## Summer 2018

These seminars (unless otherwise stated) will take place on **Wednesdays at 4pm in various rooms **on** **a bi-weekly basis ** - **see the map for further details.

## 02 May 2018 in Room 505

### Speaker: Dane Grundy (University of East Anglia)

##### Title: The Effect of Surface Stress on Interfacial Solitary Waves

**Abstract:**

The theory of solitary waves on the surface of a fluid is well developed when a purely normal stress is applied at the surface (for example due to uniform surface tension), which leads to the KdV equation. However when a liquid is subjected to an electric field [1], or surfactant [2], is present at the surface leading to non-uniform surface tension, then a tangential stress arises at the free surface. In this case, taking the large Reynolds' number limit leads to a boundary layer at the free surface and a significant increase in the complexity of the problem. Preliminary results suggest a wide range of possible solitary wave behaviour and I will focus on solutions possible when electric fields and surfactants are present. In addition, comparisons will be drawn with other approaches with numerical methods using boundary integral methods.

[1] Hammerton, P. W., Existence of solitary travelling waves in interfacial electrohydrodynamics. Wave Motion, 50 (4). pp. 676-686 (2013).

[2] P. W. Hammerton and A. P. Bassom, The effect of surface stress condition on interfacial solitary wave propagation, Q. J. Mech. Appl.Math. 66, 395-416 (2013).

## 16 May 2018 in Room 500

### Speaker: Sean Jamshidi (UCL)

##### Title: Dispersive and diffusive shock regularisation

**Abstract:**

A common problem in inviscid fluid mechanics is: how does one select the correct solution when multiple possibilities exist after the flow has developed a shock or discontinuity? One way to do this is to ‘regularise’ the problem by adding a small higher order term (viscosity or dispersion) and then take the limit of the (now unique) solution as the small parameter tends to zero. Another method is known as Lax admissibility. In many cases these two methods produce the same result, but in those cases where they do not the regularisation approach can lead to new types of solution and different physical interpretations. The study of these ‘non-convex’ problems is an active and modern area of research, and has been used in all areas of applied mathematics including, fairly recently, shallow-water theory.

In this talk I will explore how this method is applied to Burger’s equation, a simple nonlinear conservation law that has been used to model one-dimensional gas flow. The talk will be based on two papers:

Travelling-wave solutions to the modified KdV-Burgers equation (Jacobs et al, 1995)

Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws (El et al, 2015)

## 23 May 2018 in Room 500

### Speaker: Alexander Doak (UCL)

##### Title: Internal waves: a heuristic overview of the dead water effect, the mill-pond effect, and other phenomena

**Abstract:**

The existence of surface water waves is of no surprise to anyone. We see them when paddling in the sea or staring contemplatively into a shaken cup of coffee. The existence of internal waves, that is waves propagating inside stratified fluids, is less obvious. From the Rayleigh-Taylor and Kelvin-Helmholtz instability, to a look at internal solitary waves, I will cover a variety of interesting phenomena occurring in stratified flows, focusing mainly on multi-layer problems (as opposed to continuously stratified fluids).

## 07 June 2018 in Room B09, 16-18 Gordon Square

### Speaker: Chi Zhang (Department of Aeronautics, Imperial College London)

##### Title: Quasi-steady quasi-homogeneous description of near-wall turbulence

**Abstract:**

A formal definition to the two hypotheses of the quasi-steady and quasi-homogeneous (QSQH) theory is proposed. This theory is supposed to explain the phenomenon of the large-scale structures influencing the small-scale strucures in the near-wall part of the turbulent boundary layer. A multi-objective optimisation was performed to find the optimal cut-off parameters for a new large-scale filter. The new filter was proved to obtain much clearer large-scale structures than the filter suggested by the previous studies. Within the quasi-steady quasi-homogeneous theory expansions for various quantities were found up to the second order of magnitude with respect to the amplitude of the large-scale fluctuations. Including the nonlinear effects improved the agreement with numerical data. Two extrapolation methods based on QSQH theory were developed, with the advantages and disadvantages of them being discussed. The accuracy of the predictions based on the QSQH theory was observed improving when the Reynolds number increases. The results of the present work demonstrated the relevance of the quasi-steady quasy-homogeneous theory for near-wall turbulent flows.