Gravity Waves Generated by Sheared Three-Dimensional Potential Vorticity Anomalies

Abstract

The gravity waves (GWs) produced by three-dimensional potential-vorticity (PV) anomalies are examined under the assumption of constant vertical shear, constant stratification, and unbounded domain. As in the two-dimensional case analysed in an earlier paper, the disturbance near the PV anomaly is well modelled by quasi-geostrophic theory. At larger distances the nature of the disturbance changes across the two inertial layers that are located above and below the anomaly, and it takes the form of a vertically propagating GW beyond these.For an horizontally monochromatic PV anomaly of infinitesimal depth, the disturbance is described analytically using both an exact solution and a WKB approximation; the latter includes an exponentially small term which captures the change of the solution near the PV anomaly induced by the radiation boundary condition in the far field. The analytical results reveal a strong sensitivity of the emission to the Richardson number and to the orientation of the horizontal wavenumber: the absorptive properties of the inertial layers make that the emission is maximised in the northern hemisphere for wavenumbers at negative angles to the shear.For localised PV anomalies, numerical computations give the temporal evolution of the GWs field. Analytical and numerical results are also used to establish an explicit form for the Eliassen-Palm flux that could be used to parameterize GWs sources in GCMs. The properties of the Eliassen-Palm flux vector imply that in a westerly shear, the GWs exert a drag in a south-west direction in the upper inertial-layer, and exert a drag in a north-west direction at the altitudes where the GWs dissipate aloft.

Wave-vortex mode coupling in neutrally stable baroclinic flows

“…Their analysis suggests that the dynamical activity of fronts and jet streaks at Ri 1 and Ro 1 should be determined by the asymmetric perturbations rather than by the symmetric ones, in agreement with the analysis by Pieri et al [30]. On the other hand, Lott et al [31] investigated the generation of IGWs by three-dimensional PV anomalies considering asymmetric perturbations of the base flow Eq. (1) at hydrostatic equilibrium via a Wentzel-Kramers-Brillouin (WKB) approach.…”

“…In relation with recent studies on baroclinic sheared flows [29,31] we revisit both the case of nonrotating sheared gravity waves and the symmetric instability before demonstrating that the system Eq. (14) is neutrally stable.…”

“…At any time t, (x,t) is given explicitly in terms of the initial condition 0 (x) = (x,t = 0) by (see Ref. [31])…”

“…IV A). In fact, as mentioned in the Introduction, Lott et al [31] studied the stability of a homogeneous baroclinic flow submitted to nonsymmetric perturbations at hydrostatic equilibrium. In that study, the perturbed field is expanded in (singular) normal modes parameterized by the phase speed…”

“…Note that close to PV anomalies, perturbations are in nearly geostrophic balance, whereas beyond the inertia critical levels they have the form of vertically propagating IGWs with amplitudes rapidly decreasing as the Richardson number increases [31]. In the model of Lott et al [31], the wavevector is not time-dependent anymore, and mean shear advection in spectral space is treated as an additional phase. Asymptotic results in terms of the Rossby number Ro are obtained considering a localized quasihorizontal potential vorticity distribution.…”