# The fluid dynamics perspective A free convective boundary layer is governed by parameters $B_0$ and $N^2$, with each of them having a positive value. Under the assumption of horizontal homogeneity, all its time and height-varying statistics can be formulated as a function of the set $ \left\{ z, t; B_0, N^2\right\} $ If we define length scale from the parameters, which is the reference Ozmidov length $L_0 \equiv \left( B_0 / N^3 \right)^\frac{1}{2}$, then we can derive the dimensionless coordinates that should scale any boundary layer $ \left\{ \frac{z}{L_0}, t N\right\} $ We can define two limiting cases, one where boundary-layer depth $h \ll L_0$ and one where $h \gg L_0$. ## Convection into a neutrally stratified layer ($h \ll L_0$) This is convection that is controlled only by its energy input at the surface $B_0$. Hence, the evolution of its depth is $h \sim \left( B_0 t^3 \right)^\frac{1}{2}$. ## The convective boundary layer ($h \gg L_0$) This is convection that is controlled only by its energy input at the surface $B_0$ and the stratification $N^2$ that rising plumes will interact with, via entrainment. The evolution of its depth is $h \sim \left( \dfrac{B_0}{N^2} t \right)^\frac{1}{2}$. ## Studying convective boundary layer evolution With the [CLASS](https://classmodel.github.io) model, we can study the convective boundary layer evolution. Here, you can see the impact of doubling the surface flux $B_0$ or halving the initial temperature jump $\Delta \theta$. <iframe src="https://chiil.github.io/class_streamlit/index.html?c==H4sIAECEwmgC_8WRywqDMBBFf0VmrTIqgrjuF7TLUiS246MkPpNaEP-9ibEt9APs7tw7j8wlM4wkZd2UI6TnGQbVyFoQpAEmiD66cJNGWMpaJTuljcjWKlNaKSfJIEU_1G31w5A2ZbW60XuRlaER0ybQD1womRDsYyBGLvSWYj2m0TOsGyfNCXnGXmf67SG7Ouu4MqfbK_qvXGcbZgQcqaCBmivB4u4SF_34j3FPgnHu3JXo9sr7873hvnkPrco5OQVXT1guywttlHLE3gIAAA==" style="height: 800px; width: 100%; border: 1px solid #dddddd; border-radius: 8px;"> </iframe> [Launch in its own window](https://chiil.github.io/class_streamlit/index.html?c==H4sIAECEwmgC_8WRywqDMBBFf0VmrTIqgrjuF7TLUiS246MkPpNaEP-9ibEt9APs7tw7j8wlM4wkZd2UI6TnGQbVyFoQpAEmiD66cJNGWMpaJTuljcjWKlNaKSfJIEU_1G31w5A2ZbW60XuRlaER0ybQD1womRDsYyBGLvSWYj2m0TOsGyfNCXnGXmf67SG7Ouu4MqfbK_qvXGcbZgQcqaCBmivB4u4SF_34j3FPgnHu3JXo9sr7873hvnkPrco5OQVXT1guywttlHLE3gIAAA==).