Update Pearson et al., 2025 references in text

Author: BrodiePearson

paper/paper.md

@@ -43,15 +43,15 @@ where $\mathbf{x}$ denotes the position of a data point, $\delta \phi$ denotes t
 
 ![Various structure functions (SFs) calculated from a simulated 2D turbulent flow, visualized through snapshots of the vorticity field (top left) and velocity field (bottom left). The right panels show various SFs based on velocity (red lines) and vorticity (blue lines), including third-order and advective SFs (top right) and traditional second-order SFs (bottom right). The results are from the top layer snapshot of an anisotropic 2-layer quasi-geostrophic simulation conducted with GeophysicalFlows.jl. \label{fig:fig1}](figs/fig1.png)
 
-As demonstrated in \autoref{fig:fig1} and \autoref{fig:fig2}, `FluidSF` can calculate a wide array of traditional structure functions, including $SF_{\phi \phi}$ (\autoref{eq:eq1}; where the scalar field in this case is vorticity $\omega$), second- and third-order SFs of longitudinal velocity ($SF_{LL}=\overline{(\delta u_L)^2}$ and $SF_{LLL}=\overline{(\delta u_L)^3}$; where $u_L=\mathbf{u}\cdot\hat{\mathbf{r}}$) and transverse velocity ($SF_{TT}$ and $SF_{TTT}$), and blended velocity-scalar third-order SFs ($SF_{L\omega\omega}=\overline{\delta u_L \delta \omega \delta \omega}$), in addition to novel advective SFs  of velocity ($ASF_{V}$), vorticity ($ASF_{\omega}$) and scalars [@pearson:2021]. Advective SFs require fields of the local advection, and `FluidSF` has a built-in function to compute these advection terms. `FluidSF` can calculate SFs in specific separation directions (i.e., aligned with the Cartesian co-ordinates, shown in \autoref{fig:fig2}), and for 2D data it can diagnose maps showing how SFs vary with the magnitude and orientation of the separation vector $\mathbf{r}$ (\autoref{fig:fig3}). `FluidSF` also includes tools to make the calculation and processing of SFs easier, such as array shifting, diagnosis of the advection terms for novel SFs, decomposition of velocity into longitudinal (along-$\mathbf{r}$; $u_L$) and transverse (across-$\mathbf{r}$; $u_T$) components, and data binning based on separation distance.
+As demonstrated in \autoref{fig:fig1} and \autoref{fig:fig2}, `FluidSF` can calculate a wide array of traditional structure functions, including $SF_{\phi \phi}$ (\autoref{eq:eq1}; where the scalar field in this case is vorticity $\omega$), second- and third-order SFs of longitudinal velocity ($SF_{LL}=\overline{(\delta u_L)^2}$ and $SF_{LLL}=\overline{(\delta u_L)^3}$; where $u_L=\mathbf{u}\cdot\hat{\mathbf{r}}$) and transverse velocity ($SF_{TT}$ and $SF_{TTT}$), and blended velocity-scalar third-order SFs ($SF_{L\omega\omega}=\overline{\delta u_L \delta \omega \delta \omega}$), in addition to novel advective SFs  of velocity ($ASF_{V}$), vorticity ($ASF_{\omega}$) and scalars [@pearson:2021; @pearson:2025]. Advective SFs require fields of the local advection, and `FluidSF` has a built-in function to compute these advection terms. `FluidSF` can calculate SFs in specific separation directions (i.e., aligned with the Cartesian co-ordinates, shown in \autoref{fig:fig2}), and for 2D data it can diagnose maps showing how SFs vary with the magnitude and orientation of the separation vector $\mathbf{r}$ (\autoref{fig:fig3}). `FluidSF` also includes tools to make the calculation and processing of SFs easier, such as array shifting, diagnosis of the advection terms for novel SFs, decomposition of velocity into longitudinal (along-$\mathbf{r}$; $u_L$) and transverse (across-$\mathbf{r}$; $u_T$) components, and data binning based on separation distance.
 
 ![Velocity-based SFs calculated from satellite observations of the ocean surface in the North Atlantic. Maps of the inferred surface velocity from a satellite swath are shown in the top left. The region of data used for SF calculations is indicated by the red box and magnified on the top right. The bottom panel shows the advective (red) and third-order (blue) velocity structure functions calculated with separation vectors across the satellite swath (dashed) and along the swath (solid). Note the velocity fields are estimated from satellite sea surface height measurements assuming geostrophic balance. \label{fig:fig2}](figs/fig2.png)
 
 ![Maps showing the 2D spatial variation of various velocity structure functions. The left panel shows the advective velocity SF, the middle panel is the third-order velocity SF, and the right panel is the second-order velocity SF. These SFs were calculated from the same data as \autoref{fig:fig1}. \label{fig:fig3}](figs/fig3.png)
 
 ## Related Work
 
-`FluidSF` uniquely contributes to the field through a combination of expanded data support, the ability to diagnose a wide array of structure functions (including advective and blended SFs), and tools for analyzing spatial variations in SFs. `FluidSF` was used to develop new methods for estimating inter-scale geophysical energy fluxes [@pearson:2024]. There are several open source software packages available that calculate aspects of spatial SFs. `fastSF` is a parallelized C++ code designed to compute arbitrary-order SFs of velocity or scalars (but not blended) from Cartesian grids of data [@sadhukhan:2021]. @fuchs2022 created an open source `MATLAB` toolkit that performs a variety of turbulence analysis, including arbitrary-order longitudinal-velocity SFs. A complimentary and alternative method to structure functions for analyzing turbulence data is coarse-graining. `FlowSieve` is a primarily C++ package that uses coarse-graining to estimate ocean and atmospheric turbulence properties from Global Climate Model data [@storer2023].
+`FluidSF` uniquely contributes to the field through a combination of expanded data support, the ability to diagnose a wide array of structure functions (including advective and blended SFs), and tools for analyzing spatial variations in SFs. `FluidSF` was used to develop new methods for estimating inter-scale geophysical energy fluxes [@pearson:2025]. There are several open source software packages available that calculate aspects of spatial SFs. `fastSF` is a parallelized C++ code designed to compute arbitrary-order SFs of velocity or scalars (but not blended) from Cartesian grids of data [@sadhukhan:2021]. @fuchs2022 created an open source `MATLAB` toolkit that performs a variety of turbulence analysis, including arbitrary-order longitudinal-velocity SFs. A complimentary and alternative method to structure functions for analyzing turbulence data is coarse-graining. `FlowSieve` is a primarily C++ package that uses coarse-graining to estimate ocean and atmospheric turbulence properties from Global Climate Model data [@storer2023].
 
 # Acknowledgements