**March 19th 2021:**

New paper published:

In collaboration with Arvind Singh at the University of Central Florida, Paola Passalacqua at UT Austin and Efi Foufoula-Georgiou at UC Irvine, we propose a hypothesis testing framework for analysing the properties of topographic surfaces. We then use it to examine how geomorphic measures of topography vary as a function of the control parameter intrinsic to the algorithm and show the importance of diffusive processes for controlling landscape structure.

The method is based on an algorithm of mine that preserves the multifractal statistics of the surface, as well as the elevation values. The paper primarily draws upon experimental data that Arvind obtained at the St Anthony Falls laboratory in Minnesota. The work is published in Journal of Geophysical Research. The figure shows one of Arvind's original surfaces together with three variants generated using my algorithm.

**May 9th 2020:**

New paper published:

In collaboration with Arvind Singh at the University of Central Florida, Paola Passalacqua at UT Austin and Efi Foufoula-Georgiou at UC Irvine, we propose a new method for describing topographic surfaces from elevation data. We complement the traditional elevation hypsometry with a variable describing, in a formal way, the roughness characteristics. From the joint distribution function for these two terms, we then look at the conditional distributions (roughness for a given elevation; elevation for a given roughness) and propose three simple statistics to summarise these properties. The method is applied to various catchments in the USA to show how they may be distinguished. We also undertake a numerical experiment to alter the landscape roughness to show that the method is sensitive to relatively minor variations. The work is published in Water Resources Research. The figure shows a plan view of a traditional digital elevation model for the Feather River catchment in (a), while (b) is the map of Holder exponents characterizing the roughness. The two marginal distributions are shown in (c) in cumulative form where the solid line is the traditional landscape hypsometry, and the dashed line is the equivalent for the Holder exponent map; what we term the Holder exponent, catchment area scaling (HECAS).

**31st October 2019:**

New paper published:

In a collaboration with Paul Beaumard and Oli Buxton at Imperial College, we investigate the properties of spatially evolving flows using numerical and experimental data, with laminar and turbulent in-flow boundary conditions. This work is published in *Journal of Turbulence*. In particular, we apply an index from (Keylock, 2018) to measure the relative strength of normal and non-normal effects in these spatially evolving flows. We show that non-normality is particularly important in the early stages of flow development: the region where non-equilibrium turbulence effects are commonly deemed to be significant. A particularly interesting aspect of the flow evolution was shown for our mixing layer case (see figure). Positive values for the index plotted on the x-axis mean that the normal part of the tensor is greater in magnitude than the non-normal part. Having seen a dominance of non-normality close to the generation of turbulence (at x/h = 45), we then see in region 6 (the Vieillefosse tail) an early "hyperextension" of the normal contributions here with very high values for the index at x/h = 90. Beyond this distance the coherent structures break up and we recover a distribution that looks more like homogeneous, isotropic turbulence.

**25th October 2019:**

New paper published:

New work on the nature of the non-normality of the velocity gradient tensor in turbulence is published in *Journal of Fluid Mechanics*. A tight mathematical bound on the non-normality of the tensor is applied. Regions of the flow attaining this bound are identified, and the physics of how the bound is attained are determined. These tensors are grouped into thin filaments within vortices and the typical spacing between these groupings is one Taylor scale. This suggests a role for such filaments in structuring the topology of the flow and, thus, the nature of dissipation. In the figure (below) a Lagrangian trajectory is tracked and the times when the bound is attained are highlighted by the crosses.

**4th July 2019:**

New paper published:

Our work on the vertical structure of canopy turbulence is published in *Environmental Fluid Mechanics*. This was a collaboration with Duke, MIT and Western Australia and uses my velocity-intermittency method to identify new features of the structure. The results are consistent between flume experiments of water flowing through and over artificial vegetation, and air flow at the Duke Forest Experiment. Heidi wrote an *Annual Reviews* on this topic in 2012, and the figure (belows) shows the typical values for the mean velocity, velocity covariance and velocity standard deviation from Heidi and Marco's previous work, along with our results for the velocity-intermittency quadrants (quadrant 1 results were invariant with height):