15.22. Gravitational Adjustment

The goal of this test case, also known as Lock-Exchange experiment, is to evaluate different numerical advection schemes on representing the adiabatic process in a dam breaking experiment. At the initial time, a vertical density front separates two density classes. Adjustment occurs in which lighter water moves above heavier water (Shin et al., 2004). The model experiments are designed to reproduce the lock-exchange problem described in Ilicak et al., 2012). Analytical solutions to this problem exist and from Bernouilli’s equation for an ideal fluid, the front propagates with speed \(0.5 \sqrt{gH \delta \rho / \rho_0}\). This speed may be slowed down by mixing between the two layers due to numerical diapycnal diffusion.

The setup is a closed, two-dimensional (x,z) domain with a constant depth of H = 20 m and a length of L = 64 km. At t = 0 the two initial densities that represent the two water masses are separated by a vertical barrier. The right and left halves of the domain have densities of 1020 and 1025 \(\text{kg/m}^3\) respectively. To investigate the impact of the model resolution and the choice of advection scheme on spurious mixing, the model uses three different horizontal and vertical model grid spacings: coarse (dx=2 km; N=10); medium is default (dx=500 m, N=40); fine (dx=125 m, N=160).

A non-hydrostatique version can be run (#define NBQ) in a smaller domain of 3 m by 30 cm and resolution of 1 cm. In this case, Kelvin-Helmholtz instabilities develop along the front during the gravitational adjustment.

Shin, Dalziel, S., Linden, P, 2004: gravity currents produced by lock exchange. Journal of Fluid Mechanics, 521, 1–34.

Gouillon, F., 2010: Internal Wave Propagation and numerically induced diapycnal mixing in Oceanic general Circulation Models. PhD Thesis at Florida State University, 93pp.

Ilicak, M, Adcroft, A., Griffies, S., Hallberg, R., 2012: Spurious dianeutral mixing and the role of momentum closure. Ocean Modelling, 45–46, 37–58.

# define GRAV_ADJ

CPP options:

# undef  OPENMP
# undef  MPI
# undef  NBQ
# undef  XIOS
# define SOLVE3D
# define NEW_S_COORD
# define UV_ADV
# define TS_HADV_WENO5
# define TS_VADV_WENO5
# define UV_HADV_WENO5
# define UV_VADV_WENO5
# ifdef NBQ
#  define W_HADV_WENO5
#  define W_VADV_WENO5
# endif
# undef  UV_VIS2
# define ANA_GRID
# define ANA_INITIAL
# define ANA_SMFLUX
# define ANA_STFLUX
# define ANA_BTFLUX
# undef  PASSIVE_TRACER
# define NO_FRCFILE
# undef  RVTK_DEBUG

Settings :

Results :

GRAV_ADJ results : density front evolution for a medium resolution of 500m.