θ Wind Over Hot Land

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Wind 0.060
Viscosity 0.020
Land Temp 0.75
Diffusivity 0.030
Buoyancy 0.0005
Freq 0.012
Amp 0.005
Initializing...

1 Richardson Number

Ri = 0.00
Ri = g·β·ΔT·L / U². Buoyancy vs. inertia. Ri > 0.25 suppresses turbulence.

2 Potential Temperature θ

θ = T·(ρ₀/ρ)ᵒ
Parcels with equal θ have equal entropy. Switch to θ view.

3 Bejan Number

Be = ---
Be = σq / σtotal. Fraction of entropy from heat transfer vs. viscous dissipation.

4 Nusselt Number

Nu = ---
Nu = hL/k. Convective vs. conductive heat transfer at the surface.
Entropy Budget
Pr: ---   Ec: ---
σvisc dominates when Pr·Ec is large
σheat dominates when ΔT/U² is large
Drag the amber handle on the left edge to reposition and resize the inlet wind. Terrain features create flow separation and entropy hot-spots. Switch to θ or σ view to see entropy structure.

About This Experiment

Wind flows over heated terrain with rolling hills, producing thermal boundary layers, convective plumes, and flow separation. The simulation uses the Lattice Boltzmann Method (D2Q9) with thermal coupling on the GPU via WebGPU compute shaders. The central variable is potential temperature θ, a direct measure of specific entropy: s = cp ln(θ) + const. Parcels that share the same θ carry the same entropy, regardless of their pressure or density.

1 Richardson Number

The Richardson number Ri = g · β · ΔT · L / U² compares buoyancy forces (heated land driving convection) to inertial forces (wind shear). When Ri > 0.25, stratification suppresses vertical mixing and the flow remains laminar. When Ri < 0.25, shear overcomes buoyancy and turbulent mixing develops. This is the fundamental stability criterion for atmospheric boundary layers over heated surfaces.

Try it: raise Land Temp and reduce Wind speed to increase Ri. Watch convective plumes appear in Vorticity view.

2 Potential Temperature θ

Potential temperature θ = T · (ρ₀/ρ)(γ-1)/γ adjusts measured temperature for adiabatic compression or expansion. In the atmosphere, θ increases with height in stable conditions and is constant (well-mixed) in convective conditions. Since entropy s = cp ln(θ), surfaces of constant θ are isentropes. The θ view reveals the entropy structure of the flow directly.

Try it: switch to θ view. Uniform color means well-mixed (high entropy production). Sharp gradients mean stratified (low mixing).

3 Entropy Production σ

Entropy is produced by two mechanisms: viscous dissipation σv = μΦ/T (kinetic energy degraded to heat) and heat transfer across temperature gradients σq = k|∇T|²/T². The Bejan number Be = σq/(σq + σv) quantifies which mechanism dominates. Be near 1 means thermal gradients drive irreversibility; Be near 0 means viscous friction dominates.

Try it: switch to σ view. Bright spots near the surface show thermal entropy production. Bright spots behind hills show viscous entropy from flow separation.

4 Nusselt Number

The Nusselt number Nu = hL/k measures convective heat transfer relative to pure conduction. Nu = 1 means conduction only; larger Nu means convection enhances surface heat exchange. For flow over a flat plate, Nu ~ Re1/2 Pr1/3 (Blasius solution). Terrain features disrupt the boundary layer, locally increasing Nu at hilltops and in separation zones. Higher Nu means more entropy production at the surface.

Try it: increase Wind speed to raise Re and watch Nu grow. The thermal boundary layer thins, steepening temperature gradients at the surface.