Baroclinic instability in geophysical fluid dynamics

Калашник, М. В.; Kurganskii, M. V.; Chkhetiani, О. G.

doi:10.3367/ufne.2021.08.039046

Cited by 17 publications

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“…Recently a general approach to this problem, valid for arbitrary vertical distributions of PV, was developed using Green functions [30,31]. A fairly detailed analysis of these processes in geostropic flows can be found in new reviews [32][33][34]. Overall, the existing classical studies of the action/impact of the rigid boundaries on the dynamical processes in shear flows are mathematically complete and useful.…”

Section: The Subject Of the Present Study And The Proposed New Mathem...mentioning

confidence: 99%

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A new mathematical model of rigid boundary in shear flows

Chanishvili

Chagelishvili

Калашник

et al. 2023

J. Phys. A: Math. Theor.

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The present investigation is devoted to the revealing of the physical essence of the action of the rigid boundary on the linear dynamics of perturbations in plane shear flows. \emph{A new mathematical approach is proposed which accurately and completely replaces the horizontal rigid boundary by the actions of certain localized sources placed on the plane of the boundary ($z = 0$) in the original/canonical shear flow dynamical equations for wave and vortex mode perturbations}, i.e., for perturbations with zero and nonzero potential vorticity (PV). The approach is elaborated on the example of the well-known problem of geophysical hydrodynamics -- the linear dynamics of perturbations in semi-infinite ($z \geq 0$) flow of stratified rotating fluid with a vertical shear of velocity, ${\textbf{U}}_0(Az,0,0)$, zero beta, $\beta=0$, and horizontal rigid boundary at $z = 0$ -- which analytical wave and vortex mode solutions are well-known and serve as the reference solutions of our model equations. From the beginning, we have replaced the rigid boundary with localized sources for vortices and wave modes separately. The sources are the sum of the delta function and its first derivative the coefficients in front of which were unknown at this stage. In what follows, we accurately calculated these coefficients and thus determined the exact expressions for localized sources. Subsequent mathematical analysis showed that the localized sources give rise to new perturbations which can be labeled as secondary. The revealed physical essence of the action of the rigid boundary is as follows: being the external (localized) source of the analyzed open complex flow system, the rigid boundary puts an additional energy into perturbation harmonics that becomes an important power supplier supporting the linear dynamics of the system under study.

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Section: The Subject Of the Present Study And The Proposed New Mathem...mentioning

confidence: 99%

“…which is satisfied in −∞ < z < ∞. Similar to the above case, the coefficients A(t) and B(t) of the localized sources should be determined from the conditions of zero solution of equation (34) for −∞ < z < 0 and matching with equation ( 18) for 0 < z < ∞.…”

Section: Generation Of Secondary Wave Mode By the Rigid Boundarymentioning

confidence: 99%