Wave-induced topographic formstress in baroclinic channel flow

Abstract

Large-scale zonal flow driven across submarine topography establishes standing Rossby waves. In the presence of stratification the wave pattern can be represented by barotropic and baroclinic Rossby waves of mixed planetary-topographic nature which are locked to the topography. In the balance of momentum the wave pattern manifests itself as topographic formstress. This wave-induced formstress has the net effect of braking the flow and reducing the zonal transport. Locally it may lead to acceleration and the parts induced by the barotropic and baroclinic waves may have opposing effects. This flow regime occurs in the circumpolar flow around Antarctica. The different roles which the wave-induced formstress plays in homogeneous and stratified flows through a zonal channel is analyzed with the BARBI model. It is used in complete form and in a low-order version to clarify the different regimes. It is shown that the barotropic formstress arises by topographic locking due to viscous friction and the baroclinic one due to eddy-induced density advection. For the sinusoidal topography used in this study the transport obeys a law in which friction and wave-induced formstress act as additive resistances, and windstress, the effect of Ekman pumping on the density stratification, and the buoyancy forcing (diapycnal mixing of the stratified water column) of the potential energy stored in the stratification act as additive forcing functions. The dependence of the resistance on the systems parameters (lateral viscosity , lateral diffusivity K of eddy density advection, Rossby radius λ, and topography height δ) as well as the dependence of transport on the forcing functions are determined. While the current intensity in a channel with homogeneous density decreases from the viscous flat bottom case in an inverse quadratic law ∼ δ −2 with increasing topography height and always depends on , a stratified system runs into a saturated state in which the transport becomes independent of δ and and is determined by the density diffusivity K rather than the viscosity: K/λ 2 acts as a vertical eddy viscosity and the transport is λ 2 /K times the applied forcing. Critical values for the topographic heights in these regimes are identified.

Barotropic and baroclinic processes in the transport variability of the Antarctic Circumpolar Current

“…The bottom formstress builds up by propagation of planetarytopographic Rossby waves, generated by the zonal flow crossing the submarine topographic barriers and adjusting to them by friction (see Olbers et al 2006Olbers et al , 2007. The formstress in the barotropic state relates to the zonal transport, and withŪ B ∼ T and hP x ∼Ū/t T with appropriate geometric scales (essentially the width B of the current), we obtain Eq.…”

“…For the circulation through the narrow f/ h tunnel in the barotropic case, frictional and wave timescales are indeed of the order of t trop . Further details on these wave equilibration processes are given by Olbers et al (2006), and for a low-order version of the relevant balances, see Olbers et al (2007). To determine the barotropic time constant, the barotropic Rossby waves in the transport record were smoothed with a Gaussian low pass filter.…”