KOZWavinar is the online conference series for the KOZWaves community.

Each KOZWavinar features three 30-minute talks followed by a 30-minute discussion session with the speakers (i.e. 2h in total).

To be added to the mailing list __send an email to kozwavinar@gmail.com with the subject "add me"__.

Visit the KOZWavinar YouTube channel.

Marie Graff, University of Auckland

Amin Chabchoub, Kyoto University

Luke Bennetts, University of Adelaide

Miro Erkintalo, University of Auckland

Takahito Iida, Osaka University

Nicole Kessissoglou, University of New South Wales

Nicole Jones, University of Western Australia

**The dynamics of bottom boundary layers forced by tidal and nonlinear internal waves**

The interaction between ocean currents and the seabed generates a turbulent bottom boundary layer (BBL). Despite the BBL often being thin with respect to the total ocean depth, the dynamics of this layer are of great physical, biological, and engineering importance. In a stratified water column, the BBL produces a bottom mixing-layer (BML) capped by a strongly stratified pycnocline, which confines bottom-generated turbulence close to the seabed. The BBL plays a dominant role in dissipating kinetic energy, it contributes significantly to net mixing across the global ocean, it facilitates the exchange of sediments, nutrients, and organic matter between the seabed and the ocean interior, and it dictates the loading, undermining (i.e., scour), and embedment of seabed infrastructure. Here we use a combination of field observations and idealised large-eddy simulations to explore the stratified BBL under both tidal and nonlinear internal wave forcing.

We found that the BML height depends upon ambient stratification, tidal frequency and turbulence intensity, and can be approximated by a steady-state empirical model for a stratified Ekman layer, substituting the inertial frequency with the tidal frequency. The transport of turbulence, rather than local shear production, was the primary source of turbulence in the pycnocline. This has implications for the growth rate of the BML; as the BML height increases, turbulence transport to the pycnocline diminishes and the BML growth rate decreases. Nonlinear internal waves and internal tides compressed and expanded the BML, impacting on both the mean velocity profile and the turbulent flow in this layer.

Our predictive model of the BML height and pycnocline characteristics can be used to refine BBL parameterisations and inform grid resolution requirements for ocean models, inform the estimation of hydrodynamic loads on sub-sea engineering infrastructure and guide sampling for future observational studies.

co-authors: Andrew Zulberti, Madi Rosevear, Matthew Rayson and Gregory Ivey

Kei Matsushima, University of Tokyo

**Tailoring acoustic and electromagnetic waves based on structural optimization**

Recent studies have discovered novel physics behind the classical wave propagation and scattering. For example, some scattering systems exhibit resonant states that are completely confined in the vicinity of the scatterer despite of the continuous radiation spectrum. This phenomenon, bound state in the continuum, is expected to open up new possibilities for realizing innovative sensors, filters, and lasers. In this talk, we discuss some structural optimization-based techniques to realize such anomalous wave phenomena in acoustics and electromagnetics. First, we introduce the concept of structural optimization and explain its basic algorithm. The optimization algorithm is then incorporated into finite/boundary element software, which solves exterior time-harmonic scattering problems numerically. We show that the proposed method can realize the following three properties: (1) bound state in the continuum in open waveguide systems (2) unidirectional invisibility (cloaking) in a parity-time symmetric system (3) omnidirectional acoustic cloaking induced by a locally resonant sonic material.

Harald Schwefel, University of Otago

**Waves and nonlinear wave mixing in high quality optical resonators**

Waves bounded by convex boundaries can from a phenomenon called Whispering Gallery Modes. The name stems from acoustic waves creeping along a convex wall, such as found in Temple of Heaven or the St Paul’s Cathedral, first described mathematically by Lord Rayleigh. We use a similar phenomenon in circularly shaped disks of dielectric materials, where the electromagnetic radiation is trapped via total internal reflection close to the rim of the disk. As total internal reflection in a transparent structure much larger than the wavelength is nearly lossless, the confinement can be very high, leading to very localized and high electromagnetic fields.

We use such high quality whispering gallery modes to harness non-linear effects within the dielectric, in particular the second order nonlinear effects such as sum- and difference frequency generation, where two electromagnetic fields of different frequency can produce fields at either the sum or the difference frequency. The talk will provide the background and show application of these resonator for the generation of optical frequency combs and for quantum transduction.

Ross McPhedran, University of Sydney

**The Kronig-Penney Model: Applications to Wave Scattering**

The Kronig-Penney Model (published in 1931) is one of the most influential early works linking quantum mechanics to the properties of the solid state materials. It consisted in the application of the scalar Schrödinger equation to a periodic structure having a piecewise potential function taking alternately two different values, and its solution underpinned the development of the energy band concept for solids.

Fifty years later, an adaptation of the model to a periodic electromagnetic system was developed by the author and collaborators, and almost simultaneously by Ping Sheng and a collaborator. It consisted of a lamellar grating structure, having a dielectric constant varying periodically between two values, with the electromagnetic fields obeying the Helmholtz equation and a quasi-periodicity (Bloch/Floquet) condition. Within the grating, modes were expressed in trigonometric form, and the dispersion equation from the boundary conditions and quasiperiodicity again taking a trigonometric form. A complete set of modes could be obtained from numerical solution of the dispersion equation, with their inner products and normalisation factors being analytic. Scattering problems then could be solved by matching between plane waves and modes.

For lossless dielectrics, the modes are self-adjoint, but for lossy dielectrics and metals, adjoint modes are needed as well. The scattering problem in electromagnetism is strongly polarisation dependent, with diffraction anomalies being particularly strong for the polarisation supporting surface waves.

This work was well cited, and extended in various ways by later authors. It forms an elegant method for solving scattering by a particular type of scatterer, and the analytic nature of the expressions permits much insight to be gained into strong scattering phenomena.

Ludmila Adam, University of Auckland

**Sensing for changes in the Earth with waves**

Elastic (seismic) waves are all around us. These can be naturally generated via geological or environmental processes or human-made. The way seismic waves interact with a medium makes them highly sensitive to rock type, the fluids within and the physical conditions they experience (e.g., pressure and temperature). The sensitivity of all these parameters makes seismic waves ideal to detect small changes in the subsurface. Monitoring these changes are the building blocks for current and future early warning systems in geological hazards such as earthquakes and volcanic eruptions. I’ll discuss how we monitor volcanic processes with waves in the laboratory from three approaches: elastic wave signatures generated during volcanic unrest, monitoring the development of the seal cap within a volcano and the high sensitivity of linear and non-linear wave propagation of waves to small variations in temperature. The talk will focus on the nature and properties of waves, complemented with micro images of the medium (rocks) these waves sample to understand the implications at the field scale.

Hidetaka Houtani, University of Tokyo

**On the crest height amplification of unstable Stokes wave trains in deep water**

Rogue waves in the ocean can cause devastating structural damage to ships and offshore platforms. Modulational instability due to nonlinear quasi-resonant interaction is one of the possible causes of such rogue-wave formation. The modulational instability phenomenon is first found by Benjamin and Feir (1967). They discovered that Stokes wave is unstable to modulated perturbations. The present study focuses on the maximum crest height of unstable Stokes wave trains. The Akhmediev breather (AB) solution of the nonlinear Schrödinger equation is well known to describe the long-term nonlinear evolution of unstable Stokes wave trains. However, several fully nonlinear numerical simulations indicated that the maximum crest height of unstable Stokes wave trains exceeds the AB prediction. To clarify the physical mechanism of the crest height amplification, we performed a numerical simulation of unstable Stokes wave trains based on the higher-order spectral method (HOSM) and corresponding tank experiment. HOSM is capable of wave trains with higher nonlinearity and broader spectral bandwidth beyond the AB regime. The tank experiment demonstrated that the crest height amplification of the unstable Stokes wave trains was larger than the AB prediction at high initial wave steepness. Moreover, from the HOSM results, we will discuss the physics behind the crest-height amplification from the perspective of spectral broadening, bound-wave production, and phase-convergence.

KOZWavinar is inspired by the UK Wavinar.