Update README.md

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Author: johnryantaylor

Project2/README.md

@@ -55,6 +55,6 @@ Finally, try making a plot of the gradient Richardson number as a function of de
 In a stratified flows, kinetic energy can be converted to potential energy by mixing the stable density profile, raising the center of mass of the fluid. Some kinetic energy is also lost to viscous dissipation. The mixing efficiency, $\Lambda$,of great interest in the stratified turbulence literature, is the ratio of the kinetic energy used to mix the density profile to the loss to viscous dissipation. Set up and run a simulation of K-H instability using Oceananigans, and let the flow evolve long enough so that it settles back into a non-turbulent state (you may need to decrease the resolution for this, and you might also want to increase the size of the domain in $z$ to minimise boundary effects). Calculate the kinetic and potential energy at the start and end of the simulation, and the change over the simulation, $\Delta KE$ and $\Delta PE$. Calculate the flux coefficient $\Gamma \equiv B/\epsilon \simeq \Delta PE/(-\Delta KE-\Delta PE)$, where $B$ is the buoyancy flux, and $\epsilon$ is the kinetic energy dissipation. Then, use the flux coefficient to estimate the mixing efficiency, $\eta$, using the relation $\Gamma=\eta/(1-\eta)$. Many parameterizations for mixing in the ocean and atmosphere use a constant mixing efficiency with a value close to $\eta \simeq 0.2$. How does your result compare?  Using time series of the kinetic and potential energy, can you estimate the instantaneous mixing efficiency as a function of time?
 
 ## Holmboe instability
-When the profiles of shear and stratification are not identical, a second type of instability called 'Holmboe instability' can develop. Specifically, this instability develops when the width of the shear layer is larger than the width of the stratified layer. Holboe instability is characterized by disturbances that propagate relative to the mean flow, while the billows associated with Kelvin-Helmholtz instability remain nearly stationary. Repeat the process used to analyze K-H instability (starting from the linear stability analysis), but use a buoyancy profile where the width of the tanh used to create the initial buoyancy profile is smaller than for the velocity. The parameters listed in Table 1 from [Salehipour et al.]("./papers/Salehipour.pdf") should provide a good starting point. Can you identify Holmboe instability based on the stability analysis? Once you find a set of parameters where Holmboe instability grows faster than K-H, try simulating it in Oceananigans. Note that you may need to increase the Reynolds number or Prandtl number in this simulation to prevent the density interface from smearing out too broadly before the simulation begins.
+When the profiles of shear and stratification are not identical, a second type of instability called 'Holmboe instability' can develop. Specifically, this instability develops when the width of the shear layer is larger than the width of the stratified layer. Holboe instability is characterized by disturbances that propagate relative to the mean flow, while the billows associated with Kelvin-Helmholtz instability remain nearly stationary. Repeat the process used to analyze K-H instability (starting from the linear stability analysis), but use a buoyancy profile where the width of the tanh used to create the initial buoyancy profile is smaller than for the velocity. The parameters listed in Table 1 from [Salehipour et al.](./papers/Salehipour.pdf) should provide a good starting point. Can you identify Holmboe instability based on the stability analysis? Once you find a set of parameters where Holmboe instability grows faster than K-H, try simulating it in Oceananigans. Note that you may need to increase the Reynolds number or Prandtl number in this simulation to prevent the density interface from smearing out too broadly before the simulation begins.