Similarity

• Turbulent fluxes


  Fluxes such as sensible and latent heat flux that can be determined from gradients in the context of the surface energy balance
• Determining turbulent fluxes from gradients

  1. Discuss similarity relationships for vertical gradients

  2. Use similarity relationships to obtain expressions for vertical fluxes in terms of vertical gradients for neutral and non-neutral conditions

  3. Discover how turbulent diffusivity depends on height and stability

  4. Find a way to determine sensible and latent heat fluxes from vertical gradients of temperature and humidity
• Turbulent diffusivity


  The factor that connects fluxes to gradients, an efficiency of the transport mechanism
• Dimensional analysis to determine relationship between flux and gradient

  1. Identify relevant quantities

  2. Make dimensionless groups

  3. Conduct experiment to measure dimensionless groups

  4. Find unique relationship between dimensionless groups
• Vertical temperature gradient


  • Depends on surface heat flux, height, and intensity of turbulence
• Monin-Obukhov similarity theory (MOST)


  The particular set of variables and dimensionless groups that forms the basis for the analysis of turbulence in the atmospheric surface layer
• Stability indicator Z/L


  Negative for unstable conditions, positive for stable conditions, zero for neutral conditions
• Flux-gradient relationships (stability functions)

  Functions Φ that relate the dimensionless gradient to the stability indicator Z/L, with different forms for stable and unstable conditions
• Determining heat flux from temperature gradient

  1. Start with expressions for dimensionless temperature gradient and heat flux

  2. Derive expression for temperature scale Θ*

  3. Combine to get expression for heat flux in terms of temperature gradient

  4. Obtain expression for turbulent diffusivity
• Turbulent diffusivity is larger for unstable (daytime) conditions and smaller for stable (nighttime) conditions compared to neutral conditions