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Governing equation Assume that the flow is two-dimensional, and incompressible. The governing equations are as follows. $\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0$ $\frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} = -\frac{\partial P}{\partial x} + \nu \left(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}\right)$ $\frac{\partial v}{\partial t} + u\frac{\partial v}{\partial x} + v\frac{\partial v}{\partial y} = -\frac{\partial P}{\partial y} + \nu \left(\frac{\partial^2 v}{\partial x^2} + \frac{\partial^2 v}{\partial y^2}\right)$ $\frac{\partial \theta}{\partial t} + u\frac{\partial \theta}{\partial x} + v\frac{\partial \theta}{\partial y} = \kappa \left(\frac{\partial^2 \theta}{\partial x^2} + \frac{\partial^2 \theta}{\partial y^2}\right)$ Here, $u$ and $v$ are the velocity components in the $x$ and $y$ directions, respectively. $P$ denotes the pressure. $\theta$ is the passive scalar. $\nu$ and $\kappa$ are kinematic viscosity and passive-scalar diffusion coefficients, respectively. The boundary conditions are as follows.

          Governing equation
Assume that the flow is two-dimensional, and incompressible. The governing equations are as follows.
$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0$
$\frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} = -\frac{\partial P}{\partial x} + \nu \left(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}\right)$
$\frac{\partial v}{\partial t} + u\frac{\partial v}{\partial x} + v\frac{\partial v}{\partial y} = -\frac{\partial P}{\partial y} + \nu \left(\frac{\partial^2 v}{\partial x^2} + \frac{\partial^2 v}{\partial y^2}\right)$
$\frac{\partial \theta}{\partial t} + u\frac{\partial \theta}{\partial x} + v\frac{\partial \theta}{\partial y} = \kappa \left(\frac{\partial^2 \theta}{\partial x^2} + \frac{\partial^2 \theta}{\partial y^2}\right)$
Here, $u$ and $v$ are the velocity components in the $x$ and $y$ directions, respectively. $P$ denotes the pressure.
$\theta$ is the passive scalar. $\nu$ and $\kappa$ are kinematic viscosity and passive-scalar diffusion coefficients, respectively.
The boundary conditions are as follows.

Governing equation
Assume that the flow is two-dimensional, and incompressible. The governing equations are as follows.
(∂ u)/(∂ x) + (∂ v)/(∂ y) = 0
(∂ u)/(∂ t) + u(∂ u)/(∂ x) + v(∂ u)/(∂ y) = -(∂ P)/(∂ x) + ν((∂^2 u)/(∂ x^2) + (∂^2 u)/(∂ y^2))
(∂ v)/(∂ t) + u(∂ v)/(∂ x) + v(∂ v)/(∂ y) = -(∂ P)/(∂ y) + ν((∂^2 v)/(∂ x^2) + (∂^2 v)/(∂ y^2))
(∂θ)/(∂ t) + u(∂θ)/(∂ x) + v(∂θ)/(∂ y) = κ((∂^2 θ)/(∂ x^2) + (∂^2 θ)/(∂ y^2))
Here, u and v are the velocity components in the x and y directions, respectively. P denotes the pressure.
θ is the passive scalar. ν and κ are kinematic viscosity and passive-scalar diffusion coefficients, respectively.
The boundary conditions are as follows.

Added by Lisa S.

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