Finite difference approximations for the determination of dynamic instability
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Authors
Haltiner, G.J.
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Date of Issue
1963
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Abstract
Approximate forms of the vorticity and thermal equations are linearized and combined
to yield a second-order partial differential equation for the amplitude of harmonic
perturbations. Finite-difference approximations for the derivatives yield a homogeneous
system of algebraic equations; and the condition that its determinants vanish
for a non-trivial solution yields the “frequency” equation, which may be solved to
give the phase velocities of the harmonic waves. Solutions are obtained for zonal
currents in which the wind varies vertically and horizonally and for a variety of
conditions with respect to grid distances, latitude and current width. Generally speaking,
the computations showed that decreasing the latitude and shear and increasing
the static stability were all destabilizing influences, not without some exceptions, however.
In addition, very short waves were found to be stable; however, instability was
found for very long waves, including a retrogressive unstable mode. Moreover, multiple
unstable modes were found for many wavelengths.
Calculations based on actual observations of the jet stream in December show it to
be dynamically unstable, both baroclinically and barotropically, with one mode of
maximum instability at a wavelength of about 3000 to 4000 km and a secondary
maximum at about 10,000 km.
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Article
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Naval Postgraduate School (U.S.)
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11 p.
Citation
Haltiner, G. J. "Finite difference approximations for the determination of dynamic instability." Tellus 15.3 (1963): 230-240.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.