In strictly speaking, all the natural phenomena on the earth should be treated under rotating coordinate. The existence of baroclinic nonequivalent barotropic laminar solution for rotating fluids is still open though the laminar solutions for the irrotational fluid had been well studied. In this letter, all the possible equivalent barotropic (EB) laminar solution are firstly explored and all the possible baroclinic non-EB elliptic circulations and hyperbolic laminar modes are discovered. The baroclinic EB circulations (including the vortex streets and hurricane like vortices) possess rich structures because either the arbitrary solutions of arbitrary nonlinear Poison equations can be used or an arbitrary two-dimensional stream function is revealed. The discovery of the baroclinic non-EB modes disproves a known conjecture. The results may be broadly applied in atmospheric and oceanic dynamics, plasma physics, astrophysics and so on.
"Eddy saturation" is the regime in which the total time-mean volume transport of an oceanic current is relatively insensitive to the wind stress forcing and is often invoked as a dynamical description of Southern Ocean circulation. We revisit the problem of eddy saturation using a primitive-equations model in an idealized channel setup with bathymetry. We apply only mechanical wind stress forcing; there is no diapycnal mixing or surface buoyancy forcing. Our main aim is to assess the relative importance of two mechanisms for producing eddy saturated states: (i) the commonly invoked baroclinic …
Interfacial internal waves in a stratified fluid excited by periodic free-surface perturbations in a closed tank are studied experimentally. Barotropic-baroclinic energy conversion is induced by the presence of a bottom obstacle. The connection between horizontal surface velocities and internal wave amplitudes is investigated, the developing flow patterns are described qualitatively, and the wave speeds of internal waves are systematically analyzed and compared to linear 2- and 3-layer theories. We find that, despite of the fact that the observed internal waves can have considerable amplitudes…
The linear response function (LRF) of an idealized GCM, the dry dynamical core with Held-Suarez physics, is used to accurately compute how eddy momentum and heat fluxes change in response to the zonal wind and temperature anomalies of the annular mode at the low-frequency limit. Using these results and knowing the parameterizations of surface friction and thermal radiation in Held-Suarez physics, the contribution of each physical process (meridional and vertical eddy fluxes, surface friction, thermal radiation, and meridional advection) to the annular mode dynamics is quantified. Examining the…
Geophysical turbulence is observed to self-organize into large-scale flows such as zonal jets and coherent vortices. Previous studies on barotropic beta-plane turbulence have shown that coherent flows emerge out of a background of homogeneous turbulence as a bifurcation when the turbulence intensity increases and the emergence of large scale flows has been attributed to a new type of collective, symmetry breaking instability of the statistical state dynamics of the turbulent flow. In this work we extend the analysis to stratified flows and investigate turbulent self-organization in a two-layer…
In this paper we examine triad resonances in a rotating shallow water system when there are two free interfaces. This allows for an examination in a relatively simple model of the interplay between baroclinic and barotropic dynamics in a context where there is also a geostrophic mode. In contrast to the much-studied one-layer rotating shallow water system, we find that as well as the usual slow geostrophic mode, there are now two fast waves, a barotropic mode and a baroclinic mode. This feature permits triad resonances to occur between three fast waves, with a mixture of barotropic and barocli…
In theoretical models of tropical dynamics, the effects of both surface friction and upward wave radiation through interaction with the stratosphere are oft-ignored, as they greatly complicate mathematical analysis. In this study, we relax the rigid-lid assumption and impose surface drag, which allows the barotropic mode to be excited in equatorial waves. In particular, a previously developed set of linear, strict quasi-equilibrium tropospheric equations is coupled with a dry, passive stratosphere, and surface drag is added to the troposphere momentum equations. Theoretical and numerical model…
We present an investigation of rapidly rotating (small Rossby number $Ro\ll 1$) and stratified turbulence where the stratification strength is varied from weak (large Froude number $Fr\gg1$) to strong ($Fr\ll1$). The investigation is set in the context of a reduced model derived from the Boussinesq equations that efficiently retains anisotropic inertia-gravity waves with order-one frequencies and highlights a regime of wave-eddy interactions. Numerical simulations of the reduced model are performed where energy is injected by a stochastic forcing of vertical velocity, which forces wave modes o…
Carter and Lichnerowicz have established that barotropic fluid flows are conformally geodesic and obey Hamilton's principle. This variational approach can accommodate neutral, or charged and poorly conducting, fluids. We show that, unlike what has been previously thought, this approach can also accommodate perfectly conducting magnetofluids, via the Bekenstein-Oron description of ideal magnetohydrodynamics. When Noether symmetries associated with Killing vectors or tensors are present in geodesic flows, they lead to constants of motion polynomial in the momenta. We generalize these concepts to…
