An infinite Gaussian ridge with a height of 1000 m and half width of 5 km is used to simulate the scale of SHV. Vertical sounding values are applied to the right-hand side of the model with trade-wind-like (eastern boundary) flows with equivalent Froude numbers of 0.375 shown in Figure 3.14, 0.75 shown in Figure 3.15 and 1.5 shown in Figure 3.16. Due to the nature of the simulation there is no ’sideways’ component of horizontal wind and air cannot move horizontally around the ridge. Only the central part of the model is shown in Figures3.14-3.16. The F r = 0.375
Figure 3.14: 2D WRF flow across an infinite ridge shown in black, horizontal ve- locity is shown by wind barbs (ms−1) and vertical velocity is colour-coded (ms−1). Initial sounding equivalent to F r = 0.375 from the right.
initial wind forcing case shown in Figure3.14 has an area of uplift at the top of the ridge at the surface. Strengthening windspeeds correspond to an area of uplift that runs from the top of the ridge to the windward side with increasing height. This is consistent with the idea of a jet forming over the ridge.
The F r = 0.75 initial wind forcing case shown in Figure 3.15has deviation from a uniform wind field strengthening from the surface at about 10 km and 0 km to the windward side with increasing height. Between these two bands of increased wind
Figure 3.15: 2D WRF flow across an infinite ridge shown in black, horizontal ve- locity is shown by wind barbs (ms−1) and vertical velocity is colour-coded (ms−1). Initial sounding equivalent to F r = 0.75 from the right.
speeds there is a region of low wind speeds. The development of low windspeed linear mountain waves is evident in the vertical velocity field as a series of uplift and downdraft zones running from the leeside to the windward side, stronger on the leeside and strengthening in the lower levels across the top of the ridge.
The F r = 1.5 initial wind forcing case shown in Figure 3.16 shows increased horizontal winds at 0 km and an inclined zone of increasing uplift dipping to the leeside and decreasing in strength in that direction. A inclined down draft zone across the top of the ridge has increased winds in the lower levels. An inclined zone of uplift of smaller magnitude is tilted to the windward side.
In all cases linear mountain waves are present between the surface and 1 km [Hammouya, 1994].
Developing the WRF Montserrat Model (WMM): Results
Figure 3.16: 2D WRF flow across an infinite ridge shown in black, horizontal ve- locity is shown by wind barbs (ms−1) and vertical velocity is colour-coded (ms−1). Initial sounding equivalent to F r = 1.5 from the right.
3.4.1.2 3D mountain
A three dimensional approximation to a bell-shaped, symmetrical mountain of height 1000 m and spread of 4 km is used to simulate flow around an obstacle of the scale of SHV for 10 hours of simulation.
For the F r = 0.375, Figure 3.17, initial forcing case, surface flow is characterised by the formation of a well defined vortex pair in the mountain wake. On the wind- ward slope flow is opposed at the foot of the mountain but then changes to upslope flow over the mountain. Downstream of the mountain the vortices are centred on two areas ±2.5 − 5km of the centre of the y-axis. In the region between the vortex pair the flow is reversed and goes upslope. The wind on the central plane shows a very well defined layer of reversed flow, and a possible hydraulic jump after the mountain peak. Regions with significant vertical velocities are associated with the weak jump close to the mountain peak and the upwind formation of lee waves.
formation seen in Figure 3.12, even though the mountain in [Miranda and James,
1992] is larger and flattened at the summit (which may alter flow characteristics) and the Froude number in Figure3.12 is slightly less. These results are also similar to [Hunt and Snyder, 1980] and [Smolarkiewicz and Rotunno, 1989].
For the F r = 0.75, Figure 3.18, initial forcing case, there is a small vortex pair formed in the mountain wake and reversed flow on the windward slopes between the vortex pair. These are weaker and do not have as great extent as in Figure3.17. On the vertical plane mountain linear waves are forming above the lee and windward slopes and a hydraulic jump at the summit of the mountain.
These features compare well with the extent of the reduced reversed leeside flow and stronger mountain linear wave formation exhibited in Figure 3.13. The reduction is size of the vortex pair is also consistant with [Hunt and Snyder, 1980]. For the F r = 1.5 case, Figure 3.19, initial forcing shows no streamline splitting, the flow accelerating straight over the crest of the mountain. After the summit of the mountain there is an increase in the vertical component of the wind. Stronger linear mountain waves are forming and lower, at a height of about 50 m.
From these simulations we can expect in normal trade-wind conditions (F r = 0.375-F r = 1.5) that a mountain of similar size on Montserrat, e.g. Soufri‘ere Hills Volcano (SHV), will have reduced wind speeds on its windward side at the surface. If these trade winds are weak we can expect flow-splitting and increased wind speeds around the sides of the mountainl. If the trade winds are strong (F r = 1.5) we can expect flow over the mountain causing orographic convection on the leeward side accompanied by an increased wind strength. As the strength of trade winds increases we can also expect the formation of mountain linear waves of increasing strength.
The work of [Miranda and James, 1992] to explore wind velocity around a 3D mountain is consistant in its conclusions with my study. Therefore in normal trade- wind conditions (F r = 0.375-F r = 1.5) idealised mountain WRF models accurately represent true wind flow.
Turbulent water vapour fields are formed by wind-flow patterns. Regions of velocity stagnation are where water vapour pools and regions of increased velocity are where water vapour disperses. Therefore low and moderate trade-wind values (F r = 0.375 -F r = 0.75) will create a tendency for water vapour to split around a mountain like SHV whereas stronger trade-wind velocities (F r = 1.5 will create a tendency for water vapour to go over the summit of the mountain and pool on its leeside. This pattern should be more evident with the introduction of non-idealised modelling.
Developing the WRF Montserrat Model (WMM): Results
(a) y-plane.
(b) Surface level.
Figure 3.17: WRF simulated 3D flow over an approximation to a bell-shaped, isolated mountain. Initial sounding equivalent to F r = 0.375 from the right (east). (a) mountain shown in black, wind barbs (u,w) and vertical velocity is colour-coded (ms−1). Wind barbs vertical velocity multiplied by 4. (b) mountain contours lines every 100m in centre of diagram (grey), streamlines show direction of horizontal flow
(a) y-plane.
(b) Surface level.
Figure 3.18: WRF simulated 3D flow over an approximation to a bell-shaped, isolated mountain. Initial sounding equivalent to F r = 0.75 from the right (east). (a) mountain shown in black, wind barbs (u,w) and vertical velocity is colour-coded (ms−1). Wind barbs vertical velocity multiplied by 4. (b) mountain contours lines every 100m in centre of diagram (grey), streamlines show direction of horizontal flow (black) and corresponding wind speeds are colour-coded (ms−1).
Developing the WRF Montserrat Model (WMM): Results
(a) y-plane.
(b) Surfacel level.
Figure 3.19: WRF simulated 3D flow over an approximation to a bell-shaped, iso- lated mountain. Initial sounding equivalent to F r = 1.5 from the right (east). (a) mountain shown in black, wind barbs (u,w) and vertical velocity is colour-coded (ms−1). Wind barbs vertical velocity multiplied by 4. (b) mountain contours lines every 100m in centre of diagram (grey), streamlines show direction of horizontal flow