Interacting Motion of Rectilinear Geostrophic Vortices I Linear Stability Anal
Interacting Motion of Rectilinear Geostrophic Vortices I Linear Stability Anal
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I9) can be associated with the double zero eigenvalues, eliminating unstable solutions of the form t^""*" where p. Is the multiplicity. But at a neutral stability point such as K = for N = 7, the quadruple zero eigenvalues yields a linearly time-increasing solution.
The linear invariants (3. 17) and (3-19) are apparently valid for 7^ 7^ 0; but since these invariants are independent of the position of the center vortex, we suspect that a linearized description of the motion may not be strictly v...alid. If these invariants cannot be invoked, the double zero roots yield an algebraic instability proportional to t over the entire range of parameters (except for 7 =0).
23 The implication is that the center vortex motion is Inherently non-linear. Thus we must study the non-linear initial value problem in order to determine the range of validity of the linearized stability analysis. In deriving the linearized equations (3«5) to (3. 8), some peculiarities of the center vortex were already evident: first, mixed cartesian and polar coordinates were needed to describe the motion of the center and circle vortices; and second, the center vortex terms introduced periodic coefficients which fortuitously could be made constant by transformation to an appropriate rotating coordinate system.
What to read after Interacting Motion of Rectilinear Geostrophic Vortices I Linear Stability Anal?
You can find similar books in the "Read Also" column, or choose other free books by G K Morikawa to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
I9) can be associated with the double zero eigenvalues, eliminating unstable solutions of the form t^""*" where p. Is the multiplicity. But at a neutral stability point such as K = for N = 7, the quadruple zero eigenvalues yields a linearly time-increasing solution.
The linear invariants (3. 17) and (3-19) are apparently valid for 7^ 7^ 0; but since these invariants are independent of the position of the center vortex, we suspect that a linearized description of the motion may not be strictly v...alid. If these invariants cannot be invoked, the double zero roots yield an algebraic instability proportional to t over the entire range of parameters (except for 7 =0).
23 The implication is that the center vortex motion is Inherently non-linear. Thus we must study the non-linear initial value problem in order to determine the range of validity of the linearized stability analysis. In deriving the linearized equations (3«5) to (3. 8), some peculiarities of the center vortex were already evident: first, mixed cartesian and polar coordinates were needed to describe the motion of the center and circle vortices; and second, the center vortex terms introduced periodic coefficients which fortuitously could be made constant by transformation to an appropriate rotating coordinate system.
What to read after Interacting Motion of Rectilinear Geostrophic Vortices I Linear Stability Anal?
You can find similar books in the "Read Also" column, or choose other free books by G K Morikawa to read onlineMoreLess
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