Planetary geostrophic Boussinesq dynamics: barotropic flow, baroclinic instability and forced stationary waves

<p>Motions on planetary spatial scales in the atmosphere are governed by<br>the planetary geostrophic equations. However, not much attention has<br>been paid to the interaction between the baroclinic and barotropic<br>flow within the planetary geostrophic scaling. This is the focus of<br>the present study by utilizing planetary geostrophic equations for a<br>Boussinesq fluid supplemented by an asymptotically derived evolution<br>equation for the barotropic flow. The latter is effected by meridional<br>momentum flux due to baroclinic flow and drag by the surface wind. The<br>barotropic wind on the other hand affects the baroclinic flow through<br>buoyancy advection. By relaxing towards a prescribed buoyancy profile<br>the model produces realistic major features of the zonally symmetric<br>wind and temperature fields. We show that there is considerable<br>cancelation between the barotropic and the baroclinic surface zonal<br>mean zonal wind. The linear and nonlinear model response to steady<br>diabatic zonally asymmetric forcing is investigated. The arising<br>stationary waves are interpreted in terms of analytical solutions. We<br>also study the problem of baroclinic instability on the sphere within<br>the present model.</p><p>Reference: Dolaptchiev, S. I., Achatz, U. and Th. Reitz, 2019: Planetary<br>geostrophic Boussinesq dynamics: barotropic flow, baroclinic<br>instability and forced stationary waves, Quart. J. Roy. Met. Soc., 145: 3751-3765.</p>

Modulation-resonance mechanism for surface waves in a two-layer fluid system

We propose a Boussinesq-type model to study the surface/interfacial wave manifestation of an underlying, slowly varying, long-wavelength baroclinic flow in a two-layer, density-stratified system. The results of our model show numerically that, under strong nonlinearity, surface waves, with their typical wavenumber being the resonant $k_{res}$, can be generated locally at the leading edge of the underlying, slowly varying, long-wavelength baroclinic flow. Here, the resonant $k_{res}$ satisfies the class 3 triad resonance condition among two short-mode waves and one long-mode wave in which all waves propagate in the same direction. Moreover, when the slope of the baroclinic flow is sufficiently small, only one spatially localized large-amplitude surface wave packet can be generated at the leading edge. This localized surface wave packet becomes high in amplitude and large in group velocity after the interaction with its surrounding waves. These results are qualitatively consistent with various experimental observations including resonant surface waves at the leading edge of an internal wave. Subsequently, we propose a mechanism, referred to as the modulation-resonance mechanism, underlying these surface phenomena, based on our numerical simulations. The proposed modulation-resonance mechanism combines the linear modulation, ray-based, theory for the spatiotemporal asymmetric behaviour of surface waves and the nonlinear class 3 triad resonance theory for the energy focusing of surface waves around the resonant wavenumber $k_{res}$ in Fourier space.

Erosion of the thermocline in the Gulf of Patras, due to a severe wind event

Three-dimensional numerical simulations, performed using the MIKE 3 FM (HD) code, have been used to study the effect of a severe wind event on the early stratification structure in the Gulf of Patras, Greece. Before the onset of the severe wind event thermocline was at an approximately mean depth of ~ 10 m. The wind action deepened the well mixed layer of the epilimnion at the surface and redistributed the thermal stratification to a new stable formation where tilt and erosion of the thermocline occurred. Under the effect of wind the thermocline was established in a new mean depth of ~ 60 m. Furthermore, strong wind - generated internal waves, in the area of Rio-Antirio straits, were found to affect the exchange flowrate at the straits. Comparison of the exchange flowrate between the barotropic and the baroclinic flow, under the same severe wind conditions, revealed a deviation of approximately 20% of the resulting flowrate, under steady wind conditions. The hydrodynamic response of the Gulf, under these wind conditions, i.e., wind-induced currents, turbulence structure in the water column, internal waves and flow patterns, has been simulated indicating basic, unique, flow characteristics for the baroclinic flow in contrast with the barotropic ones.

On the energetics of a two-layer baroclinic flow

The formation, evolution and co-existence of jets and vortices in turbulent planetary atmospheres is examined using a two-layer quasi-geostrophic $\unicode[STIX]{x1D6FD}$-channel shallow-water model. The study in particular focuses on the vertical structure of jets. Following Panetta & Held (J. Atmos. Sci., vol. 45 (22), 1988, pp. 3354–3365), a vertical shear arising from latitudinal heating variations is imposed on the flow and maintained by thermal damping. Idealised convection between the upper and lower layers is implemented by adding cyclonic/anti-cyclonic pairs, called hetons, to the flow, though the qualitative flow evolution is evidently not sensitive to this or other small-scale stochastic forcing. A very wide range of simulations have been conducted. A characteristic simulation which exhibits alternation between two different phases, quiescent and turbulent, is examined in detail. We study the energy transfers between different components and modes, and find the classical picture of barotropic/baroclinic energy transfers to be too simplistic. We also discuss the dependence on thermal damping and on the imposed vertical shear. Both have a strong influence on the flow evolution. Thermal damping is a major factor affecting the stability of the flow while vertical shear controls the number of jets in the domain, qualitatively through the Rhines scale $L_{Rh}=\sqrt{U/\unicode[STIX]{x1D6FD}}$.

The 2D dynamics of the differentially rotating envelope of massive stars

We build a 2D model of the radiative envelope of main sequence massive stars. We set a dynamical boundary condition at the bottom of the radiative envelope at η = rC/R (where rC is the core size and R the radius of the star) to account for the differential rotation of the convective core as computed in 3D simulations (e.g. Browning et al. (2004, IAUS, 224, 149). We seek the differential rotation and associated meridional circulation induced by such a shear competing with the baroclinic flow of the stably stratified radiative envelope using the Boussinesq approximation.

Multiple Zonal Jets in a Differentially Heated Rotating Annulus*,+

A laboratory experiment of multiple baroclinic zonal jets is described, thought to be dynamically similar to flow observed in the Antarctic Circumpolar Current. Differential heating sets the overall temperature difference and drives unstable baroclinic flow, but the circulation is free to determine its own structure and local stratification; experiments were run to a stationary state and extend the dynamical regime of previous experiments. A topographic analog to the planetary β effect is imposed by the gradient of fluid depth with radius supplied by a sloping bottom and a parabolic free surface. New regimes of a low thermal Rossby number (RoT ~ 10−3) and high Taylor number (Ta ~ 1011) are explored such that the deformation radius Lρ is much smaller than the annulus gap width L and similar to the Rhines length. Multiple jets emerge in rough proportion to the smallness of the Rhines scale, relatively insensitive to the Taylor number; a regime diagram taking the β effect into account better reflects the emergence of the jets. Eddy momentum fluxes are consistent with an active role in maintaining the jets, and jet development appears to follow the Vallis and Maltrud phenomenology of anisotropic wave–turbulence interaction on a β plane. Intermittency and episodes of coherent meridional jet migration occur, especially during spinup.