chapter 4: surface roughness & local advection

Question 1

aerodynamic

Answer 1

study of the properties of moving air and the interaction between the air and solid bodies (land)

Question 2

wind profile relations involve the parameters:

Answer 2

• zero plane displacement (d)
• aerodynamic roughness length (z0)

Question 3

aerodynamic charactaristics of the land

Answer 3

• zero plane displacement (d)
  
  • if the height of the PBL > 10x canopy height than the height above the tree tops can be neglected
• Aerodynamic roughness length (Z₀)
  
  • For NEUTRAL conditions: the height at which the wind speed becomes zero
  • can change with individual roughness elements (higher roughness means higher Z₀)
    
    • height and coverage
    • errection of fences
    • deforestation
    • construction of houses
  • cannot change with
    
    • wind speed
    • stability
    • wind sress
  • Z₀ < the physical height

Question 4

zero plane displacement (d) equation

Answer 4

d- zero plane displacement

z0- aerodynamic roughness length

for z> 10 hc then d can be neglected

Question 5

aerodynamic roughness lenght can be estimated as:

Answer 5

where S_L= (total ground surface area)/(no. of elements)

S_L: the lot size per element

Question 6

Z₀ depends on

Answer 6

individual roughness elements:

• h^*: vertical ht of roughness elements (average)
• S_s: average vertical cross section area presented to the wind by one element (how much cross section the wind cross)

Question 7

if a garden is planted with 1000 trees per square km. where each tree is 4 m tall and has a vertical cross section area of 5m². calculate Z₀

Answer 7

ans: 0.5h^*(Ss/S_L)

=0.5 (4)(5/100)

=0.01

S_L=1 km/1000= (1000x1000)/1000

=1000

Question 8

For aerodynamically smooth flow, Z₀ can be expressed as

Answer 8

(when the viscous sublayer is deeper than surface roughness protuberances)

v= kinamatic viscosity coeff

u*0 = friction velocity at the surface

Question 9

wind flow over canopy and within canpy

Answer 9

• without: logarithmic increase
• within: increase in the middle then reduce at top of canopy and then exponentially increase

within canopy, branches and leaves (diffusivly distributed) act as a sink for momentum

the mean wind speed and shearing stress decay with depth bellow the canopy top

Question 10

wind flow over canopy and within canpy

wind profile results in

Answer 10

exponential form

n: coeffecient depends on canopy density and structure

values between 1 to 4

Question 11

temperature and humidity profiles within canopy

Answer 11

• temperature profile shows maximum near mid canopy
• humidity decreases upwards with largest gradient near the ground

Question 12

flow over the sea

Answer 12

differe from that over land because of

• large heat capacity of the oceans
• mobile wavy nature of the ocean/sea surface

flow over sea follows logarithmic wind profile but modified due to mobile nature of the sea

us is the surface drift velocity

Question 13

Z0 for smooth flow (light wind)

Answer 13

Question 14

Z0 for rough flow (strong winds)

Answer 14

alpha is the charnocks constant

𝑔, as an essential dynamic parameter and characterizes the

• equilibrium between wind and waves, with the spectrum of gravity waves acting as roughness elements.

Question 15

drag coefficients:

Answer 15

• used to quantifiy the resistance (or drag) of an object in a fluid environmnet (like air or water)
• dimentionless quantity while magnitude varies with roughness of the underlying surface

Question 16

drag coefficients under neutral conditions

Answer 16

C_DN= k²/ln(z/z_p)²

Question 17

drag coefficients for smooth flow

Answer 17

Question 18

drag coefficients for rough flow

Answer 18

Question 19

C_DN in terms of wind speed

Answer 19

Question 20

Internal boundary layer (IBL)

Answer 20

• occurs when sudden changes in surface roughness disturb the wind flow
  
  • suddent changes occur when wind flows from the current surface to new surface
  • the influence of the new surface on the wind flow depends on the charactaristics of the
    
    • new surface and
    • old surface
  • discontinuity in properties forms high gradient
    
    • therefore advection
• new equilibrium layer forms between the two surfaces called IBL

Question 21

the thickness (S_IBL) increases with

Answer 21

the distance from the edge

Question 22

compare wind profile above and bellow(inside) the IBL

Answer 22

• above: remains in balance with previous surface
• bellow (inside): adjusted to the new surface

there is a sharp discontinuity in the atm. properties across the IBL ht which results in advection

Question 23

Types of IBL

Answer 23

IBL caused by advection of air across discontinuity

• surface temperature
  
  • thermal IBL (TIBL)
• surface roughness
  
  • mechanical IBL (MIBL)

Question 24

local advection

Answer 24

the effects of surface changes do not propagate above the depth of IBL (S_IBL) is called local advection