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The stability properties of 24 experimentally generated internal solitary waves (ISWs) of extremely large amplitude, all with minimum Richardson number less than 1/4, are investigated. The study is supplemented by fully nonlinear calculations in a three-layer fluid. The waves move along a linearly stratified pycnocline (depth h2) sandwiched between a thin upper layer (depth h1) and a deep lower layer (depth h3), both homogeneous. In particular, the wave-induced velocity profile through the pycnocline is measured by particle image velocimetry (PIV) and obtained in computation. Breaking ISWs were found to have amplitudes (a1) in the range $a_1\,{>}\,2.24\sqrt{h_1h_2}(1+h_2/h_1)$, while stable waves were on or below this limit. Breaking ISWs were investigated for 0.27 < h2/h1 < 1 and 4.14 < h3/(h1 + h2) < 7.14 and stable waves for 0.36 < h2/h1 < 3.67 and 3.22 < h3/(h1 + h2) < 7.25. Kelvin–Helmholtz-like billows were observed in the breaking cases. They had a length of 7.9h2 and a propagation speed 0.09 times the wave speed. These measured values compared well with predicted values from a stability analysis, assuming steady shear flow with U(z) and ρ(z) taken at the wave maximum (U(z) horizontal velocity profile, ρ(z) density along the vertical z). Only unstable modes in waves of sufficient strength have the chance to grow sufficiently fast to develop breaking: the waves that broke had an estimated growth (of unstable modes) more than 3.3–3.7 times than in the strongest stable case. Evaluation of the minimum Richardson number (Rimin, in the pycnocline), the horizontal length of a pocket of possible instability, with wave-induced Ri < 14, (Lx) and the wavelength (λ), showed that all measurements fall within the range Rimin = −0.23Lx/λ + 0.298 ± 0.016 in the (Lx/λ, Rimin)-plane. Breaking ISWs were found for Lx/λ > 0.86 and stable waves for Lx/λ < 0.86. The results show a sort of threshold-like behaviour in terms of Lx/λ. The results demonstrate that the breaking threshold of Lx/λ = 0.86 was sharper than one based on a minimum Richardson number and reveal that the Richardson number was found to become almost antisymmetric across relatively thick pycnoclines, with the minimum occurring towards the top part of the pycnocline.

Fully nonlinear solitary waves in a layered stratified fluid, each layer with a constant Brunt–Väisälä frequency, are investigated. The stream function satisfies the Helmholtz equation in each layer and is expressed in terms of singularity distributions. As the Green function, a combination of Bessel functions of order zero, of the second and first kind is advocated. Computations performed for two- and three-layer cases show that the wave speed increases with increasing stratification of the top layer. The thickness of the pycnocline increases with wave amplitude when the top layer is homogeneous but decreases when the top layer is stratified. The wave width depends little on the pycnocline thickness. The fluid velocity may exceed the wave speed in the upper part of the water column when the top layer is stratified, but is always smaller than the wave velocity if the top layer is homogeneous. A large vertical excursion of the individual isopycnals contributes to a small Richardson number $Ri$. The smallest value of $Ri$ is observed in the main body of the fluid. Solitary waves of increasing strength are investigated until the wave-induced fluid velocity equals the wave speed, or the minimal $Ri$ becomes smaller than one quarter. The results may support experimental studies of breaking internal solitary waves.

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Laboratory study has been carried out to investigate the instability of an internal solitary wave of depression in a shallow stratified fluid system. The experimental campaign has been supported by theoretical computations and has focused on a two layered stratification consisting of a homogeneous dense layer below a linearly stratified top layer. The initial background stratification has been varied and it is found that the onset, and intensity of breaking are affected dramatically by changes in the background stratification. Manifestations of a combination of shear and convective instability are seen on the leading face of the wave. It is shown that there is interplay between the two instability types and convective instability induces shear by enhancing isopycnal 1 compression. Variation of the upper boundary condition is also found to have an effect on stability. In particular, the implications for convective instability are shown to be profound and a dramatic increase in wave amplitude is seen for a fixed (as opposed to free) upper boundary condition.