# Monin Obukhov Stratified

**Scope**

The benchmark is open to participants of the Wakebench project using surface layer models with stratification. This is the first element of the building-block approach so it should be mandatory if you intend to participate in other test cases down the line where thermal stratification is present.

The benchmark consists on empty domain (flat terrain) simulations of the thermally stratified surface boundary layer in steady-state conditions.

**Objectives**

Demonstrate that the flow model, when run in M-O conditions, is able to reproduce the analytical expressions of the profiles predicted by the theory for stratified flow. At the same time, it will be possible to check the compatibility of the wall treatment with the flow model for a range of heat flux conditions.

**Data Accessibility**

The benchmark is offered to participants of the IEA Task 31 Wakebench. In the future it will be open for public access.

**Input data**

The conditions for simulating the M-O profiles in stratified conditions are:

von karman constant: κ = 0.4

Roughness length: z0 = 0.03 m.

Obukhov length: L = [-100, ∞, 100] m

Use dry air with a density ρ = 1.225 kg/m3 and dynamic viscosity μ = 1.73e-5 kg/ms.

**Validation data**

The validation profiles are obtained from the analytical expressions of the test case guide using the following Dyer stability functions (Panofsky and Dutton, 1984):

**Model runs**

An empty domain of 3x0.5x0.5 km (x,y,z) dimensions should be simulated with three different values of the M-O length.

Run 1: L = -100 m, for unstable conditions equivalent to a kinematic heat flux of wΘ = 0.047 mK/s

Run 2: L = ∞, for neutral conditions

Run 3: L = 100m, for stable conditions equivalent to a kinematic heat flux of wΘ = -0.047 mK/s

The origin of the coordinate system will be placed in the middle of the bottom edge of the inlet wall. The modeler is free to configure the computational grid according to own criteria.

**Output data**

Please provide output vertical profiles of mean velocity (U), potential temperature (Θ) and turbulent kinetic energy (tke) at the outlet (x = 3000m, y = 0) using the file naming and format convention described in the Windbench user's guide with profID=outlet# (# is the run number = [1,2,3]). Hence, the required outputs are, in this order: Z(m), U(m/s), T(K), tke(m2/s2). Mention the friction velocity (u*) and surface temperature (Θ0) used in the study since these inputs will be used to normalize the results.

**Remarks**

Please describe in detail the way stratification is handled by the model in terms of stability functions, boundary conditions, contributions to turbulence equations, etc.

**Terms andConditions**

Not applicable.