TY - JOUR

T1 - Rossby Waves on Non-zonal Currents

T2 - Structural Stability of Critical Layer Effects

AU - Gnevyshev, Vladimir G.

AU - Badulin, Sergei I.

AU - Belonenko, Tatyana V.

N1 - Funding Information:
The work was funded by Russian Foundation for Basic Research # 20-05-00066. Section was supported by Russian Science Foundation Grant # 19-72-30028 with the contribution of MIGO GROUP ( http://migogroup.ru ).
Funding Information:
The work was funded by Russian Foundation for Basic Research # 20-05-00066. Section was supported by Russian Science Foundation Grant # 19-72-30028 with the contribution of MIGO GROUP ( http://migogroup.ru ). Acknowledgements
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020/11

Y1 - 2020/11

N2 - The problem of the propagation of linear Rossby waves in horizontally inhomogeneous non-zonal flows is studied. The explicit solution within the geometric optics (WKBJ) approximation is found to be identical to the exact Cauchy problem solution for the case of a constant horizontal velocity shear.The effect of the short-wave transformation of Rossby waves near the so-called critical layer is detailed for the arbitrary direction of non-zonal flow. In the general case, this transformation can occur in two ways: (1) as an adhering, a monotonic approaching of wave packets to the critical layer for an infinitely long time. The sign of the intrinsic frequency of the packet remains the same all the time; (2) as an adhering with overshooting when the wave packet, first, crosses its critical layer at finite wavenumber. The wave changes the sign of the intrinsic frequency when overshooting the critical layer and then keeps the sign when it is adhering to this layer asymptotically similarly to the previous scenario. The latter regime does not exist for zonal flows, that degenerates the short-wave dynamics of Rossby waves in this special case. On the contrary, the anisotropy of the dispersion relation permits both positive and negative frequencies in a non-zonal flow. It allows for the effective use of the concept of waves of negative energy for the analysis of the stability of large-scale currents.

AB - The problem of the propagation of linear Rossby waves in horizontally inhomogeneous non-zonal flows is studied. The explicit solution within the geometric optics (WKBJ) approximation is found to be identical to the exact Cauchy problem solution for the case of a constant horizontal velocity shear.The effect of the short-wave transformation of Rossby waves near the so-called critical layer is detailed for the arbitrary direction of non-zonal flow. In the general case, this transformation can occur in two ways: (1) as an adhering, a monotonic approaching of wave packets to the critical layer for an infinitely long time. The sign of the intrinsic frequency of the packet remains the same all the time; (2) as an adhering with overshooting when the wave packet, first, crosses its critical layer at finite wavenumber. The wave changes the sign of the intrinsic frequency when overshooting the critical layer and then keeps the sign when it is adhering to this layer asymptotically similarly to the previous scenario. The latter regime does not exist for zonal flows, that degenerates the short-wave dynamics of Rossby waves in this special case. On the contrary, the anisotropy of the dispersion relation permits both positive and negative frequencies in a non-zonal flow. It allows for the effective use of the concept of waves of negative energy for the analysis of the stability of large-scale currents.

KW - adhering overshooting phenomenon

KW - critical layer

KW - enstrophy

KW - Rossby waves

KW - WKBJ-approximation (geometric optics)

KW - zonal and non-zonal flows

UR - http://www.scopus.com/inward/record.url?scp=85089487060&partnerID=8YFLogxK

U2 - 10.1007/s00024-020-02567-0

DO - 10.1007/s00024-020-02567-0

M3 - Article

AN - SCOPUS:85089487060

VL - 177

SP - 5585

EP - 5598

JO - Pure and Applied Geophysics

JF - Pure and Applied Geophysics

SN - 0033-4553

IS - 11

ER -