COMAP 1999 Downslope Wind Lab
Objectives:
Exercise I: Idealized Mountain Wave Simulations
The following exercise is based on a series of 2D mountain wave simulations for a family of idealized atmospheric profiles. This family of idealized atmospheric profiles is designed to illustrate how forward and reverse shear, layers of increased stability, and mean-state critical levels affect the characteristics of mountain waves. A smooth bell-shaped mountain profile,
otherwise known as a Witch of Agnesi profile, with a height, ho,
of 1.0 km and a half-width, a, of 10 km was used in each of these simulations.
Reference simulation
The imposed background flow for the reference simulation is characterized by a constant
static stability (N) of 0.01 s-1 and a constant cross-barrier wind speed
(U) of 15 ms-1.
The Scorer Parameter for this particular flow (l = N/U) is constant with height.
The cross-barrier wind speed does not equal zero at any level (U(z) ¹ 0), so the flow does not contain a mean-state critical level. The
potential temperature, horizontal velocity, and vertical velocity fields generated by the
interaction between this background flow and the smooth bell-shaped mountain profile are
shown in the following panels:
This combination produces a vertically-propagating mountain wave. Note the upstream tilt of the phase lines clearly evident in the horizontal and vertical velocity fields. This upstream tilt is indicative of upward energy propagation. The horizontal velocity perturbations associated with this vertically-propagating mountain wave decelerate the flow near the surface along the windward slopes and accelerate the flow along the lee slope. This behavior is consistent with the predictions of linear theory, which, in turn, suggests there is a natural tendency for mountain waves to accelerate flow in the lee of significant terrain. Also note the region of small negative horizontal velocities directly above the mountain at ~15 km. This region corresponds to a region of vertically-orientated isentropes (¶q/ ¶z£ 0). The mountain wave is just beginning to overturn or break in this region. Since a region of wave breaking corresponds to a region where the total horizontal velocity (U + u’) goes to zero, this region is referred to as a wave-induced critical level. Note that the presence of a wave-induced critical level does not guarantee the formation of the shooting-type lee-slope flow indicative of a downslope windstorm.
Influence of shear and layers of increased stability on mountain wave structure:
The following exercise will take you through a number of variations on the above-described reference basic state that will illustrate how the structure of the mountain wave responds to the addition of wind shear and/or layers of increased stability. As you work through each case, start by familiarizing yourself with the characteristics of the imposed background flow, answer the set of questions prior to viewing the output fields for each of the six cases, and then view the output fields to see how well your answers agree with the results from the numerical simulations.
Initial conditions
The imposed background flow for Case 1 is characterized by a constant static stability (N) of 0.01 s-1, constant-wind-speed layers below 2 km and above 8 km, and forward shear between 2 and 8 km.
MODEL FIELDS:
Potential Temperature
Horizontal Velocity
Vertical Velocity
Initial conditions
The imposed background flow for Case 2 is characterized by a constant static stability (N) of 0.01 s-1, constant-wind-speed layers below 2 km and above 8 km, and reverse shear between 2 and 8 km.
MODEL FIELDS:
Potential Temperature
Horizontal Velocity
Vertical Velocity
Initial conditions
The imposed background flow for Case 3 is characterized by a constant static stability (N) of 0.01 s-1, constant-wind-speed layers below 2 km and above 6 km, and reverse shear between 2 and 6 km. Note that the shear in Case 3 is weaker than that for Case 2 and extends over a shallower layer.
MODEL FIELDS:
Potential Temperature
Horizontal Velocity
Vertical Velocity
Initial conditions
The imposed background flow for Case 4 is characterized by three layers of constant static stability (0.01 s-1, 0.025 s-1, 0.01 s-1, respectively) and a constant wind speed of 15 ms-1.
MODEL FIELDS:
Potential Temperature
Horizontal Velocity
Vertical Velocity
Initial conditions
The imposed background flow for Case 5 is also characterized by three layers of constant static stability (0.01 s-1, 0.025 s-1, 0.01 s-1, respectively) and a constant wind speed of 15 ms-1, but the middle layer has been moved upward 2 km.
MODEL FIELDS:
Potential Temperature
Horizontal Velocity
Vertical Velocity
Initial conditions
The imposed background flow for Case 6 combines the static stability profile from Case 4 with the wind profile from Case 2.
MODEL FIELDS:
Potential Temperature
Horizontal Velocity
Vertical Velocity
