Topographic RossbyWaves in Basins of Simple Geometry

Abstract

In the last chapter, topographic Rossby-waves on the f-plane were studied with emphasis of their mathematical description as extracted from the governing equations of fluid mechanics. Their possible observation by synoptic measurements was also discussed: they pertain to horizontal velocity and temperature-time series from moored thermistor chains and current recorders. It was shown by appropriately scaling the adiabatic Boussinesq approximated equations that in lakes with shallow epilimnion and deep hypolimnion – more specifically lakes which satisfy the so-called Gratton-scaling – the barotropic-baroclinic coupling is one-sided from the barotropic to the baroclinic TWs but not vice versa. In other words, if a topographic wave or a free or wind-induced oscillation in a lake, whose spectral component can be associated with a barotropic topographic wave mode, is acting in a lake, then this spectral component exerts a sizeable effect on the vertical baroclinic water movement which is (in principle) measurable in isotherm–depth–time series. Conversely, a baroclinic wave signal has a negligible influence on the barotropic TW response. This implies that for all those lakes whose geometry and stratification falls into the range of Gratton’s scaling – most Alpine lakes satisfy this scaling – the spectral structure can be found from the spectral analysis of the TW-operator, yet observational inferences can be drawn not only from cross-correlation analyses of moored current meters but equally also from such analyses involving isotherm–depth or temperature–time series.