Adds some general info in docs + minor enhancements

docs/make.jl

@@ -28,8 +28,8 @@ makedocs(
 )
 
 withenv("GITHUB_REPOSITORY" => "FourierFlows/PassiveTracerFlowsDocumentation") do
-  deploydocs(        repo = "github.com/FourierFlows/PassiveTracerFlowsDocumentation.git",
+  deploydocs(       repo = "github.com/FourierFlows/PassiveTracerFlowsDocumentation.git",
                 versions = ["stable" => "v^", "v#.#", "dev" => "dev"],
-            push_preview = true
+            push_preview = false
             )
 end

docs/src/index.md

@@ -3,6 +3,18 @@
 
 ## Overview
 
+`PassiveTracerFlows.jl` is a collection of modules which leverage the 
+[FourierFlows.jl](https://github.com/FourierFlows/FourierFlows.jl) framework to solve for
+advection-diffusion problems on periodic domains.
+
+!!! info "Unicode"
+    Oftentimes unicode symbols are used in modules for certain variables or parameters. For 
+    example, `κ` is commonly used to denote the diffusivity, or `∂` is used 
+    to denote partial differentiation. Unicode symbols can be entered in the Julia REPL by 
+    typing, e.g., `\kappa` or `\partial` followed by the `tab` key.
+
+    Read more about Unicode symbols in the 
+    [Julia Documentation](https://docs.julialang.org/en/v1/manual/unicode-input/).
 
 
 ## Developers

docs/src/modules/traceradvectiondiffusion.md

@@ -2,27 +2,30 @@
 
 ### Basic Equations
 
-This module solves the advection diffusion equation for a passive tracer
-concentration ``c(x, y, t)`` in two-dimensions:
+This module solves the advection diffusion equation for a passive tracer concentration 
+``c(x, y, t)`` in two-dimensions by an advecting flow ``\bm{u}(x, y, t)``:
 
 ```math
-\partial_t c + \boldsymbol{u} \boldsymbol{\cdot} \boldsymbol{\nabla} c = \underbrace{\eta \partial_x^2 c + \kappa \partial_y^2 c}_{\textrm{diffusivity}} + \underbrace{\kappa_h (-1)^{n_{h}} \nabla^{2n_{h}}c}_{\textrm{hyper-diffusivity}}\ ,
+\partial_t c + \bm{u} \bm{\cdot} \bm{\nabla} c = \underbrace{\eta \partial_x^2 c + \kappa \partial_y^2 c}_{\textrm{diffusivity}} + \underbrace{\kappa_h (-1)^{n_{h}} \nabla^{2n_{h}}c}_{\textrm{hyper-diffusivity}}\ ,
 ```
 
-where ``\boldsymbol{u} = (u,v)`` is the two-dimensional advecting flow, ``\eta`` the ``x``-diffusivity and ``\kappa`` is the ``y``-diffusivity. If ``\eta`` is not defined then the code uses isotropic diffusivity, i.e., ``\eta \partial_x^2 c + \kappa \partial_y^2 c\mapsto\kappa\nabla^2``. The advecting flow could be either compressible or incompressible. 
+where ``\bm{u} = (u, v)`` is the two-dimensional advecting flow, ``\eta`` the ``x``-diffusivity and ``\kappa`` is the ``y``-diffusivity. If ``\eta`` is not defined then the code uses isotropic diffusivity, i.e., ``\eta \partial_x^2 c + \kappa \partial_y^2 c \mapsto \kappa \nabla^2``. The advecting flow could be either compressible or incompressible. 
 
 
 ### Implementation
 
 The equation is time-stepped forward in Fourier space:
 
 ```math
-\partial_t \widehat{c} = - \widehat{\boldsymbol{u} \boldsymbol{\cdot} \boldsymbol{\nabla} c} - \left[ (\eta k_x^2 + \kappa k_y^2) +\kappa_h k^{2\nu_h} \right]\widehat{c}\ .
+\partial_t \widehat{c} = - \widehat{\bm{u} \bm{\cdot} \bm{\nabla} c} - \left[ (\eta k_x^2 + \kappa k_y^2) + \kappa_h |\bm{k}|^{2\nu_h} \right] \widehat{c}\ ,
 ```
+where ``\bm{k} = (k_x, k_y)``.
 
 Thus:
 
 ```math
-\mathcal{L} = -\eta k_x^2 - \kappa k_y^2 - \kappa_h k^{2\nu_h}\ , \\
-\mathcal{N}(\widehat{c}) = - \mathrm{FFT}(u \partial_x c + \upsilon \partial_y c)\ .
+\begin{aligned}
+L & = -\eta k_x^2 - \kappa k_y^2 - \kappa_h |\bm{k}|^{2\nu_h} , \\
+N(\widehat{c}) &= - \mathrm{FFT}(u \partial_x c + v \partial_y c) .
+\end{aligned}
 ```