\[ \begin{align}\begin{aligned}\newcommand{\b}[1]{\boldsymbol{#1}} \newcommand{\r}[1]{\mathrm{#1}} \newcommand{\bz}{\b{z}} \newcommand{\bu}{\b{u}} \newcommand{\bcdot}{\b{\cdot}} \newcommand{\d}{\partial}\\\newcommand{\p}{\, .} \newcommand{\c}{\, ,}\\\newcommand{\bnabla}{\b{\nabla}} \newcommand{\bcdot}{\b{\cdot}}\end{aligned}\end{align} \]

Fluid models

dedaLES provides solvers for

• Boussinesq flow in a channel

Boussinesq Channel flow

The rotating, stratified Boussinesq equations are

\[ \begin{align}\begin{aligned}\begin{split}\d_t \bu + \left ( \bu \bcdot \bnabla \right ) \bu - f \bz \times \bu + \bnabla p = b \bz + \nu \bnabla^2 \bu + \bnabla \bcdot \b{F}^{\bu} \c \\\end{split}\\\d_t b + \bu \bcdot \bnabla b + w N^2 = \kappa \bnabla^2 b + \bnabla \bcdot \b{F}^b \c\end{aligned}\end{align} \]

where \(\bu = (u, v, w)\) is the velocity field, \(p\) is pressure, \(b\) is buoyancy, \(f\) is the Coriolis frequency, \(\nu\) is viscosity, \(\kappa\) is diffusivity, \(N^2\) is the background buoyancy gradient and squared buoyancy frequency, \(F^{\bu}_{ij}\) is the subgrid stress and \(\b{F}^b\) is the subgrid buoyancy flux. The subgrid stress and buoyancy flux are determined by the subgrid turbulence closure. When these terms are zero, the simulation is a direct numerical simulation.