Editorial Type:
Article
Article Type:
Research Article

Laboratory Measurements of Heat Transfer and Drag Coefficients at Extremely High Wind Speeds

Satoru Komori Research Center for Highly-Functional Nanoparticles, Doshisha University, Kyotanabe, Japan
Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan
Department of Mechanical Engineering and Science, Kyoto University, Kyoto, Japan

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Koji Iwano Department of Mechanical Systems Engineering, Nagoya University, Nagoya, Japan

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Naohisa Takagaki Department of Mechanical Engineering, University of Hyogo, Himeji, Japan

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Ryo Onishi Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

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Ryoichi Kurose Department of Mechanical Engineering and Science, Kyoto University, Kyoto, Japan

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Keiko Takahashi Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

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Naoya Suzuki Department of Mechanical Engineering, Kindai University, Higashiosaka, Japan

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Print Publication:
01 Apr 2018
DOI:
https://doi.org/10.1175/JPO-D-17-0243.1
Page(s):
959–974
Full access

Abstract

Heat and momentum transfer across the wind-driven breaking air–water interface at extremely high wind speeds was experimentally investigated using a high-speed wind-wave tank. An original multi-heat-balance method was utilized to directly measure latent and sensible heat transfer coefficients. The results show that both heat transfer coefficients level off at low and normal wind speeds but increase sharply at extremely high wind speeds. The coefficients have a similar shape for wind speeds at a height of 10 m. Therefore, the wind speed dependence on the latent and sensible heat transfer coefficients can be represented by that of the enthalpy coefficient even in the extremely high-speed region. To show how significantly the drag and enthalpy coefficients affect the intensity of tropical cyclones, the coefficients were applied to Emanuel’s analytic model. The analytic model shows that the difference between the present laboratory and conventional correlations significantly affects the maximum storm intensity predictions, and the present laboratory enthalpy and drag coefficients have the remarkable effect on intensity promotion at extremely high wind speeds. In addition, the simulations of strong tropical cyclones using the Weather Research and Forecasting (WRF) Model with the present and conventional correlations are shown for reference in the appendix. The results obtained from the models suggest that it is of great importance to propose more reliable correlations, verified not only by laboratory but also by field experiments at extremely high wind speeds.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Satoru Komori, komori@mech.kyoto-u.ac.jp

Abstract

Heat and momentum transfer across the wind-driven breaking air–water interface at extremely high wind speeds was experimentally investigated using a high-speed wind-wave tank. An original multi-heat-balance method was utilized to directly measure latent and sensible heat transfer coefficients. The results show that both heat transfer coefficients level off at low and normal wind speeds but increase sharply at extremely high wind speeds. The coefficients have a similar shape for wind speeds at a height of 10 m. Therefore, the wind speed dependence on the latent and sensible heat transfer coefficients can be represented by that of the enthalpy coefficient even in the extremely high-speed region. To show how significantly the drag and enthalpy coefficients affect the intensity of tropical cyclones, the coefficients were applied to Emanuel’s analytic model. The analytic model shows that the difference between the present laboratory and conventional correlations significantly affects the maximum storm intensity predictions, and the present laboratory enthalpy and drag coefficients have the remarkable effect on intensity promotion at extremely high wind speeds. In addition, the simulations of strong tropical cyclones using the Weather Research and Forecasting (WRF) Model with the present and conventional correlations are shown for reference in the appendix. The results obtained from the models suggest that it is of great importance to propose more reliable correlations, verified not only by laboratory but also by field experiments at extremely high wind speeds.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Satoru Komori, komori@mech.kyoto-u.ac.jp
Keywords: Wave breaking; Wind waves; Hurricanes/typhoons; Tropical cyclones; Latent heating/cooling; Sensible heating

1. Introduction

Strong tropical cyclones (TCs), such as supertyphoons and hurricanes, cause extensive damage to property and communities. Therefore, it is important to predict the tracks and intensities of TCs precisely. Recent studies (e.g., Tsuboki et al. 2015) have suggested that global warming causes stronger TCs, and therefore accurate predictions will become more important in the future. Currently, numerical simulations are widely used to predict TCs. Errors in track prediction have been decreased by almost 50% in the past two decades (National Hurricane Center; http://www.nhc.noaa.gov/verification/verify5.shtml). In contrast, the accuracy of intensity predictions has not been improved (DeMaria et al. 2014). This is mainly attributed to the fact that the tracks of TCs are controlled by large-scale atmospheric structures surrounding TCs, such as pressure patterns or westerlies, whereas intensities are very sensitive to the small-scale physics in TCs, such as air–sea momentum and heat transfer. This means that TCs develop from the balance between the supply of thermal energy from the ocean and loss of kinetic energy caused by the drag acting on the sea surface. Therefore, one of the primary ways to accurately predict the development of TCs is to precisely estimate heat and momentum fluxes across the sea surface beneath the TCs. In numerical simulations of TCs, momentum flux and latent and sensible heat fluxes at the sea surface are calculated using the following bulk equations, where the drag coefficient is CD, the latent heat transfer coefficient is CE, and the sensible heat transfer coefficient is CH:
e1
e2
e3
Here, ρ is the air density, LV is the latent heat of vaporization, CP is the specific heat of humid air at a constant pressure, U is the wind speed, q is the specific humidity, and T is the temperature. The subscripts i and 10 indicate the sea surface and a height of 10 m above the sea level, respectively. The transfer coefficients are usually parameterized against wind speed U10 at a height of 10 m, using the field measurement data. In spite of a long history of field measurements (e.g., Friehe and Schmitt 1976; Large and Pond 1982; DeCosmo et al. 1996; Pedreros et al. 2003; Drennan et al. 2007; Zhang et al. 2008; Richter and Stern 2014) and laboratory experiments using a wind-wave tank (e.g., Garratt and Hyson 1975; Hasse et al. 1978; Ocampo-Torres et al. 1994; Haus et al. 2010; Komori et al. 2011; Jeong et al. 2012), a large degree of uncertainty still remains in the transfer coefficients, particularly at extremely high wind speeds.

Recent laboratory and field measurements, as well as previous field measurements, have suggested that CD increases with U10 in the normal wind speed region (Johnson et al. 1998; Mitsuyasu and Nakayama 1969), whereas CD tends to level off (Donelan et al. 2004; Takagaki et al. 2012, 2016a,b) or decrease with wind speed at extremely high wind speeds (Powell et al. 2003). Therefore, a constant or decreasing value of CD for high wind speeds has been used in more recent formulas for the numerical predictions of TCs (e.g., Green and Zhang 2013) instead of the conventional (traditional) formulas for increasing CD (Skamarock et al. 2008; Charnock 1955; Hawkins and Rubsam 1968) (see the dashed line in Fig. 1). Recently a new correlation for CD, which follows the field measurements (Powell et al. 2003) with a decreasing trend against U10 at extremely high wind speeds, was proposed (Zweers et al. 2010) (see the dotted line in Fig. 1). The simulation results (Zweers et al. 2010) suggested that a decreasing correlation of CD can lead to a significant improvement in hurricane intensity forecasting by conducting numerical experiments on Hurricanes Katrina (August 2005) and Ivan (September 2004). However, the field measurements of CD were too scattered to definitively determine whether CD actually decreased for extremely high wind speeds. In fact, in contrast to the field measurements (Powell et al. 2003) with CD decreasing with U10 under hurricane conditions, another field study (Bell et al. 2012) with scattered data roughly suggested constant values for extremely high wind speeds (see the red triangles in Fig. 1).

Fig. 1.
Fig. 1.

Laboratory and field measurements of drag coefficient CD for varying U10.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

Heat transfer at high wind speeds has not been thoroughly investigated owing to the difficulty in performing accurate measurements of temperature and humidity at extremely high wind speeds with a large number of dispersed spray droplets. Conventionally, heat transfer coefficients extrapolated from measurements at normal wind speeds of less than U10 ≲ 30 m s−1 have been used for extremely high wind speeds. Instead of directly measuring the latent and sensible heat fluxes at high wind speeds, the enthalpy flux was indirectly estimated (Bell et al. 2012; Richter and Stern 2014) by applying a total energy budget method and the Monin–Obukhov theory to dropsonde data at extremely high wind speeds. The results (Bell et al. 2012; Richter and Stern 2014) suggested that the averaged data of the enthalpy transfer coefficient CK is almost constant or increases slightly with wind speeds of U10 > 35 m s−1. However, these results were not definitive since the raw data demonstrated excessive scatter with U10. Moreover, in order to apply the measurements of CK to TC forecasting using the Weather Research and Forecasting (WRF) Model (see http://www.wrf-model.org/), we have to assume that the latent and sensible heat transfer coefficients, CE and CH, have the same value as CK, which is tested and supported by Zhang et al. (2008) for the limited wind speed range of U10 = 20–30 m s−1. This assumption implies that the latent and sensible heats are transported by the same mechanism:
e4
Here, the moist air enthalpy k is defined by k = [(1 − q)CPa + qCPl]T + qLV, where CPa and CPl are the specific heat of dry air and water vapor at constant pressure, respectively. However, in previous field studies, the assumption CE = CH has not been verified for extremely high wind speeds. Therefore, the heat transfer mechanism at extremely high wind speeds is not well understood. To clarify this, reliable laboratory measurements of the heat transfer coefficients are an alternative to field measurements because laboratory experiments enable the measurement of heat fluxes more accurately than field measurements under rough conditions. Therefore, in this study we aimed to measure CE and CH independently, for up to U10 ≈ 60 m s−1, using a new heat flux measuring method in a high-speed wind-wave tank, to illustrate the importance of proposing reliable correlations for the heat transfer and drag coefficients on TC tracking developments using analytical and numerical models.

2. Experiments

a. Experimental setup

The high-speed wind-wave tank in Kyoto University (see Fig. 2) was used in this study to investigate heat transfer across the breaking air–water interface. The tank has a glass test section 15 m long, 0.8 m wide, and 1.6 m high. Heat was transferred across the 13-m-long interface, excluding the guide plate at the entrance and wave absorber at the exit of the test section. The water depth was 0.8 m and the height of the airflow above the water surface was 0.8 m. Uniform airflow was introduced from a settling chamber through a contraction section, and the wind waves were generated on the air–water interface in the test section. The air velocity and Reynolds stress were measured at the fetch of x = 6.5 m using a phase Doppler anemometer (Dantec Dynamics PDA). Laser beams were shot through the plate-glass sidewall, and to avoid irregular reflection by the wall impingement of the droplets dispersed from the intensively breaking wind waves, we prepared a small droplet-adherent prevention device (DAPD). The DAPD had a size of 0.07 m × 0.07 m × 0.007 m and was fixed on the inside glass wall as shown in Fig. 3. Four orifices with a diameter of 0.005 m were installed on the device, and the four laser beams were introduced through the orifices into the test section. Clean compressed air was also blown through the orifices along the plate-glass sidewall. Therefore, even if dispersed droplets impinged on and adhered to the orifices, the compressed air blew the droplets off, creating a clear path for the laser beam. The effect of the compressed airflow on the velocity measurements by the PDA in the main airflow was negligibly small, since the flow volume of the compressed air was 1.46 × 10−3 m3 s−1 through the orifices and was significantly smaller than the main airflow volume of ~20 m3 s−1 in the wind tunnel section above the air–water interface. The seeding particles for the PDA measurements were varied; scattering mists with diameters of ~1 μm from a fog generator (Dantec Dynamics F2010 Plus) were mainly used for normal wind speeds and small droplets with diameters of dp < 30 μm generated by wave breaking were used for extremely high wind speeds. In fact, the PDA measurements of the streamwise mean droplet velocity Up and correlation of streamwise and vertical droplet velocity fluctuations against a droplet diameter dp showed that small droplets with dp < 30 μm sufficiently followed the ambient airflow at an extremely high wind speed of U10 = 56 m s−1 (see Fig. 4). The free stream wind speed outside the turbulent air boundary layer above the wavy air–water interface U∞ ranged from 6.1 to 43 m s−1, which corresponded to a U10 from 7.3 to 67 m s−1. The air-friction velocity was directly calculated from the Reynolds stress measured in the vicinity of the interface and the 10-m wind speed U10 was estimated from the log law in the airflow. The drag coefficient CD was obtained by substituting the surface Reynolds stress for the surface momentum flux in (1). Our measurements of CD (Takagaki et al. 2012) are represented by the red circles in Fig. 1.

Fig. 2.
Fig. 2.

(a) Schematic diagram of the high-speed wind-wave tank. Photographs of the wind waves at (b) U10 = 7.25, (c) U10 = 48.0, and (d) U10 = 67.1 m s−1.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

Fig. 3.
Fig. 3.

Droplet-adherent prevention device attached at the plate-grass sidewall. (a) View on the x–z plane and (b) view on the y–z plane. The four circles in (a) indicate the four orifices.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

Fig. 4.
Fig. 4.

Distributions of (a) mean droplet velocity and (b) correlation between streamwise and vertical droplet velocity fluctuations against droplet diameter (U10 = 56 m s−1).

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

The number of dispersed droplets and their streamwise and vertical velocities in the high wind speed region were also measured using a shadow-sizing technique (Dantec Dynamics Shadow Sizer) in the region above significant waves. (The measurement principles of the shadow-sizing technique can be found at http://www.dantecdynamics.com/shadow-sizing.)

A virtually homogeneous temperature was maintained during each experimental run by circulating warmed water between the wind-wave tank and a big stirred tank with a volume of 5.4 m3. At extremely high wind speeds, the water volume in the wind-wave tank decreased over time owing to both large numbers of droplets dispersed mainly from the rearmost wave crest in the test section and high waves that splashed out from the outlet of the wind tunnel. To keep the water depth of the wind-wave tank constant, the water loss was compensated by regulating the flow rate of water from the big stirred tank to the wind-wave tank during experimental runs lasting more than 30 min. Prior to starting each experiment, warm water was supplied from a boiler to the stirred tank and was mixed by circulating it between the stirred and wind-wave tanks. In addition, the heat flux lost by conduction across the walls in both the wind-wave and stirred tanks QCON was estimated in advance by using a blind interface covered by a foam polystyrene plate, perfectly stopping heat transfer across the air–water interface. The temperatures on the air and water sides were measured using thermocouples (Anritsu AM8000). The bulk specific humidity was measured using an infrared absorption humidity meter (LI-COR LI7000) at a fetch of x = 6.5 m corresponding to the center of the test section interface. The water surface temperature was measured using an infrared radiation thermometer (Nippon Avionics TVS-8502) at the same fetch, as was the bulk air temperature. Nine water temperature readings were taken at points with fetches of x = 0.5, 6.5, and 11.5 m and depths of z = −0.1, −0.35, and −0.6 m to confirm the homogeneity of the temperature field in the tank.

b. Estimating heat transfer coefficients by MHBM

At extremely high wind speeds, the large number of dispersed droplets made it difficult to measure air temperature and specific humidity in the air boundary layer above the interface. This makes it problematic to directly estimate the latent and sensible heat fluxes, QE and QH, respectively. Therefore, we have developed an original method, named the multi-heat-balance method (MHBM), enabling the estimation of QE and QH from the total heat flux QT. The QT is the total heat flux from water to air across both wave interfaces and surfaces of dispersing droplets that reattached on the foregoing waves in the test section. The QT can be decomposed into the latent heat flux QE, sensible heat flux QH, and radiative heat flux QR, as follows:
e5
By substituting (2) and (3) into (5) we obtain
e6
In this study, both the decreased rates of bulk water temperature and water volume dTW/dt and d(ρWVW)/dt were measured in the wind-wave tank and big stirred tank, respectively. Then, QT in (6) is given by the heat balance:
e7
Here, ρW, CP,W, VW, TW, TO, and AS are the water density, specific heat of water at constant pressure, total water volume in both the wind-wave and stirred tanks, bulk water temperature, droplet temperature at the instant of the droplet formation by wave breaking, and vertically projected water surface area, respectively. The second term on the right-hand side of (7) before deformation is the heat flux QDIS carried out both by droplets discharged from the wind tunnel outlet and by high waves that splashed out from the outlet. The QDIS was estimated by substituting the water surface temperature measured by an infrared radiation thermometer Ti into TO in (7). Although the QDIS may be overestimated because Ti = TO, it was less than 6% of QT even at the maximum wind speed. The conduction loss QCON was estimated by the method mentioned in the previous section of the experimental setup. The radiative heat flux QR was estimated from the Stefan–Boltzmann law. The QR value was ~5% of QT at the lowest wind speed and less than 1% at extremely high wind speeds of U10 > 50 m s−1.
Values of CE and CH in (6) may depend on water temperature, air temperature, and specific humidity even for the same U10. We therefore performed at least 20 experiments with varying conditions: atmospheric temperature (2°–31°C), humidity (3–22 g kg−1), and temperature difference between water and air (3°–20°C), for each U10. To determine CE and CH, we applied the following multiple linear regression analysis to the three terms in (6): QT − QR, ρLVU10(qi − q10), and ρCPU10(Ti − T10). In these terms, the specific humidity and temperature at 10-m height, q10 and T10, could not be measured directly, and therefore conventional log profiles and flux-gradient relationships (e.g., Kurose et al. 2016) were assumed:
e8
e9
e10
e11
where κ, z0, zq, and zT are the von Karman constant, the roughness length for the wind velocity, specific humidity, and temperature, respectively, and q* and T* are the friction velocities for the specific humidity and temperature, respectively. Initially zq and zT were assumed to be equal to the measured value of z0 (Takagaki et al. 2012), and q10 and T10 were estimated from (8) and (9) with the measurements of q and T, respectively, at a height of z = 0.7 m in the boundary layer. By applying multiple linear regression analysis to the three terms; QT − QR, ρLVU10(qi − q10), and ρCPU10(Ti − T10), we determined the first approximated values of CE and CH and corrected the values of zq and zT by substituting the values of CE and CH in (10) and (11), respectively. Then, using the corrected values of zq and zT, we again estimated q10 and T10 and applied the multiple linear regression analysis. Reliable values of CE and CH were determined by iterating this procedure 30 times, since CE and CH were converged in less than 30 iterations for all cases.

An example of the finalized distributions of QT − QR, ρLVU10(qi − q10), and ρCPU10(Ti − T10) in (6) for several specific humidity and temperature conditions with a high wind speed of U10 = 60 m s−1, is shown in Fig. 5. The red and blue dots in the figure indicate the data located above and below the plane, respectively. It is found that all of the data are well converged in the vicinity of the plane. This implies that the values of CE and CH did not depend significantly on the temperature and specific humidity and the values of CE and CH can be determined from the inclinations of the plane to the horizontal bottom plane. Using the values of CE and CH determined by the MHBM, CK was evaluated for several wind speeds of U10 from (2), (3), and (4).

Fig. 5.
Fig. 5.

Three-dimensional distributions of the heat flux terms in (6) at U10 = 60 m s−1. (a) General view and (b) view along the plane in (a). The red and blue dots indicate the data located above and below the plane, respectively.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

c. Estimation of the maximum heat flux due to virtual reentry of droplets blown out from the test section

A large number of droplets were dispersed from wave crests due to strong wind shear stress and then most of the droplets reattached to the water surface within the test section. In fact, by using a high-speed camera we observed that most of the dispersed droplets reattached on the surface of the foregoing waves immediately after tearing from the crest of the wind wave (see Fig. 6). That is, the flight distance of the droplets, except for small ones with little heat capacity, was close to one wavelength. Therefore, the heat flux, owing to the cooling of dispersing droplets within the test section with a long fetch corresponding to ~8 times the wavelength at the maximum wind speed, was almost included in the first term on the right-hand side of (7) before deformation. On the other hand, droplets generated over the rearmost wave crest near the air outlet of the test section and some smaller droplets blown highly up over the crests were discharged from the air outlet of the wind-wave tank (see the sketch in Fig. 7). The heat loss due to the discharged droplets was included in the second term on the right-hand side of (7) before deformation. However, if the wind-wave tank had a longer fetch than the present one, the discharged droplets would also reenter the bulk water after being cooled by the ambient air. The heat transfer rate due to the cooling effect of the virtual reentrant droplets was not considered in (7), and the cooling may affect the present measurements of heat or enthalpy transfer coefficients. We therefore tried to estimate the heat flux QSP due to the cooling of the virtual entrant droplets under the assumption that the discharged droplets from the air outlet of the tank reentered the bulk water, by measuring the droplet properties.

Fig. 6.
Fig. 6.

Snapshot of droplets dispersing over breaking waves at U10 = 47.7 m s−1.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

Fig. 7.
Fig. 7.

Sketch of breaking wind waves and dispersed droplets at high wind speeds in the wind-wave tank.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

To estimate the heat flux QSP, we used the number flux of droplets flying upward across the horizontal unit area slightly above the wave crest fup(dp), where dp is the droplet diameter. Using the number flux, the heat flux QSP was calculated by
e12
Here, LS is the wavelength of wind wave, W is the width of the tank, CP,W is the heat capacity of water, ρW is the water density, Ti is the droplet temperature at the instant of droplet formation (i.e., the surface temperature on the wavy air–water interface), and Td is the temperature of the dispersed droplet in the airflow. The number flux of a droplet fup(dp) is given by
e13
Here, Rup(dp) is the ratio of the dispersed droplets with an upward velocity to the total of the dispersed droplets. The Nup(dp) and Ndown(dp) are the measured numbers of droplets of diameter dp with upward and downward velocities, respectively. The Vup(dp) is the mean vertical velocity of the droplets with diameter dp with the upward velocity. The θ(dp) is the droplet number density of droplets with diameter dp. To calculate fup(dp), we measured θ(dp), Nup(dp), Ndown(dp), and Vup(dp) by the shadow-sizing method in the vicinity of the wave crest. Figure 8a shows a schematic diagram of the droplet measurement by the shadow-sizing method. The streamwise location x of the measurement volume was 6.5 m. The distance between the center of measurement volume and average water surface height h was varied depending on the wind speed because the wave height changes with wind speed (see Table 1). Figure 8b shows an example of images obtained by the shadow-sizing method. In the figure, two images are superimposed into one image to indicate the droplet displacement vectors. The shadow-sizing method enabled the measurement of the droplet size in the focal volume of a camera and instantaneous velocity of the droplets by two successive images as a particle-tracking velocimetry (PTV). The shadows of droplets were detected using a threshold value for the brightness in the image. Since the focal depth of the camera depended on the optical setup, the calibration was performed in advance by using transparent solid particles of varying size (Takagaki et al. 2018). Figure 9 shows the distributions of the measured θ(dp), Vup(dp), , , and with dp. Here, fup(dp) was normalized by the total number flux Fup of droplets with an upward velocity with volup(dp) corresponding to the volume flux density of a dispersed droplet with diameter dp with an upward velocity. From Fig. 9e, it is found that the integral of (12) converges for all wind speed conditions in the performed experiments.
Fig. 8.
Fig. 8.

Shadow-sizing method used in this study. (a) Measurement system and (b) images obtained by the shadow-sizing method at U10 = 48 m s−1.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

Table 1.

Distance between the center of measurement volume and average water surface height h for varying U10.

Table 1.
Fig. 9.
Fig. 9.

Distributions of the properties of dispersed droplets against droplet diameter. (a) Number density of the droplets, (b) mean vertical velocity of the droplets with upward velocity, (c) ratio of the dispersed droplets with upward velocity to the total dispersed droplets, (d) number flux of dispersed droplets with upward velocity normalized by total number flux, and (e) volume flux of dispersed droplets with upward velocity. All symbols are as in (a).

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

We assumed that the temperature of a dispersed droplet Td in (12) is the equilibrium temperature Te. Both the sensible and latent heats are released from the droplets to the ambient airflow until the temperature of the droplets dispersed from the water surface with the higher temperature reaches the equilibrium temperature. Once the equilibrium temperature has been reached, the dispersed droplets only mediate the exchange of sensible and latent heats, and substantial heat transfer (enthalpy transfer), a combination of the sensible and latent heats, does not occur between the droplets and ambient air. Clearly, the temperatures of all the droplets do not reach the equilibrium temperature, and therefore the value of QSP obtained by substituting Te for Td in (12) provides the maximum estimation. To estimate the equilibrium temperature Te, we represent the sensible heat flux QSP,H and latent heat flux QSP,E on a single droplet by
e14
e15
Here, h is the thermal conductivity coefficient, kA is the mass transfer coefficient, Td is the temperature of the droplet, Ta is the temperature of the ambient air, LV is the evaporative latent heat, asat is the saturated vapor density, and aa is the water vapor density of ambient air. When a droplet is in temperature equilibrium with the ambient air, the equilibrium relation gives
e16
Substituting (14) and (15) into (16) with Te = Td, we obtain
e17
Using the Sh (=kAdp/DL) and Nu (=hdp/λ) numbers for a single droplet (Ranz and Marshall 1952a,b), we obtain
e18
Here, DL and λ are the diffusion coefficient and thermal conductivity of the vapor, respectively. The ReP, Sc, and Pr numbers are defined as ΔUdP/ν, ν/DL, and ρCPν/λ, respectively, where ΔU and ν are the relative velocity between a droplet and ambient air and the kinematic viscosity. Using the unity Lewis approximation, we obtain
e19
Here, Ta and aa are the bulk air temperature and bulk water vapor density, respectively. The equilibrium temperature Te under each experimental condition is obtained by numerically solving (19).

Substituting the measured fup(dp) and the droplet temperature Td (=Te) obtained from (19) into (12), we estimated the maximum heat flux QSP due to the cooling of the virtual entrant droplets under the assumption that the discharged droplets from the air outlet of the tank reentered the bulk water. The ratio of QSP to QT increases with U10 as shown in Fig. 10, and the maximum value of QSP/QT is ~18% at extremely high wind speeds of U10 > 50 m s−1. Therefore, the heat or enthalpy transfer coefficient from our laboratory experiments is at most 18% smaller than the coefficient of actual oceans or lengthy wind-wave tanks.

Fig. 10.
Fig. 10.

Ratio of the heat flux QSP due to the cooling of the virtual entrant droplets to the total air–water heat flux QT. The solid line is a best-fit curve obtained by the least squares method.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

On the other hand, Jeong et al. (2012) estimated the ratio QSP/QT by subtracting the enthalpy difference on the air side between the inlet and outlet of the test section from the total air–water heat flux estimated on the water side. They showed that the ratio is 23%, independent of U10 in the range of 13 < U10 < 28 m s−1. This ratio is a little larger than our values shown in Fig. 10. This difference may be attributed to the difficulty in producing a precise enthalpy balance in the airflow over the growing waves. In fact, Jeong et al. (2012) reported a significant error in the enthalpy balance due to the difficulty of humidity measurement, even for the low wind speed case without dispersed droplets.

3. Results and discussion

The values of CE, CH, and CK obtained by applying our MHBM are shown with U10 in Fig. 11, together with previous measurements of CK (Jeong et al. 2012; Bell et al. 2012; Richter and Stern 2014). At small and moderate wind speeds of U10 ≲ 35 m s−1, the obtained values of CE and CH are almost constant with U10. However, the obtained values of CE and CH increase sharply for extremely high wind speeds of U10 ≳ 35 m s−1. From the definition of CE and CH in (2) and (3), it is found that the heat flux is proportional to U10 and to the larger power of U10 at moderately and extremely high wind speeds, respectively. This sharp increase in CE and CH suggests that heat transfer is greatly enhanced by the intensive wind-wave breaking at U10 ≳ 35 m s−1. Recent laboratory measurements (Iwano et al. 2013; Krall and Jähne 2014) also demonstrated that the mass (CO2) transfer coefficient across the air–water interface kL increased rapidly because of intensive wave breaking at U10 ≳ 35 m s−1. Considering that heat and mass are scalar quantities, the rapid increase of kL may support the rapid enhancement of heat transfer at extremely high wind speeds.

Fig. 11.
Fig. 11.

Distributions of heat and enthalpy transfer coefficients, CE, CH, and CK for various U10.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

In contrast to CE and CH, our measurements of CD (Takagaki et al. 2012) increase at U10 ≲ 35 m s−1 and level off at U10 ≳ 35 m s−1. This trend can be explained as follows. The total shear stress is given by the sum of form and friction drags, τN and τT, respectively, and the friction velocity u* and CD are defined as
e20
From the increase in CD with U10 at low and moderately high wind speeds of U10 ≲ 35 m s−1 together with the definition of CD in (20), we can presume that the form drag significantly increases, owing to the development of wind waves, and the total drag τ increases as a result of the proportional relation (see Fig. 12). Meanwhile, the constant value of CD at extremely high wind speeds of U10 ≳ 35 m s−1 shows that the increasing rate of τ with U10 is decelerated and τ is proportional to (see Fig. 12). This also suggests that the form drag due to significant waves is suppressed by intensive wave breaking at extremely high wind speeds. In fact, this transition is easily seen in the distribution of the wave slope with U10, as shown in Fig. 13. Here, the data in Figs. 12 and 13 were reproduced using the measurements by Takagaki et al. (2012, 2016b). Takagaki et al. (2016b) also showed that the kinetic energy of significant waves relatively decreased for U10 ≳ 35 m s−1. In contrast, the heat (enthalpy) transfer is not significantly affected by the increasing form drag at U10 ≲ 35 m s−1 but is promoted by intensive wave breaking and turbulence at U10 ≳ 35 m s−1. In fact, our measurements of the heat flux show a rapid increase in the extremely high wind speed region associated with intensive wave breaking. Moreover, the dispersed droplets generated by the intensive wave breaking may promote the heat transfer on the air side, as suggested by Andreas (2011), but we could not eliminate the effects of droplets on the heat transfer promotion from the total heat flux QT in our experiment. However, by simply assuming that the heat flux QT is proportional to , as well as the shear stress τ, we can presume that the heat transfer coefficients defined by (2) and (3) are proportional to U10 at U10 ≳ 35 m s−1 as seen in Fig. 11.
Fig. 12.
Fig. 12.

Relationship between shear stress τ and U10.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

Fig. 13.
Fig. 13.

Relationship between wave slope HS/LS and U10.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

In numerical simulations of tropical cyclones, the enthalpy transfer coefficient CK in (4) has often been used with the assumption that CK = CE = CH. In Fig. 11, the obtained value of CK is almost the same as those of CE and CH over the entire wind speed range, verifying the conventional assumption CK = CE = CH for extremely high wind speeds. Therefore, we compared the dependency of CK on the wind speed between the obtained laboratory measurements, and previous laboratory (Jeong et al. 2012) and field (Bell et al. 2012; Richter and Stern 2014) measurements, in Fig. 11. The present measurements of CK are close to the laboratory measurements (Jeong et al. 2012) for wind speeds of U10 < 35 m s−1. However, at extremely high wind speeds of U10 > 50 m s−1, the present values of CK are significantly larger than those in the averaged field data (Bell et al. 2012; Richter and Stern 2014). This difference may be due to measurement errors relating to the difficulties in measuring temperature and humidity using dropsondes in real tropical cyclones. In fact, the wind speed and temperature in the TCs were measured using instruments installed in sondes dropped from aircrafts, and CK was estimated by performing energy balance measurements in controlled volumes arranged in the TC (Bell et al. 2012). The raw data (Bell et al. 2012) were very scattered as shown in Fig. 11. It is therefore difficult to determine how much of the measurement error in CK was caused by the field measurements relying on azimuthal averaging and interpolation of the data in addition to the measurement errors of the temperature and humidity.

To investigate the effects of the variations in the enthalpy and momentum transfer coefficients on the maximum intensity of tropical cyclones, we used the analytic model developed by Emanuel (1995). According to the analytic model, the maximum storm intensity (maximum wind speed) is proportional to (CK/CD)1/2. Therefore we compared the dependency of (CK/CD)1/2 on U10 between our new laboratory and previous conventional correlations of CD and CK. Here, our new correlations of CD and CK derived from the measurements in Figs. 1 and 11, respectively, were approximated by the following:
e21
e22
These curves are shown by the red lines in Fig. 14. It should be noted that the CD and CK correlation curves outside the wind speed region of 5 ≲ U10 ≲ 65 m s−1 only show the extrapolated values because of the lack of measurements. Conventional CD and CK are based on a Monin–Obukhov-type model with a Carlson–Boland viscous sublayer and standard similarity functions, that is, one of the conventional surface layer models:
e23
e24
where z0 = 1.85 × 10−2(u*2/g) + 1.59 × 10−5 and zk = z0/(1 + 4.166 × 104κu*z0). The conventional CD and CK increased monotonously with U10 as shown by blue dashed and solid lines in Fig. 14 and are given as the default option 0 in Green and Zhang (2013).
Fig. 14.
Fig. 14.

The CK and CD as a function of U10.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

Figure 15 shows the dependence of (CK/CD)1/2 on U10 against four pairs of present and conventional correlations. For the present CD and CK, (CK/CD)1/2 decreases with U10 at normal and high wind speeds of U10 ≲ 35 m s−1 and then increases at extremely high wind speeds of U10 ≳ 35m s−1 as shown by a solid line. In contrast, (CK/CD)1/2 for the conventional CD and CK decreases with U10 in the whole wind speed region as shown by a dashed line. The comparisons between four pairs with the present and conventional CD and CK show that both the present CD and CK act to promote the maximum intensity of tropical cyclones at extremely high wind speeds and the effect of CD on the intensity is stronger than that of CK. The promotion effect of the present CD and CK correlations on the tropical cyclone intensity can also be seen in the simulations of actual strong tropical cyclones using the Weather Research and Forecasting Model as shown for reference in the appendix.

Fig. 15.
Fig. 15.

Dependence of (CK/CD)1/2 on U10.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

4. Summary

In this study, we investigated the heat transfer across the wind-driven breaking air–water interface at extremely high wind speeds, using a high-speed wind-wave tank, and proposed heat transfer coefficients using a new multi-heat-balance method. Our laboratory measurements show that the latent and sensible heat transfer coefficients become constant at low and normal wind speeds but increase sharply for extremely high wind speeds of U10 > 35 m s−1. The transition at U10 ≈ 35 m s−1 corresponds to that of the drag coefficient and is caused by intensive wave breaking. The latent and sensible heat transfer coefficients also have the same shape with U10. Therefore, the wind speed dependence of the latent and sensible heat transfer coefficients can be represented by that of the enthalpy coefficient. By applying both our laboratory correlations of the enthalpy and drag coefficients and conventional correlations to Emanuel’s (1995) analytic model, we estimated the effects of the coefficients on the maximum intensity of tropical cyclones at extremely high wind speeds. The results show that the present CD and CK significantly promote the maximum storm intensity, compared to the conventional coefficients. The WRF simulations in the appendix also show the similar promotion effects of the coefficients. Although our new laboratory correlations have not yet been verified in real oceans, the model predictions suggest the importance of proposing more reliable heat and drag coefficients, verified by field experiments at extremely high wind speeds.

Acknowledgments

We thank M. Ishida, H. Muroya, and M. Nishihira for their help in conducting the experiments. This work was supported by the Ministry of Education, Culture, Sports, Science, and Technology, Grant-in-Aid (25249013 and 16K18015). The numerical simulations were carried out on the supercomputer system of the Japan Agency for Marine-Earth Science and Technology.

APPENDIX

Numerical Predictions of Track and Intensity for Strong Tropical Cyclones Using the WRF Model

To show the effects of the variations in the enthalpy and momentum transfer coefficients on the practical predictions of tropical cyclones, we numerically simulated strong typhoon Haiyan (2013) and Hurricanes Katrina (2005) and Ivan (2004) using the WRF Model with our new correlations of (21) and (22) or conventional correlations of (23) and (24) of CD and CK (=CE and CH) with U10.

The simulations of the three TCs were performed for three days: from 1800 UTC on 5 November 2013 for Haiyan (2013), from 1800 UTC on 27 August 2005 for Katrina (2005), and from 0000 UTC on 13 September 2004 for Ivan (2004). The computational horizontal domains were set to 4700 km × 4000 km on 1620 × 1440 grids for Haiyan (2013) and 3500 km × 3200 km on 1260 × 1152 grids for both Katrina (2005) and Ivan (2004). The top layer was set at 50 hPa and 51 vertical layers were used for all of the TC simulations. We performed two simulations for each TC, one with our new correlations, (21) and (22), and the other with the conventional correlations, (23) and (24), to investigate the effects of our new correlations on the TC simulations. The initial conditions were obtained from a final reanalysis database provided by the National Centers for Environmental Prediction (NCEP). The lateral and surface boundary conditions of wind speed, pressure, and temperatures including sea surface temperature were replicated every 6 h using the NCEP database. Except for the correlation models for CD and CK, we used conventional schemes implemented in the WRF: the WSM6 option was used for the cloud microphysics model. The RRTM option and Dudhia option were used for shortwave and longwave radiation models, respectively. The Mellor–Yamada–Nakanishi–Niino Level 2.5 (MYNN2) option was used for the planetary boundary layer physics model. The detailed descriptions for the above options can be found in the users’ guide of the WRF homepage.

Figure A1 shows the comparison between the predictions and observations. The track predictions are insensitive to the correlation models for CD and CK, while the intensity predictions are dependent on them. The observed Haiyan is in its strongest stage with UMAX = 64 m s−1 at simulation times t ranging from 42 to 58 h. The simulated Haiyan with the conventional correlations reaches its maximum for UMAX = 55 m s−1 at t = 60 h, while that of our new correlations have UMAX = 69 m s−1 at t = 62 h. Thus, the intensity prediction using our new correlations agrees better with the observation, whereas the conventional correlations significantly underestimate the intensity. Similar results are obtained for Katrina. The observed Katrina reaches its maximum with UMAX = 77 m s−1 at t = 24 h. The simulated Katrina with the conventional correlations reaches its maximum with UMAX = 54 m s−1 at t = 40 h, while that with the new correlations predicts UMAX = 68 m s−1. For the Ivan case, the initial conditions of the simulation seem to disagree with the actual conditions, and the simulated TC is initially much weaker than the observed TC. The simulated TC develops slightly in the first half of the simulated period and more closely resembles the observed one, which is decaying for the whole period. The simulated TC with the new correlations develops more than that with the conventional correlations and agrees better with the observation after t = 21 h. These WRF simulations also support the estimation of the maximum storm intensity by Emanuel’s (1995) analytic model.

Fig. A1.
Fig. A1.

Predictions of (a) track and (b) intensity (maximum 10-m wind speed) for (top) typhoon Haiyan (2013), (middle) Hurricane Katrina (2005), and (bottom) Hurricane Ivan (2004). Predictions from the present and conventional correlations are shown in red and blue, respectively. Observed values from the Digital Typhoon website (http://agora.ex.nii.ac.jp/digital-typhoon/index.html.en) are shown in black.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0243.1

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Journal of Physical Oceanography

  • Andreas, E. L., 2011: Fallacies of the enthalpy transfer coefficient over the ocean in high winds. J. Atmos. Sci., 68, 1435–1445, https://doi.org/10.1175/2011JAS3714.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Bell, M. M., M. T. Montgomery, and K. A. Emanuel, 2012: Air–sea enthalpy and momentum exchange at major hurricane wind speeds observed during CBLAST. J. Atmos. Sci., 69, 3179–3222, https://doi.org/10.1175/JAS-D-11-0276.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Charnock, H., 1955: Wind stress on a water surface. Quart. J. Roy. Meteor. Soc., 81, 639–640, https://doi.org/10.1002/qj.49708135027.

  • DeCosmo, J., K. B. Katsaros, S. D. Smith, R. J. Anderson, W. A. Oost, K. Bumke, and H. Chadwick, 1996: Air-sea exchange of water vapor and sensible heat: The Humidity Exchange Over the Sea (HEXOS) results. J. Geophys. Res., 101, 12 001–12 016, https://doi.org/10.1029/95JC03796.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • DeMaria, M., C. Sampson, J. A. Knaff, and K. D. Musgrave, 2014: Is tropical cyclone intensity guidance improving? Bull. Amer. Meteor. Soc., 95, 387–398, https://doi.org/10.1175/BAMS-D-12-00240.1.

    • Search Google Scholar
    • Export Citation

  • Donelan, M. A., B. K. Haus, N. Reul, W. J. Plant, M. Stiassnie, H. C. Graber, O. B. Brown, and E. S. Saltzman, 2004: On the limiting aerodynamic roughness of the ocean in very strong winds. Geophys. Res. Lett., 31, L18306, https://doi.org/10.1029/2004GL019460.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Drennan, W. M., J. A. Zhang, J. R. French, C. McCormick, and P. G. Black, 2007: Turbulent fluxes in the hurricane boundary layer. Part II: Latent heat flux. J. Atmos. Sci., 64, 1103–1115, https://doi.org/10.1175/JAS3889.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Emanuel, K. A., 1995: Sensitivity of tropical cyclones to surface exchange coefficients and a revised steady-state model incorporating eye dynamics. J. Atmos. Sci., 52, 3969–3976, https://doi.org/10.1175/1520-0469(1995)052<3969:SOTCTS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Friehe, C. A., and K. F. Schmitt, 1976: Parameterization of air-sea interface fluxes of sensible heat and moisture by the bulk aerodynamic formulas. J. Phys. Oceanogr., 6, 801–809, https://doi.org/10.1175/1520-0485(1976)006<0801:POASIF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Garratt, J. R., and P. Hyson, 1975: Vertical fluxes of momentum, sensible heat and water vapour during the Air Mass Transformation Experiment (AMTEX) 1974. J. Meteor. Soc. Japan, 53, 149–160, https://doi.org/10.2151/jmsj1965.53.2_149.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Green, B. W., and E. Zhang, 2013: Impacts of air–sea flux parameterizations on the intensity and structure of tropical cyclones. Mon. Wea. Rev., 141, 2308–2324, https://doi.org/10.1175/MWR-D-12-00274.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Hasse, L., M. Grunewald, J. Wucknitz, M. Dunckel, and D. Schriever, 1978: Profile derived turbulent fluxes in the surface layer under disturbed and undisturbed conditions during GATE. “Meteor” Forschungsergeb., 13B, 24–40.

    • Search Google Scholar
    • Export Citation

  • Haus, B. K., D. Jeong, M. A. Donelan, J. A. Zhang, and I. Savelyev, 2010: Relative rates of sea‐air heat transfer and frictional drag in very high winds. Geophys. Res. Lett., 37, L07802, https://doi.org/10.1029/2009GL042206.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Hawkins, H. F., and D. T. Rubsam, 1968: Hurricane Hilda, 1964: II. Structure and budgets of the hurricane on October 1, 1964. Mon. Wea. Rev., 96, 617–636, https://doi.org/10.1175/1520-0493(1968)096<0617:HH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Iwano, K., N. Takagaki, K. Kurose, and S. Komori, 2013: Mass transfer velocity across the breaking air–water interface at extremely high wind speeds. Tellus, 65B, 21341, https://doi.org/10.3402/tellusb.v65i0.21341.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Jeong, D., B. K. Huas, and M. A. Donelan, 2012: Enthalpy transfer across the air–water interface in high winds including spray. J. Atmos. Sci., 69, 2733–2748, https://doi.org/10.1175/JAS-D-11-0260.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Johnson, H. K., J. Hjstrup, H. J. Vested, and S. E. Larsen, 1998: On the dependence of sea surface roughness on wind waves. J. Phys. Oceanogr., 28, 1702–1716, https://doi.org/10.1175/1520-0485(1998)028<1702:OTDOSS>2.0.CO;2.

    • Crossref
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  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    Laboratory and field measurements of drag coefficient CD for varying U10.

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    (a) Schematic diagram of the high-speed wind-wave tank. Photographs of the wind waves at (b) U10 = 7.25, (c) U10 = 48.0, and (d) U10 = 67.1 m s−1.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    Droplet-adherent prevention device attached at the plate-grass sidewall. (a) View on the x–z plane and (b) view on the y–z plane. The four circles in (a) indicate the four orifices.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    Distributions of (a) mean droplet velocity and (b) correlation between streamwise and vertical droplet velocity fluctuations against droplet diameter (U10 = 56 m s−1).

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    Three-dimensional distributions of the heat flux terms in (6) at U10 = 60 m s−1. (a) General view and (b) view along the plane in (a). The red and blue dots indicate the data located above and below the plane, respectively.

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    Snapshot of droplets dispersing over breaking waves at U10 = 47.7 m s−1.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    Sketch of breaking wind waves and dispersed droplets at high wind speeds in the wind-wave tank.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    Shadow-sizing method used in this study. (a) Measurement system and (b) images obtained by the shadow-sizing method at U10 = 48 m s−1.

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    Distributions of the properties of dispersed droplets against droplet diameter. (a) Number density of the droplets, (b) mean vertical velocity of the droplets with upward velocity, (c) ratio of the dispersed droplets with upward velocity to the total dispersed droplets, (d) number flux of dispersed droplets with upward velocity normalized by total number flux, and (e) volume flux of dispersed droplets with upward velocity. All symbols are as in (a).

  • <sc>Fig</sc>. 10.
    View in gallery
    Fig. 10.

    Ratio of the heat flux QSP due to the cooling of the virtual entrant droplets to the total air–water heat flux QT. The solid line is a best-fit curve obtained by the least squares method.

  • <sc>Fig</sc>. 11.
    View in gallery
    Fig. 11.

    Distributions of heat and enthalpy transfer coefficients, CE, CH, and CK for various U10.

  • <sc>Fig</sc>. 12.
    View in gallery
    Fig. 12.

    Relationship between shear stress τ and U10.

  • <sc>Fig</sc>. 13.
    View in gallery
    Fig. 13.

    Relationship between wave slope HS/LS and U10.

  • <sc>Fig</sc>. 14.
    View in gallery
    Fig. 14.

    The CK and CD as a function of U10.

  • <sc>Fig</sc>. 15.
    View in gallery
    Fig. 15.

    Dependence of (CK/CD)1/2 on U10.

  • <sc>Fig</sc>. A1.
    View in gallery
    Fig. A1.

    Predictions of (a) track and (b) intensity (maximum 10-m wind speed) for (top) typhoon Haiyan (2013), (middle) Hurricane Katrina (2005), and (bottom) Hurricane Ivan (2004). Predictions from the present and conventional correlations are shown in red and blue, respectively. Observed values from the Digital Typhoon website (http://agora.ex.nii.ac.jp/digital-typhoon/index.html.en) are shown in black.

Fig. 1.

Laboratory and field measurements of drag coefficient CD for varying U10.
Fig. 2.

(a) Schematic diagram of the high-speed wind-wave tank. Photographs of the wind waves at (b) U10 = 7.25, (c) U10 = 48.0, and (d) U10 = 67.1 m s−1.
Fig. 3.

Droplet-adherent prevention device attached at the plate-grass sidewall. (a) View on the x–z plane and (b) view on the y–z plane. The four circles in (a) indicate the four orifices.
Fig. 4.

Distributions of (a) mean droplet velocity and (b) correlation between streamwise and vertical droplet velocity fluctuations against droplet diameter (U10 = 56 m s−1).
Fig. 5.

Three-dimensional distributions of the heat flux terms in (6) at U10 = 60 m s−1. (a) General view and (b) view along the plane in (a). The red and blue dots indicate the data located above and below the plane, respectively.
Fig. 6.

Snapshot of droplets dispersing over breaking waves at U10 = 47.7 m s−1.
Fig. 7.

Sketch of breaking wind waves and dispersed droplets at high wind speeds in the wind-wave tank.
Fig. 8.

Shadow-sizing method used in this study. (a) Measurement system and (b) images obtained by the shadow-sizing method at U10 = 48 m s−1.
Fig. 9.

Distributions of the properties of dispersed droplets against droplet diameter. (a) Number density of the droplets, (b) mean vertical velocity of the droplets with upward velocity, (c) ratio of the dispersed droplets with upward velocity to the total dispersed droplets, (d) number flux of dispersed droplets with upward velocity normalized by total number flux, and (e) volume flux of dispersed droplets with upward velocity. All symbols are as in (a).
Fig. 10.

Ratio of the heat flux QSP due to the cooling of the virtual entrant droplets to the total air–water heat flux QT. The solid line is a best-fit curve obtained by the least squares method.
Fig. 11.

Distributions of heat and enthalpy transfer coefficients, CE, CH, and CK for various U10.
Fig. 12.

Relationship between shear stress τ and U10.
Fig. 13.

Relationship between wave slope HS/LS and U10.
Fig. 14.

The CK and CD as a function of U10.
Fig. 15.

Dependence of (CK/CD)1/2 on U10.
Fig. A1.

Predictions of (a) track and (b) intensity (maximum 10-m wind speed) for (top) typhoon Haiyan (2013), (middle) Hurricane Katrina (2005), and (bottom) Hurricane Ivan (2004). Predictions from the present and conventional correlations are shown in red and blue, respectively. Observed values from the Digital Typhoon website (http://agora.ex.nii.ac.jp/digital-typhoon/index.html.en) are shown in black.
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