event
Thursday 19 Jan 2012: Balanced models of boundary-layer convergence
Bob Beare - University of Exeter
107 15:00-16:00
In the tropics, warm sea surface temperature anomalies are often
coupled to the well-mixed boundary layer. The boundary layer then typically forces convergence and ascent; the ascent can trigger moist convection.
Established diagnostic models of boundary layer convergence employ
the steady-state Ekman (geotriptic) balance. Here, we extend the steady-state balance to include non-stationarity.
Within an idealised one-dimensional shallow water framework, we identify
three time-varying balanced models:
planetary geotriptic (PGT) and semi-geotriptic (SGT-A and SGT-B). These models are verified against the shallow water (SWE) model. The PGT model has prognostic mass and diagnostic momentum, whilst the SGT models also include prognostic momentum. The SGT models have separate Ekman-balanced and advecting winds. The friction term in the SGT-A model is a function of twice the balanced wind minus the advecting wind.
We show that the SGT-A model has stable solutions in time, and is between first and second order accurate. In contrast, the SGT-B model's friction is a function of just the advecting wind.
Although second order accurate, the SGT-B is also unstable and thus unusable.
For cases of significant non-linear advection, the SGT-A model predicts more accurate convergence than the PGT model.
However, the SGT-A model has a less accurate geopotential field than the PGT model.
After a period, the SWE model breaks down into near grid-scale gravity waves and the solutions are no longer numerically reliable. The
SGT-A and PGT models then maintain a smooth solution with the gravity waves filtered out, and thus a more robust evolution in convergence.
For cases of diurnal forcing with a fast frictional timescale, the SGT-A model follows the growth phase of the SWE model more closely than the PGT model.
