On the Single-Layer Hydraulics Model for Flows and Ventilation over Unban Areas in Stable Stratification

Abstract:

Atmospheric stability has substantial effects on the flows and heat/mass transport processes. While extensive studies have been conducted for neutral and unstable stabilities, rather limited studies have been devoted to stable stratification. Major technical reason is the demanding spatio-temporal resolution required to solve the small scales in stratified turbulent flows.

Instead of continuous density variation, we use the single-layer hydraulics model (analogous to shallow water equations for global dynamics), to simulate the stratified flows and turbulence structure over hypothetical urban areas. An array of identical ribs in cross flows is used to model an idealized urban surface and the aerodynamic resistance is controlled by the separation among the ribs. Two immiscible fluids (water and air) with a large density difference (three order of magnitude) are used to simulate the stratification. The key assumption is that the density in the (lower) single layer is uniform. As a result, the stratification is measured by the Froude number Fr (= U/(gH)^1/2; where U is the flow speed, g the gravitational acceleration and H the single-layer depth).

One of the characteristics of single-layer hydraulics model is hydraulic jump which occurs when the flows are slowing down from Fr > 1 (high-speed flows over smoother surfaces) to Fr < 1 (lower-speed flows over rougher surfaces). It is noteworthy that kinetic energy does not conserve across hydraulic jump that, unavoidably, cascades to turbulent kinetic energy (TKE). We thus hypotheses that the elevated TKE could modify the street-level ventilation mechanism in the stratified flows across an abrupt change in surface roughness entering urban areas.

Large-eddy simulation and laboratory-scale water channel experiments are sought to improve our understanding of the occurrence of hydraulic jump and the associated street-level ventilation mechanism in the stratified flows over urban areas. Preliminary results, by comparing the dynamics at Fr = 2.4 and Fr = 2.8, demonstrate the notable changes in ventilation performance in the first several rows of ribs of urban areas. Substantial changes in the mean and fluctuating velocities are observed that contribute to the different street-level ventilation mechanism. Detailed results will be reported in the upcoming AGU fall meeting.