A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

1995 ◽  
Vol 182 (5) ◽  
pp. 665-675 ◽  
Author(s):  
S.N. Chandler-Wilde ◽  
D.C. Hothersall
Keyword(s):  
Asymptotic Expansion ◽  
Green Function ◽  
Far Field ◽  
Two Dimensional ◽  
Impedance Plane ◽  
The Green Function

The stability of filamentary vorticity in two-dimensional geophysical vortex-dynamics models

1991 ◽  
Vol 231 ◽  
pp. 575-598 ◽  
Author(s):  
D. W. Waugh ◽  
D. G. Dritschel
Keyword(s):  
Green Function ◽  
Shear Flow ◽  
Stream Function ◽  
Potential Vorticity ◽  
Two Dimensional ◽  
Interaction Range ◽  
Inversion Operator ◽  
The Green Function ◽  
The Stability ◽  
Background Shear

The linear stability of filaments or strips of ‘potential’ vorticity in a background shear flow is investigated for a class of two-dimensional, inviscid, non-divergent models having a linear inversion relation between stream function and potential vorticity. In general, the potential vorticity is not simply the Laplacian of the stream function – the case which has received the greatest attention historically. More general inversion relationships between stream function and potential vorticity are geophysically motivated and give an impression of how certain classic results, such as the stability of strips of vorticity, hold under more general circumstances.In all models, a strip of potential vorticity is unstable in the absence of a background shear flow. Imposing a shear flow that reverses the total shear across the strip, however, brings about stability, independent of the Green-function inversion operator that links the stream function to the potential vorticity. But, if the Green-function inversion operator has a sufficiently short interaction range, the strip can also be stabilized by shear having the same sense as the shear of the strip. Such stabilization by ‘co-operative’ shear does not occur when the inversion operator is the inverse Laplacian. Nonlinear calculations presented show that there is only slight disruption to the strip for substantially less adverse shear than necessary for linear stability, while for co-operative shear, there is major disruption to the strip. It is significant that the potential vorticity of the imposed flow necessary to create shear of a given value increases dramatically as the interaction range of the inversion operator decreases, making shear stabilization increasingly less likely. This implies an increased propensity for filaments to ‘roll-up’ into small vortices as the interaction range decreases, a finding consistent with many numerical calculations performed using the quasi-geostrophic model.

Green Function Cloud Computing Representation with Free Water Surface

2012 ◽  
Vol 170-173 ◽  
pp. 1962-1965
Author(s):  
Xue Jiao Li ◽  
Xing Wang ◽  
Chao Liu ◽  
Meng Yu Li ◽  
She Sheng Zhang
Keyword(s):  
Boundary Condition ◽  
Green Function ◽  
Water Surface ◽  
Free Water ◽  
Two Dimensional ◽  
Function Representation ◽  
Free Water Surface ◽  
The Green Function ◽  
Cloud Computation ◽  
Control Equation

According to the convenient using principle of cloud computation, the control equation and boundary condition of point source with free water surface are considered, the basic analyzing solution is obtained, the Green function representation is discussed., the discrete calculation expression and calculation procedure are proposed, two-dimensional graphics of the Green function’s real and imaginary part are plotted.

TWO-DIMENSIONAL ANISOTROPIC HEISENBERG FERROMAGNET IN COEXISTING TRANSVERSE AND LONGITUDINAL MAGNETIC FIELDS

2007 ◽  
Vol 21 (22) ◽  
pp. 3877-3887 ◽  
Author(s):  
AI-YUAN HU ◽  
YUAN CHEN
Keyword(s):  
Magnetic Field ◽  
Magnetic Properties ◽  
Green Function ◽  
Magnetic Fields ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
Heisenberg Ferromagnet ◽  
Two Dimensional ◽  
Temperature Anisotropy ◽  
The Green Function

The two-dimensional spin-1/2 anisotropic Heisenberg ferromagnet is investigated in coexisting transverse and longitudinal magnetic fields. Using the Green function treatment, the magnetization and susceptibility are studied as a function of temperature, anisotropy and magnetic fields. The effects of exchange anisotropy and transverse magnetic field on the magnetic properties of the system are discussed.

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