Steady state solutions for axially-symmetric climatic variables

1968 ◽  
Vol 69 (1) ◽  
pp. 237-259 ◽  
Author(s):  
Barry Saltzman
Keyword(s):  
Steady State ◽  
Climatic Variables ◽  
Axially Symmetric ◽  
Steady State Solutions

SOME EXACT SOLUTIONS OF THE LORENTZ INVARIANT PROBLEM OF THE MOTION OF TWO ELECTRIC FLUIDS

1955 ◽  
Vol 33 (12) ◽  
pp. 819-823 ◽  
Author(s):  
J. J. Gibbons
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Cylindrical Symmetry ◽  
Axially Symmetric ◽  
Two Fluids ◽  
Body Forces ◽  
Steady State Solutions

Methods of generating exact steady-state solutions for the flow of superimposed positive and negative fluids are developed for the cases of linear and cylindrical motion. The two fluids are assumed to be subject only to body forces arising from the total E and B fields. It is shown that the only axially symmetric solutions are of cylindrical symmetry, i.e. rotating spheres or rings of charge cannot satisfy the equations where the two fluids overlap.

scholarly journals Global Circulation in an Axially Symmetric Shallow-Water Model, Forced by Off-Equatorial Differential Heating

2010 ◽  
Vol 67 (4) ◽  
pp. 1275-1286 ◽  
Author(s):  
Ori Adam ◽  
Nathan Paldor
Keyword(s):  
Steady State ◽  
Shallow Water ◽  
Hadley Circulation ◽  
Present Theory ◽  
Water Model ◽  
Tropical Region ◽  
Axially Symmetric ◽  
Shallow Water Model ◽  
Differential Heating ◽  
Steady State Solutions

Abstract An axially symmetric inviscid shallow-water model (SWM) on the rotating Earth forced by off-equatorial steady differential heating is employed to characterize the main features of the upper branch of an ideal Hadley circulation. The steady-state solutions are derived and analyzed and their relevance to asymptotic temporal evolution of the circulation is established by comparing them to numerically derived time-dependent solutions at long times. The main novel feature of the steady-state solutions of the present theory is the existence of a tropical region, associated with the rising branch of the Hadley circulation, which extends to about half the combined width of the Hadley cells in the two hemispheres and is dominated by strong vertical advection of momentum. The solutions in this tropical region are characterized by three conditions: (i) the meridional temperature gradient is very weak but drastically increases outside of the region, (ii) moderate easterlies exist only inside this region and they peak off the equator, and (iii) angular momentum is not conserved there. The momentum fluxes of the new solutions at the tropics differ qualitatively from those of existing nearly inviscid theories and the new flux estimates are in better agreement with both observations and axially symmetric simulations. As in previous nearly inviscid theories, the steady solutions of the new theory are determined by a thermal Rossby number and by the latitude of maximal heating.

Explicit steady state solutions for a particularM(x)/M/1 queueing system

1977 ◽  
Vol 24 (4) ◽  
pp. 651-659 ◽  
Author(s):  
George L. Jensen ◽  
Albert S. Paulson ◽  
Pasquale Sullo
Keyword(s):  
Steady State ◽  
Queueing System ◽  
Steady State Solutions

Nonlinear Vibrations of Viscoelastic Plane Truss Under Harmonic Excitation

2014 ◽  
Vol 14 (04) ◽  
pp. 1450009 ◽  
Author(s):  
Andrew Yee Tak Leung ◽  
Hong Xiang Yang ◽  
Ping Zhu
Keyword(s):  
Steady State ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Homotopy Continuation ◽  
Response Curves ◽  
System A ◽  
Structural Responses ◽  
Voigt Model ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

This paper is concerned with the steady state bifurcations of a harmonically excited two-member plane truss system. A two-degree-of-freedom Duffing system having nonlinear fractional derivatives is derived to govern the dynamic behaviors of the truss system. Viscoelastic properties are described by the fractional Kelvin–Voigt model based on the Caputo definition. The combined method of harmonic balance and polynomial homotopy continuation is adopted to obtain steady state solutions analytically. A parametric study is conducted with the help of amplitude-response curves. Despite its seeming simplicity, the mechanical system exhibits a wide variety of structural responses. The primary and sub-harmonic resonances and chaos are found in specific regions of system parameters. The dynamic snap-through phenomena are observed when the forcing amplitude exceeds some critical values. Moreover, it has been shown that, suppression of undesirable responses can be achieved via changing of viscosity of the system.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

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