Magda Carr

Simultaneous synthetic schlieren and PIV measurements for internal solitary waves

Large-amplitude internal solitary waves in a stratification comprising a thick, lower, homogeneous layer separated from a thin, upper, homogeneous layer by a broad gradient region are studied using simultaneous measurements of the density and velocity fields. Density field measurements are achieved through synthetic schlieren, operating in an absolute mode to allow efficient and accurate measurements of density in systems with strong curvatures and large perturbations to the density field. The images used for these density measurements are interleaved with images used for particle image velocimetry by phase locking two video cameras (one configured for the density measurements and the other for the velocity measurements) with a computer-driven LCD monitor, allowing the background texture required for synthetic schlieren to be turned off for the particle image velocimetry measurements on the mid-plane of the experimental tank. The simultaneous measurements of both density and velocity fields not only allow greater insight into the internal wave dynamics, but also allow the velocity measurements to be corrected for the normal errors associated with the refractive index variations. As an illustration of the power of this technique, we determine for the first time in an internal solitary wave the spatial structure of the local gradient Richardson number, finding regions where this falls below the limit for linear stability.

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.

Experimental evidence of internal solitary wave-induced global instability in shallow water benthic boundary layers

Experimental evidence is presented in support of the theoretical prediction of Diamessis and Redekopp [J. Phys. Oceanogr. 36, 784 (2006)] for wave-induced vortex shedding at the lower solid boundary of a stratified fluid system as a result of global instability. The time-dependent boundary layer induced by a strongly nonlinear internal wave of depression in shallow water is examined experimentally. Measurements of the velocity field close to the bottom boundary illustrate coherent periodic shedding of vortex structures at the lower boundary in the adverse pressure gradient region aft of the wave. The vortical structures ascend high into the water column and cause significant benthic turbulence. It is shown that global instability has a critical threshold dependent on the Reynolds number of the flow and the amplitude of the wave. The critical amplitudes observed are approximately half that predicted by Diamessis and Redekopp [J. Phys. Oceanogr. 36, 784 (2006)], indicating that internal wave-induced benthic...

The steady-state form of large-amplitude internal solitary waves

A new numerical scheme for obtaining the steady-state form of an internal solitary wave of large amplitude is presented. A stratified inviscid two-dimensional fluid under the Boussinesq approximation flowing between horizontal rigid boundaries is considered. The stratification is stable, and buoyancy is continuously differentiable throughout the domain of the flow. Solutions are obtained by tracing the buoyancy frequency along streamlines from the undisturbed far field. From this the vorticity field can be constructed and the streamfunction may then be obtained by inversion of Laplace’s operator. The scheme is presented as an iterative solver, where the inversion of Laplace’s operator is performed spectrally. The solutions agree well with previous results for stratification in which the buoyancy frequency is a discontinuous function. The new numerical scheme allows significantly larger amplitude waves to be computed than have been presented before and it is shown that waves with Richardson numbers as low as 0.062 can be computed straightforwardly. The method is also extended to deal in a novel way with closed streamlines when they occur in the domain. The new solutions are tested in independent fully nonlinear time-dependent simulations and are verified to be steady. Waves with regions of recirculation are also discussed.

Experiments on the structure and stability of mode-2 internal solitary-like waves propagating on an offset pycnocline

The structure and stability of mode-2 internal solitary-like waves is investigated experimentally. A rank-ordered train of mode-2 internal solitary waves is generated using a lock release configuration. The pycnocline is centred either on the mid-depth of the water column (the 0% offset case) or it is offset in the positive vertical direction by a fraction of 5%, 10%, or 20% of the total fluid depth. It is found that offsetting the pycnocline has little effect on the basic wave properties (e.g., wave speed, wave amplitude, and wavelength) but it does significantly affect wave stability. Instability takes the form of small K-H-like billows in the rear of the wave and small scale overturning in the core of the wave. In the 0% offset case, instability occurs on both the upper and lower interfaces of the pycnocline and is similar in extent and vigour over the two interfaces. As the offset percentage is increased, however, instability is more pronounced on the lower interface with little or no evidence of instability being observed on the upper interface. In the 20% offset case, a mode-1 tail is associated with the wave and the wave characteristics resemble qualitatively the recent field observations of Shroyer et al. [“Mode 2 waves on the continental shelf: Ephemeral components of the nonlinear internal wavefield,” J. Geophys. Res. 115, C07001, doi:10.1029/2009JC005605 (2010)].

Boundary layer flow beneath an internal solitary wave of elevation

The wave-induced flow over a fixed bottom boundary beneath an internal solitary wave of elevation propagating in an unsheared, two-layer, stably stratified fluid is investigated experimentally. Measurements of the velocity field close to the bottom boundary are presented to illustrate that in the lower layer the fluid velocity near the bottom reverses direction as the wave decelerates while higher in the water column the fluid velocity is in the same direction as the wave propagation. The observation is similar in nature to that for wave-induced flow beneath a surface solitary wave. Contrary to theoretical predictions for internal solitary waves, no evidence for either boundary layer separation or vortex formation is found beneath the front half of the wave in the adverse pressure gradient region of the flow.

Instability in internal solitary waves with trapped cores

A numerical method that employs a combination of contour advection and pseudo-spectral techniques is used to investigate instability in internal solitary waves with trapped cores. A three-layer configuration for the background stratification in which the top two layers are linearly stratified and the lower layer is homogeneous is considered throughout. The strength of the stratification in the very top layer is chosen to be sufficient so that waves of depression with trapped cores can be generated. The flow is assumed to satisfy the Dubriel-Jacotin-Long equation both inside and outside of the core region. The Brunt-Vaisala frequency is modelled such that it varies from a constant value outside of the core to zero inside the core over a sharp but continuous transition length. This results in a stagnant core in which the vorticity is zero and the density is homogeneous and approximately equal to that at the core boundary. The time dependent simulations show that instability occurs on the boundary of the cor...

Interaction of a mode-2 internal solitary wave with narrow isolated topography

Numerical and experimental studies of the transit of a mode-2 internal solitary wave over an isolated ridge are presented. All studies used a quasi-two-layer fluid with a pycnocline centred at the mid-depth. The wave amplitude and total fluid depth were both varied, while the topography remained fixed. The strength of the interaction between the internal solitary waves and the hill was found to be characterized by three regimes: weak, moderate, and strong interactions. The weak interaction exhibited negligible wave modulation and bottom surface stress. The moderate interaction generated weak and persistent vorticity in the lower layer, in addition to negligible wave modulation. The strong interaction clearly showed material from the trapped core of the mode-2 wave extracted in the form of a thin filament while generating a strong vortex at the hill. A criterion for the strength of the interaction was found by non-dimensionalizing the wave amplitude by the lower layer depth, a/l. A passive tracer was used to measure the conditions for resuspension of boundary material due to the interaction. The speed and prevalence of cross boundary layer transport increased with a/l.