Introduction
Urban heat islands (hereinafter UHIs) are defined as the warmth produced by cities [see Oke (1995) and Fernando et al. (2001) for comprehensive reviews]. The difference in terrain coverage of urban and rural areas is mainly responsible for nighttime and daytime urban–rural temperature differences that can reach, in the case of large cities, 10°C or more. During the day, concrete and asphalt store larger amounts of incoming solar radiation than those typically retained by grassy rural terrain. As a consequence, the upward sensible heat flux of urban soils is greater than that of their rural counterparts. If the retained energy is sufficiently large, the upward sensible heat flux can persist during the night, giving rise to nocturnal urban mixed layers. Therefore, urban boundary layers may form above cities during both daytime and nighttime, with peculiar characteristics with respect to atmospheric boundary layers generally existing in rural areas.
If synoptic winds are absent or weak, the flow pattern associated with the UHI generally consists of a closed circulation characterized by strong updraft motion (thermal plume) at the city center, by horizontal convergent flow above the surface, and by divergent flow at the elevated layers. A slow downdraft far from the city closes the circulation. The UHI circulation plays a significant role in contaminant dispersion in cities, particularly in winter, when vehicular traffic and pollutant emissions from domestic heating can lead to exceptionally poor air quality.
Most studies found in literature describe UHIs by means of field experiments (cf. Bornstein 1968; Shreffler 1978; Uno et al. 1988, 1992) or numerical approaches (Estoque and Brumalkar 1969; Bornstein 1975; Saway 1978; Richiardone and Brusasca 1989). Raman and Cermak (1974, 1975), Torrance (1979), Giovannoni (1987), Noto (1996), and Lu et al. (1997a,b) demonstrated how the basic features of UHIs can also be investigated by means of laboratory models.
Because many large cities are located in the vicinity of shorelines, it is also of great interest to investigate the circulation associated with the interaction between a UHI and a sea breeze. Basic aspects of such a flow have been described in the past by several authors through field observations and numerical experiments. Remarkable contributions have been made by Yoshikado (1990a, 1992) by means of a two-dimensional hydrostatic boundary layer model configured to simulate the circulation associated with a large urban complex (Tokyo, Japan). He showed that UHIs adjacent to the coast produced an intensification of the sea-breeze velocity, in particular during their growing stage. In addition, he showed that the inland penetration of the sea-breeze current was delayed by several hours and that pollutants emitted from sources located above the urban area stagnated above the inland side of the city until the arrival of the sea-breeze front. Similar characteristics have been observed in field experiments conducted in the Tokyo region (Yoshikado and Kondo 1989; Yoshikado 1990b; Yoshikado and Tsuchida 1996). Yoshikado (1994) also examined the role played by the size, the distance from the shore, and the heating anomaly of the city (UHI intensity). In particular, he found that significant disturbances of the sea-breeze current arose if the city width exceeded 10 km and that the intensification of the sea-breeze velocity decreased as the city was shifted inland. Yoshikado (1994) also noted that, contrary to the case of cities adjacent to the sea, when the urban complex was located away from the shore the UHI and the sea breeze interacted in a stronger way. He explained this result by conjecturing that inland UHIs have enough time to reach a mature stage before the arrival of the sea breeze. As a result, they can pose a more effective obstacle to the landward advance of sea-breeze currents.
More recent, Ohashi and Kida (2002), using a 3D mesoscale incompressible hydrostatic atmospheric model, analyzed the circulation associated with two nearby urban areas: one coastal and one inland. Among the main results, they found the presence of a chain flow, that is, a current from the upper layer of the coastal urban area directed downward to the lower layer of the inland urban area. They also noted that the chain flow amplified the transport of scalars (pollutants and heat) toward the inland urban area with respect to the case without the coastal city.
Although the aforementioned studies covered a broad class of situations, it is instructive to pay more attention to the case of inland UHIs located away from the shore. As stated earlier, their interaction with sea-breeze flows shows different dynamics as compared with coastal UHIs. Therefore, given the large number of situations in which cities are located several tens of kilometers away from the shore, focusing on inland UHIs seems particularly appropriate. The main objective of this study is to investigate in the laboratory the flow field induced by the simultaneous presence of an inland three-dimensional daytime low-aspect-ratio UHI and a sea-breeze current, in the absence of prevailing winds.
As is well known, one of the advantages of using laboratory models lies in the fact that it is generally easy to control the boundary conditions and to analyze accurately the role played by the nondimensional variables governing the flow field. However, note that it is sometimes complicated to attain the matching of nondimensional parameters of models with their full-scale flow counterparts. For example, the major restriction in laboratory simulations of UHIs is caused by the difficulty in reproducing the small aspect ratio (urban boundary layer height–UHI diameter ratio) typically observed in real environments. Also, details on vegetation, street canyons, and buildings, as well as investigations of their effects on UHI circulations, are too fine to be resolved with laboratory models.
The experiments described here were performed in a temperature-controlled water tank, the same one employed by Cenedese et al. (2000) to investigate land and sea-breeze flows that occur in coastal zones. The experimental and data analysis methods used are given in section 2. The study considered three basic configurations. The first one concerned the simulation of a UHI that develops in a calm, stably stratified environment (nocturnal UHI) without influences from other local and large-scale circulations. The results, discussed in section 3a, were compared with those based on a similar laboratory experiment (Lu et al. 1997a,b), on field data (Clarke 1969; Clarke and McElroy 1974; Uno et al. 1988), and on numerical simulations (Yoshikado 1992). In the second configuration, described in section 3b, basic characteristics of daytime UHIs and differences from nocturnal UHIs were examined. The former takes place during the day, when statically unstable situations occur. Section 3c describes the analysis of the flow pattern associated with the simultaneous presence of an inland daytime UHI and a sea-breeze current. It was found that the resultant circulation differs considerably from that associated with the interaction between a sea breeze and a coastal UHI that was examined in previous works (Yoshikado 1992; Ohashi and Kida 2002). The paper concludes with a summary and discussion in section 4.
Experimental setup and flow parameters
Experiments were performed in a water-filled rectangular tank (Figs. 1, 2) with a length L of 1800 mm, a height H of 95 mm, and a width of 600 mm (along the x, z, and y axes, respectively) that is open at the top and has a horizontal aluminum surface at the bottom. To observe the flow visually, the lateral sides of the tank were made up of 10-mm-thick transparent glass. The bottom was divided into two sections. The temperature TS of the left section (“sea side,” Fig. 2) was kept constant by means of a heat exchanger connected to a heating bath circulator; a heating–cooling bath circulator (thermocryostat) controlled the temperature TL of the right section (“land side”). By doing so, it was possible to simulate both the constant temperature maintained by the sea surface throughout the day and the diurnal changes of temperature experienced by the terrain under the effect of solar heating. The separation line between the two sections represented the “coastline.” To produce the needed ambient thermal stratification, dTa/dz (here Ta represents the ambient temperature), the temperature TU of the upper surface was set to a constant value by means of a third heat exchanger. In so doing, a linear thermal stratification was established by molecular diffusion. A polystyrene sheet was placed over the top of the tank to reduce heat losses. The temperature of the sidewalls was not controlled, but it could be reasonably considered as constant throughout the experiments.
The surplus of surface heat flux H0 between the city and its rural environment was simulated by means of a thin (∼0.2 mm), circular-shaped electric heater (diameter D = 100 mm), whose center was placed above the land side at ΔxUHI = 450 mm from the coastline. The setting of H0 was obtained by means of a suitable power supply. Notice that, because of the geometry of the heater, in the absence of sea breeze the flow was axisymmetric.
Information about flow kinematics has been extracted by using particle-tracking velocimetry (PTV), a nonintrusive technique based on tracking of nonbuoyant seeding particles dispersed within the flow. PTV is a reliable method that can yield very accurate, simultaneous velocity measurements over a wide area of a flow field. Among the previous applications, PTV has been successfully employed in laboratory simulation studies of turbulent convection in the atmospheric boundary layer (Querzoli 1996).
The studied area was rectangular, lying in the vertical x–z plane orthogonal to the coastline and passing through the center of the electric heater (Fig. 2). A thin laser light sheet from a 3-W argon laser beam passing through an optical device illuminated the measurement plane. The water was seeded with pine pollen particles (∼80 μm in diameter), which were assumed to be passively transported by the flow. The framed area was Δx = 200 mm long (x axis) and Δz = 48 mm tall (z axis). We define the origin (x = 0, z = 0) at the center of the heater, where x is positive downwind from the heater and is negative upwind. Along the longitudinal direction, the investigated domain lay in the range −1 < x/D < 1, the electric heater was in −0.5 < x/D < 0.5, and the coastline (upwind of the framed area) was located at x/D = −4.5.
After the thermal stratification was established and the seeding particles were uniformly dispersed in the tank, the heater was turned on. A set of images was taken during each experiment by means of a charge-coupled-device video camera at 25 Hz for a sampling interval of Δtsamp = 1800 s. One out every four frames was automatically retrieved by using an animation controller, lowering the resulting sampling rate to 6.25 Hz. This value can be considered as a compromise among the needs to collect high-frequency velocity data, to warrant quantitative discussions on turbulence analysis, and to restrict the amount of data. However, because of slow flow velocity, a rise in sampling rate did not make significant improvements in the results. After the experiment, each frame was digitized by a frame grabber with 752 × 576 pixel resolution and 256 gray levels. Particles were recognized on each digitized frame, and the locations of the particles' centroids were computed and stored. From the trajectories evaluated at each instant from the centroid positions, the instantaneous Lagrangian velocity field was obtained by using two sequential (in time) frames and differencing. A Gaussian interpolation algorithm was applied to the velocity samples to obtain a two-dimensional Eulerian description of the motion at a rate of 6.25 Hz on a 40 × 20 regular grid along the x and z axes, respectively.
Temperatures were taken using 10 T-type (copper–constantan) thermocouples placed on a vertical rake, equally spaced every 4 mm in the vertical direction from 0 to 36 mm, at a sampling rate of 1 Hz for the same time interval Δtsamp used for the velocity measurements. Several temperature profiles were carried out at various x/D by repeating the experiments.
Because of the nonstationary nature of the flow field, the averaging time interval was chosen with caution. This choice will be discussed in section 3 in which measurements of the UHI circulation are presented.
Lu et al. (1997a) showed that, in calm and stably stratified environments, UHIs can be properly modeled by combining only three parameters: the heater diameter D, the ambient thermal stratification dTa/dz, and the surface heat flux H0. They also showed, by means of a bulk convection model, that for fully turbulent flows the Froude number Fr = U/(ND) was the only nondimensional parameter that governs the dynamics of low-aspect-ratio thermal plumes. Here, U = [(gβDH0)/(ρ0cp)]1;cl3 is the horizontal velocity scale (W = UFr is the vertical velocity scale and D/U is the timescale), N = (gβdTa/dz)1/2 is the Brunt–Väisälä frequency, g is the acceleration due to gravity, β is the thermal expansion coefficient, ρ0 is the ambient density, and cp is the specific heat. For fully turbulent flows, in fact, molecular diffusion is negligible with respect to turbulent diffusion; therefore, the basic characteristics of the flow field are insensitive to the assumed value of the Prandtl number Pr = ν/κ (where ν and κ are the kinematic viscosity and the thermal diffusivity, respectively). As a consequence, if the previous condition is satisfied, the choice to use water (Pr ≅ 7) instead air (Pr ≅ 1) as a working fluid does not put restrictions on the validity of the model. In a similar way, by keeping the Reynolds number (in terms of Re = UD/ν) above a certain critical value, the simulated large-scale structures and the mean flow can both be considered to be independent of Re (Reynolds number independence, see Snyder 1981). It will be shown in the next sections that, despite the low Reynolds numbers attained in our experiments (<103), the simulated flow fields were turbulent and the results showed only a slight dependence on Re. This result suggests that, in our laboratory model, Snyder's (1981) criterion for Reynolds number independence was satisfied. It is of note that the large discrepancy between the simulated Re and those typically observed in full-scale UHIs (Re ∼ 109) lay down limits only on the correct simulation of the small-scale structures.
Last, we point out that some problems arose in modeling the Froude numbers detected in full-scale UHIs. In fact, observations (Oke 1995) have shown that in real-world UHIs the Froude number typically falls in the range of 0.002–0.025. Because of the small size of our water tank, the Froude numbers attained in our experiments were always above 0.025. Nevertheless, it will be shown that the large-scale structures simulated in the vessel and those of full-scale UHIs are, within reasonable approximation, dynamically similar.
Results and discussion
As previously mentioned, three types of experiments were performed, namely, the UHI that develops in a calm, stably stratified environment (nocturnal UHI, hereinafter situation A), the UHI that develops in a statically unstable environment (diurnal UHI, situation B), and the interaction between a daytime UHI and a sea-breeze flow (situation C). Five values of H0 were prescribed for each one of the above situations. Thus, a total of 15 cases (cases i.A, i.B, and i.C, where i ranged from 1 to 5) were examined as listed in Table 1.
The nocturnal UHI
The temperature of the two bottom sections was set at the same value TL = TS = 27°C, and the temperature of the upper surface was kept at TU = 46°C. The resulting (constant with height) ambient temperature gradient was dTa/dz = 200°C m−1, corresponding to a Brunt–Väisälä frequency N of approximately 0.7 s−1.
Qualitative observations made during the UHI circulation growth after the heater was turned on were in agreement with those of Lu et al. (1997a). At first the UHI rapidly grew and developed until it was arrested by buoyancy effects. At large times, the circulation grew very slowly. In Fig. 3, the trajectories over 20 frames (duration ∼3 s) from case 4.A at t = 700 s are shown. The picture shows a quasi steady state of the flow, that is, when the circulation was fully established and sidewall effects were still negligible. The classical type of axisymmetrical convective cell is clearly visible, with the thermal plume axis at the center of the heater (x/D = 0), the converging flow above the bottom, and the diverging flow at the upper levels. Note that the diameter of the thermal plume became narrower with height (a feature of area-source plumes) and that the plume contraction ratio, namely, the ratio of minimum plume diameter to UHI diameter, was ∼0.25. This value fell in the range of 0.2–0.5 reported by other authors (cf. Husar and Sparrow 1968; Stout 1986; Lu et al. 1997b).
A salient feature was that the vertical plume oscillated with time, an occurrence typically observed when a fluid is heated from below (natural swaying motion). Inspection of the experimental data showed that the smaller H0 was, the larger was the time period of the plume oscillations (∼100 s for case 1.A). Because analysis of such an instability was beyond the scope of this study, the averaging time interval was set to Δtaver = 300 s. This value was substantially greater than the plume oscillation period and was sufficiently large to collect a substantial number of samples to warrant quantitative discussions of turbulence characteristics.
For given dTa/dz and D, the time at which the nearly steady condition of the flow occurred depended on the horizontal velocity scale U. Visual observations of the flow showed that, for all of the cases reported in Table 1, the UHI circulation reached a quasi steady state a few minutes after the heating started (∼30D/U). This condition continued to be valid for about 20 min, when the induced circulation arrived at the sidewalls and began to be influenced by them. To provide evidence for the reaching of the quasi steady state of the flow, a succession of time averages of velocity and temperature, performed by moving Δtaver along Δtsamp, were evaluated (not shown). It was found that when Δtaver was centered at time instants exceeding t = 1000 s, the averages did not vary appreciably for all of the cases studied. For this reason, averages and turbulent statistics in the following discussion have been calculated with Δtaver centered at t = 1000 s.
Figures 4a and 4b show the mean temperature profiles taken at various radial distances from the UHI center for cases 2.A and 4.A, respectively. Both figures illustrate that, except for the superadiabatic surface layer adjacent to the bottom, inside the middle portion of the UHI (x/D = 0 and 0.25), the temperature did not vary appreciably with height. In converse, outside of the heater (x/D = 0.75) the boundary layer remained stably stratified and was signified by a temperature profile similar to that imposed for the ambient temperature Ta. Given the temperature profiles, it appeared that the resulting UHI circulation was dome shaped, was characterized by well-mixed conditions within its central region, and had a maximum depth at x/D = 0. In particular, Fig. 4b (case 4.A) shows that at x/D = 0 the temperature was nearly constant in the vertical range 0 < z < zi = 20 mm, where zi is the mixing height. By defining ze as the distance from the bottom to where the temperature of the plume axis and Ta coincided (equilibrium height), one could observe that for ze = 16 mm < z < zi the fluid inside the plume was cooler than that outside at the same height. This occurrence, generally found in full-scale UHIs (Oke 1995) and in numerical simulations (Hertig 1995), suggested that an overshoot took place above the heating disk (crossover effect).
Figure 5 shows the vertical profiles for the temperature difference (T − Ta) scaled with the UHI intensity ΔTm for cases 2.A (Fig. 5a) and 4.A (Fig. 5b), measured at various radial distances from the heater center. The height z was scaled with zi. Here, ΔTm is defined as the difference measured at z = 0 between the temperature at the UHI center and Ta. Figure 5b also shows laboratory results carried out by Lu et al. (1997a) for Re = 2920 and Fr = 0.089, data from field experiments in Cincinnati, Ohio (Re = 1.2 × 109 and Fr = 0.013; Clarke 1969), and numerical results given by Yoshikado (1992). For the latter case, because the author did not report the value of the surface heat flux, the Froude and Reynolds numbers could not be directly evaluated. Given D = 25 km and dθa/dz = 0.007 K m−1, which are respectively the city radius and the ambient potential temperature gradient selected by Yoshikado, and by assuming H0 ≅ 40 W m−2 as a typical value for nocturnal heat fluxes, the velocity scale, the Froude number, and the Reynolds number were U ≅ 3 m s−1, Fr = 0.009, and Re = 4.8 × 109, respectively. Despite the large differences in Re and Fr, there is reasonable agreement among the curves. This fact confirmed a previous finding of Lu et al. (1997a), that is, the shape of the nondimensional mean temperature profiles of low-aspect-ratio UHIs depends on the location rather than the Reynolds and Froude numbers.
Figures 6a and 6b depict the averaged velocity field associated with the UHI circulation for cases 2.A and 4.A, respectively. Nearly 1000 velocity samples make up each one of the 40 × 20 grid cells during the averaging-time interval Δtaver. The shapes of the flow patterns for the two cases reflect the distribution of the trajectories shown in Fig. 3 and are consistent with the mean temperature profiles previously discussed.
To check the similarity among the velocity fields obtained for different values of the surface heat flux H0, in Fig. 7a the vertical profiles of the mean horizontal velocity u, normalized by U, taken at x/D = 0.5 for cases i.A are shown (cases i.B displayed in the figure will be discussed in section 3b). The profiles of the mean vertical velocity w, normalized by the vertical velocity scale W, taken at the plume axis (x/D = 0) are depicted in Fig. 7b. Both figures also report the corresponding profiles of Lu et al. (1997b) and Yoshikado (1992). The Froude and the Reynolds numbers of Lu et al.'s experiments were (Fr = 0.047, Re = 3820) and (Fr = 0.077, Re = 8280). A noteworthy observation from Fig. 7b is that, with the exclusion of case 1.A (this aspect will be examined below), the normalized vertical velocity profiles were very similar, even though Yoshikado's (1992) profile was distinctly different. Similar conclusions could be drawn for the horizontal velocity. The above discrepancies could be attributed both to the arbitrary choice for H0 used to determine U and Fr for Yoshikado's (1992) numerical runs and to the fact that his model was two-dimensional. Also note that a slight dependence on the experimental conditions was present. In essence, the Reynolds number seemed to be the distinguishing feature, in that, as the Reynolds number increased, so did the measured u/U and w/W. A possible reason for this result was that the Reynolds number attained in the experiments was not large enough to match the full Reynolds number independence of the flow. Therefore, data points for case 1.A, characterized by the smaller Re, need to be viewed with caution.
Figures 8a and 8b show the vertical profiles of the normalized standard deviation of horizontal and vertical velocities, respectively, σu/U and σw/U, calculated at the UHI center for some of the nocturnal cases studied. The figures also report the water-tank results of Lu et al. (1997b) and nighttime urban observations conducted at the city center of Sapporo, Japan, during light-wind conditions [runs 15 and 17 of Uno et al. (1988) as rearranged and presented by Lu et al. in their Fig. 9]. The standard deviations were approximately constant within the thermal plume and suddenly dropped above z = zi. The agreement with the field data was reasonably good, even though the laboratory data of σu/U showed lower values with respect to those in the field measurements. This fact was probably related to the well-known limitation of water-tank simulations that is caused by the finite size of vessels utilized in laboratories (Deardorff and Willis 1985; Cenedese and Querzoli 1994; Lu et al. 1997b). The whole pattern of the normalized quantity TKE2D = (
Last, Fig. 10 shows the ratios zi/D versus the Froude number. In general, our estimations (full circles) were close to those of Lu et al. (1997a) and Yoshikado (1992) and to field data from Columbus, Ohio (Clarke and McElroy 1974). Moreover, they corroborate the empirical relation zi/D = 2.86Fr (solid line) found by Lu et al. (1997a) and provide further convincing evidence for the attainment of the Reynolds-number independence criterion.
The daytime UHI
One of the fundamental characteristics of UHI dynamics noted by Yoshikado (1992) was the similarity between nocturnal and daytime UHIs. He found that their circulations were comparable if the sum Δθ + ΔθL had the same value (Δθ was the potential temperature anomaly between rural and urban surfaces and ΔθL was the surface potential temperature growth after sunrise, expressed as ΔTm and TL − TS, respectively, in our laboratory model). The mentioned similarity is of great interest in that it leads to the hypothesis that Lu et al.'s (1997b) bulk convection model, valid for nocturnal UHIs, might be extended to daytime UHIs. In that case, U and W would be appropriate velocity scales for daytime UHIs, too. To verify the above hypothesis, simulations of UHIs developing in statically unstable boundary layers, and comparison with nocturnal UHIs, are described here.
The experimental approach was the following. First, to avoid influences from the sea side, a removable vertical partition was positioned along the coastline. Second, stratification was established above the land side by setting TL = 27°C and TU = 46°C. Then, the land-side temperature was rapidly raised to TL = 31°C (an indirect estimation of the surface heat flux associated with this growth in temperature after the stationary conditions were established gave HL ≅ 300 W m−2). As a result, a well-mixed layer formed above the land side. The last step was to switch on the electric heater. In so doing, the UHI developed within an unstable environment, taking on the features of a daytime UHI. The procedure was repeated for each one of the five values of H0 listed in Table 1 (the corresponding situations were indicated with case i.B). Last, the horizontal velocity scale U was calculated by using H0 + HL, in contrast to H0, which was employed for nocturnal cases.
Figure 6c displays the averaged velocity field carried out for case 4.B after the UHI had become well established. Its shape is similar to that observed for the corresponding nocturnal UHI (case 4.A, Fig. 6b), even though the daytime UHI was wider and stronger relative to its nocturnal counterpart. The increased UHI depth detected for the daytime case (zi = 24 mm), as compared with that observed for the nocturnal one (zi = 20 mm), was related to the presence of the well-mixed layer, which made the vertical development of the thermal plume easier.
To verify the similarity between diurnal and nocturnal conditions, the vertical profiles of the normalized horizontal and vertical velocities calculated for the diurnal situations have been compared with those of the nocturnal cases previously discussed (Fig. 7). The figure reveals a reasonable agreement among the curves, suggesting that the velocity scales U and W were both appropriate also for diurnal UHIs. Furthermore, simply from inspection of Fig. 8, it is immediately apparent that a reasonable agreement among the normalized standard deviation of the horizontal and vertical velocities for stable (cases 2.A, 4.A, and 5.A) and unstable (cases 4.B and 5.B) environments also occurred. The validity of the mentioned similarity was further confirmed by comparing the diurnal ratios zi/D (Fig. 10, open triangles) with the Lu et al. (1997a) empirical law zi/D = 2.86Fr (line).
Daytime UHI–sea-breeze interaction
To generate the daytime UHI and the sea-breeze regime simultaneously (situation C), the experiments were made using the same procedure described in section 3b, although the vertical partition was removed from the shoreline (located at x/D = −4.5). Thus, when the land side was heated, a difference in temperature was established between the sea and the land surfaces. This disparity generated a horizontal pressure gradient directed offshore, which, in turn, caused an onshore current (sea breeze) directed toward the daytime UHI. In so doing, we simulated the interaction between an inland daytime UHI and a pure sea breeze in the case of flat terrain, without other thermally induced and/or gradient winds.
In Fig. 11, the time traces of the temporally averaged horizontal velocity component u taken upwind of the UHI (x/D ≅ −0.75, z/zi ≅ 0.125, where the sea-breeze velocity attained its maximum value UB) for cases 4.B (daytime UHI, short dashes) and 4.C (daytime UHI and sea breeze, solid line), are shown. The long dashed line depicts the time trace of u measured at the same location but without the UHI. The latter situation referred to a case of pure sea breeze, when the land surface was uniform and the sea breeze penetrated inland without alterations caused by the UHI. To highlight the circulation dynamics, averages were performed by using Δtaver = 10 s as the averaging time interval, in contrast to the previous analysis where Δtaver = 300 s was adopted. The curve for case 4.B corresponds to the situation discussed in Fig. 6c. For this latter case, u increased progressively until t ≅ 700 s, and then, because of the thermal-plume swaying motion, it oscillated around u ≅ 0.5 mm s−1. For case 4.C, the arrival of the sea breeze was clearly visible at t ≅ 480 s, when a sudden increase in u was recorded. Afterward, u continued to rise until the sea breeze was fully established (t ≅ 1000 s). It is of note that the arrival of the sea breeze caused the plume oscillations to fade out and that, as expected, the interaction between the UHI and the sea breeze did not follow linear dynamics.
A problem arose, however, with the small UB attained in the experiments. Because UB ≅ 0.45 mm s−1, the ratios UB/U for stationary conditions fell in the range of 0.08–0.13, whereas typical full-scale ratios are generally above 1. Nevertheless, this fact did not appear as a severe limitation for this study. In addition, as noted by Yoshikado (1992), composite systems of UHIs and sea breezes can be considered completely similar to those associated with UHIs and light gradient winds, where the ratio UG/U is commonly below 1 (here, UG is the gradient wind velocity). Thus, the results presented below are pertinent to the interactions of both daytime UHI and sea-breeze flow and daytime UHI and light gradient wind, even though for the former situation its natural counterpart is uncommon.
The averaged velocity fields for cases 2.C and 4.C are sketched in Figs. 12a and 12c, respectively (hereinafter we will refer again to Δtaver = 300 s). Both figures show that the circulation lost its symmetry with respect to the heater axis, in contrast to the circulation that developed in calm environments. Furthermore, part of the sea breeze was blocked by the UHI and was channeled seaward at elevated layers, strengthening the upwind diverging flow associated with the urban plume, and part of the sea breeze flowed over the plume. This pattern is clearly illustrated in Fig. 13, in which some of the longest trajectories detected in the proximity of the plume axis for ∼10 s for case 2.C are given. The figure displays a phase in which the thermal plume, because of its swaying motion, was bent over landward. Inspection of the figure reveals that part of the trajectories that originated upwind of the plume (open circles) penetrated downwind of the plume axis near the plume top while trajectories that were initiated downwind of the plume (full circles) did not cross the plume axis. A similar behavior was observed when the plume was bent over seaward. (Because of the three-dimensional nature of the circulation, the remnant of the sea-breeze current actually flowed around the UHI; to analyze this important aspect, which is planned for the near future, it is necessary to investigate the flow field along horizontal planes). The above features are summarized in Fig. 14, in which the vertical profiles of the horizontal velocity u taken upwind (x/D = −0.75) and downwind (x/D = 0.75) of the UHI for cases 4.B and 4.C are given. A noteworthy observation from the figure is the formation of a stagnation region in the lee of the UHI, which is in agreement with the numerical results given by Yoshikado (1992).
Another salient feature was the leeward shift from the city center of the thermal plume, that is, the new position attained by the maximum upward velocity WM. As noted by Yoshikado (1992), the shift depended on the incoming sea-breeze (or gradient wind) velocity, or rather on the ratio UB/U. Figure 15 presents measurements of xPA/D as a function of UB/U for cases i.C and for the corresponding results of Yoshikado (1992) in his analysis on the influence of gradient winds on UHI dynamics. Here, xPA is the landward displacement from the heater center of the thermal plume axis. Despite the fact that the ratios UB/U encompassed by the two datasets were different, the curve appeared to show a similar trend, although our results were characterized by greater xPA. Though the small number of data points did not allow for clearly defined conclusions, the results corroborated the numerical experiments of Yoshikado (1994). He noted that, when the city is located along the shore, the UHI circulation does not develop enough before the arrival of the sea breeze. In that case, the sea breeze is not blocked by the thermal plume and flows above the urban complex. As a result, the UHI circulation does not show a well-defined structure (see, also, Ohashi and Kida 2002). On the contrary, if the city is located inland, its associated UHI circulation can reach a mature stage and retains its identity when interacting with the sea breeze, provided that the distance from the shoreline exceeds a certain value.
A further comparison between this study and the numerical simulations of Yoshikado (1992) is presented in Fig. 16, in which the normalized upward velocity maximum WM/W as a function of UB/U is given. As noted in the previous sections 3a and 3b, numerical and experimental velocity data exhibited a nonnegligible discrepancy. Nevertheless, for low UB/U, the two curves suggests that as UB/U increased, so did WM/W. In other words, UHI circulations associated with large U (i.e., large heat fluxes and/or large city diameters) kept on their identity with larger values of UB. The greater z/zi observed for case 2.C with respect to that measured for case 4.C (cf. Figs. 12a,c) was a direct consequence of the above feature. Yoshikado (1992) conjectured that the sudden drop of WM when UB exceeded a certain range was caused by the stronger advection, which blew away the urban boundary layer as a whole.
Figures 12b (case 2.C) and 12d (case 4.C) show the TKE2D maps corresponding to the velocity fields previously discussed. With the exclusion of the relative maximum observed within the vortical region located upwind of the heater axis for case 4.C (not clearly evident in case 2.C), the two plots are similar. It is instructive to note that the maxima located at the upper region of the thermal plume showed approximately the same value (0.048 and 0.052 for cases 2.C and 4.C, respectively) and were comparable to that exhibited by the daytime UHI without the sea breeze (0.045, case 4.B; cf. Fig. 9). In view of this invariance, one may argue that the nondimensional turbulent kinetic energy maximum located within the thermal plume was advected leeward with, but not increased by, the sea breeze.
Examples of mean temperature profiles measured with and without the sea breeze (cases 4.B and 4.C), as a function of the radial distance from the heater axis, are displayed in Fig. 17. The figure reveals that in the proximity of the thermal plume advected leeward by the sea breeze (case 4.C, full squares, x/D = 0.25) the temperature was nearly constant with height. This result suggests that the thermal plume retained its characteristic of being well mixed, although it showed temperature values less than those present in absence of the sea breeze, when the plume was centered at the heater axis (case 4.B, open diamons, x/D = 0). Notice that the cooling, ascribable to injection of (relatively) cold current from the sea, affected the entire UHI circulation in accordance with the field measurements of Yoshikado and Kondo (1989), who noted that the temperature in Tokyo stopped increasing because of the inflow of the sea breeze.
Summary and conclusions
This study reports some laboratory results concerning the flow field associated with daytime and nocturnal low-aspect-ratio urban heat islands and analyzes the interaction between daytime UHIs and sea-breeze currents.
Experiments were performed in a temperature-controlled water tank in which a series of heat exchangers allowed the simulation of the diurnal temperature changes experienced by terrain under the effect of solar heating. A circular-shaped electric heater of diameter D modeled the surplus of surface heat flux H0 associated with urban environments. Because of the geometry of the heater, in calm environments the induced circulation was axisymmetric. Particle-tracking velocimetry, a nonintrusive technique based on tracking of nonbuoyant seeding particles dispersed within the flow, has been applied to evaluate the velocity field in a vertical section orthogonal to the coastline, passing through the center of the UHI. A rack of thermocouples measured the vertical temperature profile at various distances from the UHI center. The salient findings of the study are summarized below:
Only the Froude number governed the nocturnal UHI circulation in calm conditions. Because of the turbulent nature of the modeled UHI, other similarity parameters, such as the Prandtl and the Reynolds numbers, did not influence the circulation. The main features of the modeled nocturnal UHI were comparable to those obtained in previous laboratory experiments made in similar conditions (Lu et al. 1997a,b) and to those carried out in field experiments conducted in large cities (Clarke 1969; Clarke and McElroy 1974; Uno et al. 1988). Comparison of these results with those reported by Yoshikado (1992), based on a numerical mesoscale atmospheric model, showed reasonable agreement, although nonnegligible discrepancies in the velocity fields were present.
Temperature measurements corroborated Lu et al.'s (1997a) results, in that it was found that the mean temperature profiles scaled by the nocturnal UHI intensity depended on the radial distance from the UHI center, irrespective of the Froude and the Reynolds numbers. According to the bulk convection model proposed by Lu et al. (1997b) (valid for nocturnal UHIs) and laboratory observations performed by the same authors, the quantities U = (gβDH0/ρ0cp)1/3 and W = UFr could be properly employed to scale the horizontal and the vertical velocities, respectively, and U scaled reasonably well with the standard deviation of both the velocity components.
It was found that U, when calculated with H0 + HL, where HL was the heat flux associated with land heating after sunrise, could be employed as a velocity scale for daytime UHIs, too. This result implied the extension of Lu et al.'s (1997b) bulk convection model to daytime UHIs.
When the sea-breeze current interacted with the daytime inland UHI circulation, a general leeward shift of the plume axis was detected. The magnitude of the shift was in inverse proportion to U, confirming the results of Yoshikado (1992). A similar trend was noted for the growth of the UHI height. The mentioned interaction was accompanied by a general lowering of temperature within the entire UHI circulation and by the formation of a stagnation region in the lee of the UHI.
Qualitative comparison of the results with the numerical findings of Yoshikado (1994) and Ohashi and Kida (2002) suggested that coastal and inland UHIs behave in different ways when they interact with sea-breeze flows. The latter tended to retain their structure more efficiently than the former, in that inland UHI circulations could develop until the attainment of their mature stage before the arrival of the sea breeze.
Although the purpose of this study was to obtain further information that is useful in testing prediction methods, note that the nature of full-scale events is more complex than their simplified counterparts considered here. The simultaneous presence in real environments of large-scale systems and local circulations (e.g., orographic and thermally induced winds) is the rule rather than the exception, and the extension of the laboratory results to atmospheric cases should be done with caution. Furthermore, restrictions caused by the small dimensions of the water tank limited the range of possible scenarios. Nevertheless, this work can be considered as a step toward an understanding of such intricate phenomena, and, furthermore, the technique used is a powerful tool for investigating a number of features of UHIs that cannot be easily observed in full-scale cases.
Acknowledgments
This project was supported by the funds of the Education, University and Research Office (MIUR). The authors thank Dr. F. Ciotti, Dr. M. Marchetti, and Mr. F. Sammartino for technical support during the laboratory work. The valuable assistance of Prof. G. Querzoli in using the PTV software has been greatly appreciated.
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The experimental setup: (a) polystyrene sheet, (b) heat exchanger (upper surface), (c) thermostat (upper surface), (d) framed area, (e) thermocouple array, (f) coastline, (g) heating disk (h) personal computer (thermocouple controller), (i) heat exchanger (sea side), (j) optics (mirrors, lens), (k) heat exchanger (land side), (l) thermostat (land side), (m) video camera, (n) thermocryostat (land side), (o) personal computer (land temperature controller), and (p) laser
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Schematic of the water tank (all measurements in millimeters)
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Particle trajectories from PTV over ∼3 s for case 4.A
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Mean temperature profiles as a function of the radial distance from the UHI center for cases (a) 2.A and (b) 4.A
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Nondimensional mean temperature profiles as a function of the radial distance from the UHI center for cases (a) 2.A and (b) 4.A. Lu et al.'s (1997a) laboratory data (open squares and circles: Fr = 0.089, Re = 2920), Yoshikado's (1992) numerical runs (open triangles: Fr = 0.009, Re = 4.8 × 109), and Clarke's (1969) field observations (open diamonds: Fr = 0.013, Re = 1.2 × 109) are also shown in (b)
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Averaged velocity vectors for cases (a) 2.A, (b) 4.A, and (c) 4.B
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Vertical profiles of nondimensional velocities for nocturnal (cases 1.A–5.A) and diurnal (cases 1.B–5.B) conditions. Open symbols refer to the laboratory experiments of Lu et al. (1997b) (squares: Fr = 0.047, Re = 3820; circles: Fr = 0.077, Re = 8280) and the numerical simulation of Yoshikado (1992) (triangle: Fr = 0.009, Re = 4.8 × 109). (a) Horizontal (x/D = 0.5) and (b) vertical (x/D = 0) velocities
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Vertical profiles of nondimensional std dev of velocity taken at x/D = 0 for this study (nocturnal cases: full squares, circles and crosses; diurnal cases: full diamonds and triangles), the laboratory simulation of Lu et al. (1997b) (open squares: Fr = 0.047, Re = 3820; open circles: Fr = 0.077, Re = 8280), and the field data of Uno et al. (1988) (open diamonds: run 15, open triangles: run 17). (a) Horizontal and (b) vertical velocities
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
TKE2D = (
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Ratio of mixing height to diameter (zi/D) as a function of Fr for this study (nocturnal cases: full circles, diurnal cases: full triangles), Lu et al.'s (1997a) laboratory data (open circles), Yoshikado's (1992) numerical runs (open square), and Clarke and McElroy's (1974) field data (Columbus, open triangles); zi/D = 2.86Fr is also shown (line)
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Temporal variations of the averaged horizontal velocity component u measured upwind of the UHI (x/D = −0.75, z/zi = 0.125) for case 4.B (daytime UHI, short dashes), pure sea breeze (long dashed line), and case 4.C (daytime UHI and sea breeze, solid line). Averages over 10 s were used
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
(a), (c) Averaged velocity vectors and (b), (d) TKE2D map for cases (a), (b) 2.C and (c), (d) 4.C
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Example of the longest trajectories that originated upwind (open circles) and downwind (full circles) of the plume axis in presence of sea breeze (case 2.C)
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Averaged horizontal velocity profiles u at x/D = ±0.75 with (case 4.C: full symbols) and without (case 4.B: open symbols) the sea-breeze flow
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Ratio of landward displacement from the heater center of the thermal plume axis to diameter xPA/D vs UB/U for this study (full circles) and for Yoshikado's (1992) numerical runs (open circles)
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Same as in Fig. 15, but for the nondimensional maximum upward velocity WM/W vs UB/U
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Averaged temperature profiles as a function of the radial distance from the heater center with (case 4.C: full symbols) and without (case 4.B: open symbols) the sea-breeze flow
Citation: Journal of Applied Meteorology 42, 11; 10.1175/1520-0450(2003)042<1569:IBAIUH>2.0.CO;2
Parameters for the experiments, including the observed values of mixing height zi and UHI intensity ΔTm = (TUHI axis − Ta)z=0 , surplus of surface heat flux H 0 , land surface heat flux HL , horizontal velocity scale U = (gβDH 0 /ρ 0 cp)1/3 , Froude number Fr = U/ND, Reynolds number Re = UD/ν. The heater diameter D = 100 mm and the buoyancy frequency N = (gβdTa /dz)1/2 ≅ 0.7 s−1 were the same for all cases
