Process-oriented tests for validation of baroclinic shallow water models: The lock-exchange problem

Abstract

A first step often taken to validate prognostic baroclinic codes is a series of process-oriented tests, as those suggested by Haidvogel and Beckmann [Haidvogel, D., Beckmann, A., 1999. Numerical Ocean Circulation Modeling. Imperial College Press, London], among others. One of these tests is the so-called “lock-exchange” test or “dam break” problem, wherein water of different densities is separated by a vertical barrier, which is removed at time zero. Validation against these tests has primarily consisted of comparing the propagation speed of the wave front, as predicted by various theoretical and experimental results, to model output. In addition, inter-model comparisons of the lock-exchange test have been used to validate codes. Herein, we present a high resolution data set, taken from a laboratory-scale model, for direct and quantitative comparison of experimental and numerical results throughout the domain, not just the wave front. Data is captured every 0.2 s using high resolution digital photography, with salt concentration extracted by comparing pixel intensity of the dyed fluid against calibration standards. Two scenarios are discussed in this paper, symmetric and asymmetric mixing, depending on the proportion of dense/light water (17.5 ppt/0.0 ppt) in the experiment; the Boussinesq approximation applies to both. Front speeds, cast in terms of the dimensionless Froude number, show excellent agreement with literature-reported values. Data are also used to quantify the degree of mixing, as measured by the front thickness, which also provides an error band on the front speed. Finally, experimental results are used to validate baroclinic enhancements to the barotropic shallow water ADvanced CIRCulation (ADCIRC) model, including the effect of the vertical mixing scheme on simulation results. Based on salinity data, the model provides an average root-mean-square (rms) error of 3.43 ppt for the symmetric case and 3.74 ppt for the asymmetric case, most of which can be attributed to the shear instabilities along the density front, which are not resolved by this hydrostatic model. Front tracking and mixed layer thickness rms errors average 34.9 mm (15.7% relative to total fluid depth) and 10.2 mm (4.9%) for the symmetric test and 37.2 mm (16.8%) and 14.0 mm (6.2%) for the asymmetric test, respectively. All non-constant vertical closure schemes are able to capture the front speed, but the Mellor-Yamada 2.5 scheme most accurately captures the synoptic behavior of the mixing layer thickness.