Thermally-Driven Circulations in Mountain Terrain
Slope Winds
Terminology of slope winds
Upslope winds and downslope winds
Upslope winds are often called ‘anabatic winds’
Downslope winds also called:
drainage winds, katabatic winds
Theory of air drainage has a long history
Fleagle (1950) derived momentum equations for
A fluid cooling at the bottom of a sloped surface.
Manins and Sawford (1979)
Horst and Doran (1986)
z
1T1
2T2
PGF

1 p
 x
1 > 2
Buoyancy
g (T1  T2 ) =
T2
T1 < T2

x
Figure 1. Basic mechanisms of downslope winds (Adapted from Atkinson, 1981)
Momentum budget for slope flow
 
u
u
u
1 p
d
 u w
u
w 
 g sin  
t
x
z
 r x
r
z
I
II
III
IV
V
where u and w are velocity components in the x and z directions, r is a
reference density, p is the pressure, g is gravitational force, d is the
potential temperature deficit in the flow, r is the reference potential
temperature, and  is the slope angle.
Term I is the storage of momentum,
term II is advection,
term III is the horizontal pressure gradient force,
term IV is the buoyancy force,
term V is the turbulent momentum flux.
Heat budget for slope flow

 v
 v
 v
1 R  w v
u
w


t
x
z
 r C p z
z
I
II
III

IV
where v is virtual potential temperature, Cp is the gas constant
for dry air at constant pressure, R is the outgoing radiation flux,
and is the turbulent sensible heat flux.
The local rate of heat storage (term I) results from an imbalance
of convergence of virtual potential temperature by advection
(term II), radiative flux divergence (term III), and the
divergence of turbulent sensible heat flux (term IV).
The budget equations for pure katabatic flow have been derived
for simple situations assuming horizontally homogenous depth
along a slope of infinite length.
The slope angle for katabatic flows has been assumed to be very
small in the theoretical framework, and thus the flow to be in
hydrostatic balance.
Manins and Sawford (1979b) suggested that even in very
mountainous terrain, ‘extensive’ slopes were rarely above 10.
Furthermore, the cooling is based on the three terms (II, III, and
IV) in (1.2).
Horst and Doran 1986
Downslope flows (drainage flows)
Meteor Crater 2006
Campfire smoke plume-Shallow inversion Layer
Whiteman(2000)