Dorian Fructus

Shear-induced breaking of large internal solitary waves

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 h 2 ) sandwiched between a thin upper layer (depth h 1 ) and a deep lower layer (depth h 3 ), 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 (a 1 ) in the range a 1 > 2.24√h 1 h 2 (1 + h 2 /h 1 ), while stable waves were on or below this limit. Breaking ISWs were investigated for 0.27 0.86 and stable waves for L x /λ < 0.86. The results show a sort of threshold-like behaviour in terms of L x /λ. The results demonstrate that the breaking threshold of L x /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

Fully nonlinear solitary waves in a layered stratified fluid, each layer with a constant Brunt–Vaisala 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

Convectively induced shear instability in large amplitude internal solitary waves

Ri

An explicit method for the nonlinear interaction between water waves and variable and moving bottom topography

. The smallest value of

Dynamics of crescent water wave patterns

Ri

Simulations of crescent water wave patterns on finite depth

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

An efficient model for three-dimensional surface wave simulations

Ri

Formation of undular bores and solitary waves in the Strait of Malacca caused by the 26 December 2004 Indian Ocean tsunami

becomes smaller than one quarter. The results may support experimental studies of breaking internal solitary waves.

An efficient model for three-dimensional surface wave simulations. Part II: Generation and absorption

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 an interplay between the two instability types and convective instability induces shear by enhancing isopycnal compression. Variation in 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 ...

A note on time integrators in water-wave simulations

A fully nonlinear and fully dispersive method for the interaction between free surface waves and a variable bottom topography in space and time in three dimensions is derived. A Green function potential formulation expresses the normal velocity of the free surface in terms of the bathymetry and its motion. An explicit, fast version of the method is derived in Fourier space with evaluations using FFT. Practice shows that the explicit method captures the most essential parts of the wave field. This leads to a time-integration that is very accurate and orders of magnitude faster than existing full potential formulation methods. Fully resolved simulations of the nonlinear and dispersive wave fields are enabled from the generation to the shoaling of the waves, including the onshore flow which is handled by suitable numerical beaches.