Environmental Fluid Dynamics

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Cornelius Lyons
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1 Environmental Fluid Dynamics ME EN 7710 Spring 2015 Instructor: E.R. Pardyjak University of Utah Department of Mechanical Engineering

2 Definitions Environmental Fluid Mechanics principles that govern transport, mixing and transformation processes in environmental fluids. (e.g., physical, biological, chemical) Includes Stratification & Rotation Micrometeorology - deals with atmospheric phenomena and processes at the smaller end of the spectrum of atmospheric scales and near the earth s surface (atmospheric boundary layer - ABL). Fine scale structure is important Microclimatology same physical scales much longer time averaging scales

3 Environmental Fluid Dynamics Integrates different aspects of Thermal- Fluids Science (Not just Fluid Mechanics!) Fluid Mechanics Thermodynamics Heat Transfer (conduction, convection and radiation) Mass Transfer

4 Applications Urban Planning Air Quality (Criteria pollutants, Greenhouse gases, accidental releases) Energy and Water Budget s Green Infrastructure Defense Strategies Toxic releases bio/chem/rad Agriculture & Forest Meteorology (Evapotranspiration and Water Budget) Aeronautical Meteorology Wind Engineering Numerical Weather Prediction and Climate Simulation Many more

Scales of Motion Synoptic scales (100+ km) Meso-scale (10-1000 km)

5 Scales of Motion Synoptic scales (100+ km) Meso-scale ( km) Micro-scale (<1m - 10 km) Engineering scale (viscous - 10 m) Urban Scales (1m 100km)

6 Time and Space Scales Figure 1.1 Boundary Layer Climates Oke, 1987

7 More on Scales From Meteorology for Engineers and Scientists, Stull

8 Boundary Layer Research Aerodynamic Boundary Layer 1870s Froude carried out tow take experiments to study friction a flat plate 1905 boundary layer likely coined by Prandtl thin region of the flow near the wall where frictional effects are confined 1908 Blasius solution laminar boundary layer Atmospheric Boundary Layer -

9 Atmospheric Boundary Layer (ABL) Def. the part of the troposphere that is directly influenced by the presence of the earth s surface and responds to forcing on time scales of 1 hour or less Characterized by well developed mixing (turbulence) generated by: the atmosphere moving across the earth s rough surface mechanically driven turbulence by the bubbling up of air parcels from the heated earth buoyancy driven turbulence This turbulence is responsible for much of the heat transfer from the earth s surface to the atmosphere sensible heat flux

10 Diurnal Cycle of the Convective Boundary Layer over Simple Terrain (Stull, 1988) Note: this is an idealized view of the diurnal cycle typical of calm and clear days and nights in the desert southwest U.S., significant synoptic scale weather systems disrupt this cycle

11 Daytime Convective ABL sub-layers: Free atmosphere Entrainment zone Mixed layer Surface layer θ (Κ) U(m/s) RH

12 Early night time temperature and humidity profiles Temperature Potential Temperature Virtual Potential Temperature Relative Humidity Temperature (K) θ (K) θ v (K) RH %

13 ABL Surface Layer (Inner-Layer) sub- Layers: Inertial sub-layer variation in vertical fluxes <10% - loglaw wind profile Planetary Boundary Layer ~ 1-3km Inversion Outer Layer (Eckman Layer) Roughness sublayer O(H), Horizontal Heterogeneity Surface Layer ~ 10% of PBL ( m) Inertial Sublayer Laminar sublayer <1-2 mm Roughness Sublayer 1-3 H Laminar sublayer H canopy Roughness Elements

14 In this Environmental Fluid Dynamics Class we will focus On the following scales: Vertical < 3km Horizontal < 50 km (micro to meso-scale) Time scale ~ 1 day Night vs. Day

15 Transport in the ABL Mass pollutants particles water biological process - pollen Heat Sensible Heat Flux Latent Heat Flux Momentum Surface drag urban vs. rural vs. ocean/lake/sea Spatial variation We will need to develop equations to describe these processes

16 Stratification Variation of density with space Most introductory Engineering Fluid Mechanics classes focus on constant density problem or neutral boundary layers We will mostly consider ρ = ρ(z) The density variation in the atmosphere will typically be dominated by variations in temperature and humidity.

17 Rotation For much of the class we will neglect rotation effects, but when is rotation important? Rossby number: Ro = Inertial Rotational = U fl r f = 2Ωsinϕ ϕ Latitude Ω = Lr 5 rad / s relevant length scale Angular speed of rotation of the earth If R o >>1, rotation is assumed negligible (i.e. Coriolis acceleration is less than horizontal acceleration.

18 Example EFD Surface Layer Field Experiment PAFEX-I Setup 9.0m 3 Tethersonde Aerosol Sampler Radiation Balance Antenna 3D ATI Sonic NO x No y, O 3 Particles PC, Receiver and Processor

19 MATERHORN Experiments 172 Towers + 90 Sonic Anemometers

20 Basic Surface Energy Balance Ideas We will expand on these ideas later as we derive formal transport equations for responsive fluxes These initial ideas will allow us to understand the basic mechanisms of heat transfer near the surface of the earth

21 Radiation Balance Ideas R L R S ΔH A R L ΔH S R S H L H S R L Daytime Example H G

22 Near Surface Energy Balance (SEB) Energy Balance at the earth s surface Net Radiation ~ Response Fluxes Net Radiation is composed of: Incoming and Outgoing Solar and Long Wave Radiation Responsive Fluxes include: Sensible, Latent, Ground Heat Fluxes Wm -2 1 m 1 m

23 Why is it important? Energy/Water Use (Solar, Geothermal) Urban Heat Island Agriculture freezing/thawing Air quality Thermodynamic/fluid mechanic interplay

24 Radiation Balance Ideal Surface R N One Dimensional Balance Sign Convention H S H L H G All radiative fluxes that point toward the surface are positive All non-radiative fluxes that point away from the surface are positive R S R S R L R L R = H + H + N S L H G Assumptions about the surface: Thin no mass (heat capacity) Flat Horizontally homogenous Opaque

25 Radiation Balance Ideal Surface All radiative fluxes that point toward the surface are positive R N = R S +R S +R S +R L R S R S R L R L R s Shortwave Radiation: ~ µm (Solar) R L Longwave Radiation: ~ µm (Terrestrial)

26 Surface Energy Budget Daytime (over land) R N H S H L R = H + H + N Forcing Term S L H Response Terms G H G Nighttime (over land) R N Types of Energy Fluxes at the Surface 1. Net Radiation (R N ) 2. Sensible Heat Flux (H S ) 3. Latent Heat Flux (H L ) 4. Ground Heat Flux (H G ) H S H L H G Assumptions about the surface: Thin no mass (heat capacity) Flat Horizontally homogenous Opaque

27 Surface Energy Budget Finite Thickness Layer R N = H S + H L + H G + ΔH S Summer Fluxes Forcing Term Δ Response Terms Types of Energy Fluxes at the Surface 1. Net Radiation (R N ) 2. Sensible Heat Flux (H S ) 3. Latent Heat Flux (H L ) 4. Ground Heat Flux (H G ) 5. Heat Storage (ΔH S ) H S = ( ρct )dz t Storage can become particularly important in complex canopies such as urban areas and forests

28 Surface Energy Budget Finite Thickness Layer R N = H S + H L + H G + ΔH S Forcing Term R N Response Terms H S H L ΔH S H G Flux Convergence H in Flux Divergence H in Assumptions about the surface: Flat Horizontally homogenous Opaque ΔH S >0 H out H out ΔH S <0

29 Surface Energy Budget Mountainous Terrain - Switzerland

30 Radiometer Urban Energy Balance Q * Q H & Q E Wind Q F ΔQ S Must consider: Radiation Conduction Convection What about Energy? Q * + Q F = Q H + Q Q * = net all-wave radiation Q F = Anthropogenic heat flux Q H = Latent heat flux Q E = Senisble heat flux ΔQ S = Heat Stored E Sensible/Latent Heat Flux + ΔQ S

31 Air Pollutant Transport in the Urban Atmospheric Surface Layer F EC Wind F B F SR F H F T F S F = F + F + F + F + EC Anthropogenic Contributions Carbon Dioxide Net Ecosystem Exchange SR B T H F SR = flux of CO 2 due to soil respiration F B = flux of CO 2 due to other biogenic contributions (e.g. photosynthesis) F T = flux of CO 2 due to traffic F H = flux of CO 2 due to heating F F S = flux of CO 2 due to other household services S See Oke 1988

32 BR Bowen Ratio = H H s = L Sensible Latent Estimate BR from balloon profile or local gradients: BR θ γ z qv z Psychrometric constant - γ: C p γ = = (g water /g air )K -1 L e (NOTE: we are avoiding some issues associated with turbulence temporarily):

33 Bowen Ratio Typical BR Values: Sea 0.1 irrigated crops 0.2 Grassland 0.5 Semi-arid regions 5 Deserts 10

Atmospheric Sciences 321. Science of Climate. Lecture 13: Surface Energy Balance Chapter 4

Atmospheric Sciences 321. Science of Climate. Lecture 13: Surface Energy Balance Chapter 4 Atmospheric Sciences 321 Science of Climate Lecture 13: Surface Energy Balance Chapter 4 Community Business Check the assignments HW #4 due Wednesday Quiz #2 Wednesday Mid Term is Wednesday May 6 Practice