Abstracts

Internal solitary waves in a three-layer fluid: some recent results

Dr Ricardo Barros

In the ocean, it is estimated that 90% of the kinetic energy associated with internal solitary waves is contained within the first two baroclinic modes of propagation. A three-layer liquid system confined between two rigid walls is the simplest physical system supporting waves of these two modes. In this talk we explore some predictions by the strongly nonlinear theory and their validity, through numerical results for the fully nonlinear (Euler) equations. 

Internal Solitary Wave Shoaling; the effect of stratification and a new diagnostic tool to understanding mixing

Dr Magda Carr

Internal solitary waves (ISWs) are finite amplitude waves of permanent form that travel along density interfaces in stably stratified fluids. They owe their existence to an exact balance between non-linear wave steepening effects and linear wave dispersion. They are common in all stratified flows especially coastal seas, straits, fjords and the atmospheric boundary layer. In the ocean they can attain amplitudes as large as 250m and speeds of up to 2 m/s. Whilst ISWs can travel considerable distance over a flat bottom without change of form, under certain conditions, such as when shoaling, their form can change considerably. As they do so, dissipation produced by the motion of breaking waves, both in the benthic boundary layer and the pycnocline, is identified as a key process in the global cascade of energy from global-scale mechanical forcing to dissipation.
 

In this presentation a combined experimental and numerical study will illustrate the effect of stratification form on the shoaling characteristics of ISWs propagating over a smooth, linear topographic slope. It is found that the form of stratification directly affects the breaking type (fission, collapse, plunge, surge) associated with the shoaling wave. In addition, a new diagnostic tool for understanding mixing in stratified fluids will be presented. Paired histograms of user-selected variables are employed to identify mixing fluid and are then used to display regions of fluid in physical space that are undergoing mixing. The method identifies differences in the mixing processes associated with different ISW breaking types, including differences in the horizontal extent and advection of mixed fluid.

Hartharn-Evans SG, Carr M, Stastna M, Davies PA. Stratification effects on shoaling internal solitary waves. Journal of Fluid Mechanics. 2022.

Hartharn-Evans SG, Stastna, M, Carr M. A new approach to understanding fluid mixing in process-study models of stratified fluids. Nonlinear Processes in Geophysics. 2024.

Topography effects in shallow water modeling: hyperbolic versus dispersive 

Prof. Sergei Gavrilyuk

with M. Ricchiuto (Inria, Bordeaux, France). 

Redefining wave extremes in the Coastal Zone

Dr Ioannis Karmpadakis

This talk aims to provide new insights into the formation of extreme wave events in the coastal zone. The evolution of waves over planar coastal bathymetry is examined in a stochastic context using a unique combination of data sources. Specifically, data from field, experimental and numerical campaigns conducted in the last 5 years are used to identify shortcomings in present understanding. I will identify the key physical mechanisms leading to the formation of extreme events in different water depth regimes and explore how well present theory can describe them. Finally, I explore new methods to address uncertainty in the cases that theory is not comparing well to observations.

Evolution of internal cnoidal waves with local defects in a two-layer fluid with rotation

Dr Karima Khusnutdinova

Internal waves in a two-layer fluid with rotation are considered within the framework of Helfrich’s f-plane extension of the Miyata–Choi–Camassa (MCC) model. Within the scope of this model, we develop an asymptotic procedure which allows us to obtain a description of a large class of uni-directional waves leading to the Ostrovsky equation and allowing for the presence of shear inertial oscillations and barotropic transport. Importantly, unlike the conventional derivations leading to the Ostrovsky equation, the constructed solutions do not impose the zero-mean constraint on the initial conditions for any variable in the problem formulation. Using the constructed solutions, we model the evolution of quasi-periodic initial conditions close to the cnoidal wave solutions of the Korteweg–de Vries (KdV) equation but having a local amplitude and/or periodicity defect, and show that such initial conditions can lead to the emergence of bursts of large internal waves and shear currents. As a by-product of our study, we show that cnoidal waves with periodicity defects discussed in this work are weak solutions of the KdV equation and, being smoothed in numerical simulations, they behave as long-lived approximate travelling waves of the KdV equation, with the associated bursts being solely due to the effect of rotation. This is joint work with Korsarun Nirunwiroj and Dmitri Tseluiko.

On structural responses of the bodies exposed to water waves

Dr Sime Malenica

The lecture will include the overview and the most advanced current practices, which are in use to evaluate the structural stresses induced by water waves in both rigid and flexible floating bodies.

Deterministic wave forecasting with nonlinear dispersion corrections

Dr Raphael Stuhlmeier

Deterministic wave forecasting aims to provide a wave-by-wave prediction of the free surface elevation based on measured data. Such information about upcoming waves can inform marine decision support systems, control strategies for wave energy converters, and other applications. Unlike well-developed stochastic wave forecasts, the temporal and spatial scales involved are modest, on the order of minutes or kilometres. Due to the dispersive nature of surface water waves, such forecasts have a limited space/time horizon, which is further impacted by the effects of nonlinearity. I will discuss the application of the reduced Zakharov equation, and simple frequency corrections derived therefrom, to preparing wave forecasts. Unlike procedures based on solving evolution equations (e.g. high order spectral method), such corrections entail essentially no additional computational effort, yet show marked improvements over linear theory.