Generation of Gravity Waves by Singular Potential Vorticity Disturbances in Shear Flows

Abstract

The linear mechanism of generation of gravity waves by potential vorticity (PV) disturbances in flows with constant horizontal and vertical shears is studied. The case of the initial singular distribution of PV, in which the PV is localized in one coordinate and is periodic with respect to other coordinates, is considered. In a stratified rotating medium, such a distribution induces a vortex wave (continuous mode), the propagation of which is accompanied by the emission of gravity waves. To find the emission characteristics, a linearized system of dynamical equations is reduced to wave equations with sources that are proportional to the initial distributions of PV. The asymptotic solutions of the equations are constructed for small Rossby numbers (horizontal shear) and large Richardson numbers (vertical shear). When passing through the inertial levels symmetrically located with respect to a vortex source, the behavior of the solutions for wave amplitudes radically changes. Directly in the vicinity of the source, the solutions are of monotonic character, corresponding to a quasigeostrophic vortex wave. At long distances from the source, the solutions oscillate. The horizontal momentum flux and the Eliassen–Palm flux are estimated using asymptotic solutions. It is found that, within the indicated range of both Rossby and Richardson numbers, these fluxes are exponentially small: that is, the emission of waves is weak.

An Analytical Approach to the Determination of Optimal Perturbations in the Eady Model

“…The excitation of ERWs can also be caused by their interaction with vortex perturbations (PV 6 ¼ 0). Various aspects of this interaction (including resonance interaction) were considered by Farrell (1984), Thorncroft and Hoskins (1990), Chang (1992), Jenkner and Ehrendorfer (2006), de Vries and Opsteegh (2007), and Kalashnik (2015). The case of the singular distribution of PV, to which the singular wave mode corresponds, or in the terminology of Heifetz and Methven (2005), the kernel Rossby wave (KRW), is more fully investigated.…”

Research in dynamic meteorology in Russia in 2015–2018

“…Линейный механизм генерации гравитационных волн возмущениями ПВ в потоках с постоянными горизонтальными и вертикальными сдвигами скорости изучен в [57]. Рассмотрен случай начального сингулярного распределения ПВ, в котором ПВ локализован в одной координате и является периодическим по отношению к другим координатам.…”

On pressure perturbations caused by a moving heat source of the frontal type (hydrostatic mode)

“…Физический смысл решения (19), (20) легко понять, рассматривая предельный случай l = 0 (источник не зависит от горизонтальной координаты y). В этом случае  …”

“…Вместе с тем теоретические исследования вариаций практически отсутствуют. Основное внимание в существующих работах уделяется изучению различных механизмов генерации волновых сигналов [19,20]. В настоящей работе сделана попытка теоретического описания вариаций в рамках задачи о ВГВ, возбуждаемых движущимся нестационарным источником фронтального типа (локализованным по одной горизонтальной координате).…”