15.23. Internal Soliton¶
The non-hydrostatic solver is tested with several analytical solutions and laboratory experiments. The Internal Soliton test case is setup from the experiment of Horn et al. (2001). It illustrates the processes acting on an interfacial basin-scale standing wave known as an internal seiche, neglecting the Earth’s rotation. The propagation regimes depends on the ratio of the amplitude of the initial wave to the depth of the thermocline, and the ratio of the depth of the thermocline to the overall depth of the basin. In the present setup with moderate wave amplitude, the degeneration mechanism of the basin-scale internal wave is the generation of solitons by nonlinear steepening. As the wave steepens its horizontal lengthscale decreases until the dispersive terms can no longer be neglected. Eventually, a balance between nonlinear steepening and dispersion leads to the evolution of solitary waves, a process described by the Korteweg–de Vries (KdV) equation for the interfacial displacement \(\eta_i\):
The evolution of solitons is sensitive to the numerical damping associated with the choice of resolution, advection schemes and diffusion operators (implicit in the advection scheme or explicit).
The simulations can be compared with the laboratory experiments of Horn et al. (2001), which were carried out in a tank 6 m long and 29 cm deep. The two-layer fluid is given by a hyperbolic tangent density profile, which is rotated around the center of the basin to initiate the internal seiche at the basin scale. The resolution of the model is 10 cm horizontally and 4 mm vertically.
Horn, D.A., J. Imberger, & G.N. Ivey, (2001). The degeneration of large-scale interfacial gravity waves in lakes. J. Fluid Mech., 434:181-207.
# define ISOLITON
# undef MPI # define 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 # define W_HADV_WENO5 # define W_VADV_WENO5 # undef UV_VIS2 # undef TS_DIF2 # define ANA_GRID # define ANA_INITIAL # define ANA_SMFLUX # define ANA_STFLUX # define ANA_BTFLUX # undef PASSIVE_TRACER # define NO_FRCFILE # undef RVTK_DEBUG