A Foul-Weather Fountain 255 a plaza-sized fountain, our model will be more accurate, since our formulas for breakup and drag force are derived under less extreme conditions Wind Flow Through the Plaza Buildings and other structures in an urban environment can cause signif- icant disturbances to wind flow patterns; rooftop and street-level conditions can often be quite different. To model the plaza wind, we assume There are no significant structures between the buildings beside of the plaza The plaza is large, so effects caused when wind flow leaves the plaza negligible at the plaza center; the significant effects are entirely caused at inward boundary passage The air flow is smooth enough so that turbulent vortices are negligible Formulation We approximate the geometry of the plaza as in Figure 3 and use complex analytic flow techniques[ Fisher 1990, 225 Plaza Figure 3. Schematic representation of the relevant features of the plaza With a Schwarz-Cristoffel mapping of a smooth horizontal flow from the upper half of the complex plane onto the region above the plaza, we obtain a flow function for the wind as it enters the plaza area r0={(+(2-1y12+kg(++(+i92-1y/)} where t parametrizes a streamline for each value of c. These streamlines are plotted in Figure 4, where the acceleration of the wind as it passes over the building edge and the decreased velocity in the plaza are both clearly visible The flow velocity v is inversely proportional to the streamline spacing, so the horizontal component of it is O dcA Foul-Weather Fountain 255 a plaza-sized fountain, our model will be more accurate, since our formulas for breakup and drag force are derived under less extreme conditions. Wind Flow Through the Plaza Buildings and other structures in an urban environment can cause signif￾icant disturbances to wind flow patterns; rooftop and street-level conditions can often be quite different. To model the plaza wind, we assume: • There are no significant structures between the buildings beside of the plaza. • The plaza is large, so effects caused when wind flow leaves the plaza are negligible at the plaza center; the significant effects are entirely caused at the inward boundary passage. • The air flow is smooth enough so that turbulent vortices are negligible. Formulation We approximate the geometry of the plaza as in Figure 3 and use complex analytic flow techniques [Fisher 1990, 225]. Figure 3. Schematic representation of the relevant features of the plaza. With a Schwarz-Cristoffel mapping of a smooth horizontal flow from the upper half of the complex plane onto the region above the plaza, we obtain a flow function for the wind as it enters the plaza area: Γc(t) = h0 π (t + ic) 2 − 1 1/2 + log  t + ic + (t + ic) 2 − 1 1/2 , where t parametrizes a streamline for each value of c. These streamlines are plotted in Figure 4, where the acceleration of the wind as it passes over the building edge and the decreased velocity in the plaza are both clearly visible. The flow velocity v is inversely proportional to the streamline spacing, so the horizontal component of it is vx = Im  ∂Γc ∂c .