10 papers
Quasi-stationary solutions of the surface quasi-geostrophic equation
Zhi-Min Chen
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 ava…
Bifurcating steady-state flows involving energy dissipation over a Hartmann boundary layer
Zhi-Min Chen
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.…
Energy stability of the Charney-DeVore quasi-geostrophic equation for atmospheric blocking
Zhi-Min Chen, Xiangming Xiong
Charney and DeVore [J. Atmos. Sci. 36 (1979), 1205-1216] found multiple equilibrium states as a consequence of bottom topography in their pioneering work on the quasi-geostrophic b…
Long-time behavior for three dimensional compressible viscous and heat-conductive gases
Xiaoping Zhai, Zhi-Min Chen
We study the large-time behavior of solutions to the compressible Navier-Stokes equations for a viscous and heat-conductive gases in . More precisely, under a suitabl…
Instability of the Kolmogorov flow in a wall-bounded domain
Zhi-Min Chen
In the magnetohydrodynamics (MHD) experiment performed by Bondarenko and his co-workers in 1979, the Kolmogorov flow loses stability and transits into a secondary steady state flow…
New formulation of the finite depth free surface Green function
Zhi-Min Chen
For a pulsating free surface source in a three-dimensional finite depth fluid domain, the Green function of the source presented by John [F. John, On the motion of floating bodies…