A comparison of laboratory measurements and numerical simulations of baroclinic wave flows in a rotating cylindrical annulus

Abstract

Quantitative and qualitative comparisons are made between laboratory measurements of rotating annulus flows and corresponding numerical model simulations. Two laboratory annuli, of similar dimensions but differing in instrumentation, are used. One contains a thermocouple array for temperature measurement: the other contains no sensor array but the working fluid is seeded with minute neutrally buoyant beads (600 m̈m diameter) which enable the horizontal velocity field to be measured. Each annulus has a rigid insulating lid in contact with the working fluid. the numerical model is a finite difference formulation based on the Navier‐Stokes equations for baroclinic flow of a Boussinesq liquid. Although the atmosphere and the laboratory annulus are both rotating baroclinic fluid systems, the forcing processes acting in the annulus are much simpler than those acting in the atmosphere, and may be accurately represented by established formulae: under a wide range of conditions no parametrizations of subgrid‐scale dynamical and diabatic processes are required. Comparison of numerical model results with laboratory measurements therefore enables the explicit dynamical formulation of numerical models of rotating, baroclinic flow to be verified to an extent which would be very difficult, if not impossible, to achieve using atmospheric data. Detailed quantitative comparisons for a steady wave flow reveal good agreement for major features of the temperature and horizontal flow fields, although a significant discrepancy in total heat flux is found. Qualitative comparisons are made by investigating the ability of the numerical model to reproduce the main flow types and phenomena of the laboratory system. Numerical simulations of intransitivity, hysteresis, wavenumber transitions, amplitude vacillation and a weak structural vacillation are described. Several suggestions for further comparative studies are made in conclusion.

A rotating annulus driven by localized convective forcing: a new atmosphere-like experiment

“…The evidence of weak instability for 0.03 rad s −1 up to 0.08 rad s −1 (Bu = 3.6 and 0.65, respectively) suggests the presence of instability beyond the Eady cutoff. This is also consistent with the zone of weak waves found by Hignett et al (1985) (see symbol w in Fig. 10) suggesting a possible vertical confinement or surface intensification of baroclinic waves (Hide and Mason 1978;Jonas 1980).…”

“…Figure 10 shows the location of the different observed modes in a Ta-regime diagram on which the locations of various dynamical regimes Mason (1975) and Hignett et al (1985) in red and blue lines have been plotted for comparison.…”

“…Numbers represent mode wavenumber and added symbols that follow original annotations in Hignett et al (1985) with a, axisymmetric; w weak waves, S steady waves, AV amplitude vacillation, SV shape vacillation, I irregular. See also movies in supplementary material from previous thermally driven annulus experiments using the classical configuration (Mason 1975;Hignett et al 1985) are superimposed.…”

“…See also movies in supplementary material from previous thermally driven annulus experiments using the classical configuration (Mason 1975;Hignett et al 1985) are superimposed. This indicates a reasonably good agreement with our experiments in the regions of different wave regimes, between the new locally forced atmosphere-like configuration compared to the classic rotating annulus case.…”

“…Thus, this setup has proven to be a simple enough system to capture the fundamental physics and with enough complexity to represent nonlinear features and transition sequences to chaos similar to those of atmospheric dynamics (Hignett et al 1985;Früh and Read 1997;Bastin and Read 1998;Read 2003;Von Larcher and Egbers 2005;Wordsworth et al 2008;Vincze et al 2014). It has also proved valuable as a tractable 'test bed' within which to test numerical codes and methods (Harlander et al 2011;Vincze et al 2015) as well as to benchmark statistical-dynamical analysis methods in widespread use in meteorology, such as data assimilation (Young and Read 2013).…”