boundary layer

Quasi-stationary solutions of the surface quasi-geostrophic equation

Contact Info

Product

Resources

About