Properties of large-amplitude internal waves

Abstract

Properties of solitary waves propagating in a two-layer fluid are investigated comparing experiments and theory. In the experiments the velocity field induced by the waves, the propagation speed and the wave shape are quite accurately measured using particle tracking velocimetry (PTV) and image analysis. The experiments are calibrated with a layer of fresh water above a layer of brine. The depth of the brine is 4.13 times the depth of the fresh water. Theoretical results are given for this depth ratio, and, in addition, in a few examples for larger ratios, up to 100:1. The wave amplitudes in the experiments range from a small value up to almost maximal amplitude. The thickness of the pycnocline is in the range of approximately 0.13-0.26 times the depth of the thinner layer. Solitary waves are generated by releasing a volume of fresh water trapped behind a gate. By careful adjustment of the length and depth of the initial volume we always generate a single solitary wave, even for very large volumes. The experiments are very repeatable and the recording technique is very accurate. The error in the measured velocities non-dimensionalized by the linear long wave speed is less than about 7-8% in all cases. The experiments are compared with a fully nonlinear interface model and weakly nonlinear Korteweg-de Vries (KdV) theory. The fully nonlinear model compares excellently with the experiments for all quantities measured. This is true for the whole amplitude range, even for a pycnocline which is not very sharp. The KdV theory is relevant for small wave amplitude but exhibit a systematic deviation from the experiments and the fully nonlinear theory for wave amplitudes exceeding about 0.4 times the depth of the thinner layer. In the experiments with the largest waves, rolls develop behind the maximal displacement of the wave due to the Kelvin-Helmholtz instability. The recordings enable evaluation of the local Richardson number due to the flow in the pycnocline. We find that stability or instability of the flow occurs in approximate agreement with the theorem of Miles and Howard.

Transformation of internal solitary waves at the "deep" and "shallow" shelf: satellite observations and laboratory experiment

“…Both asymptotic theory and numerical solutions have displayed a very good mutual agreement and correlation with experimental measurements of parameters of internal solitary waves obtained for the present tank configuration by Grue et al (1999).…”

“…The applicability of the Gardner equation can be analysed by comparison to the limiting solitary waves in the full Euler and the Gardner equations. According to Euler equations solitary waves also exist for amplitudes less than the maximal value a lim = (h 1 −h 2 )/2 (Choi and Camassa, 1999;Grue et al, 1999).…”

“…The profile of the solitary waves generated in the tank was calculated with the full Euler numerical model (Grue et al, 1999).…”

“…The construction of the tank, the procedure of formation of the stratification profile and the method of flow visualization are described in Grue et al (1999). The tank with its overall dimensions L × B × H = 12.0 × 0.5 × 1.0 m 3 (Fig.…”

Convectively induced shear instability in large amplitude internal solitary waves

“…Upon release of the gate, a single solitary wave of depression of very large amplitude was quickly generated. The leading part of the wave almost instantly attained the shape of a wave in steady motion (see also Grue et al 5,12 ). Focus was on generating ISWs of very large amplitude.…”