Quantifying the Airflow Distortion over Merchant Ships. Part I: Validation of a CFD Model

Bengamin I. Moat National Oceanography Centre, Southampton, United Kingdom

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Margaret J. Yelland National Oceanography Centre, Southampton, United Kingdom

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Robin W. Pascal National Oceanography Centre, Southampton, United Kingdom

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Anthony F. Molland School of Engineering Sciences, Ship Science, University of Southampton, Southampton, United Kingdom

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Abstract

The effects of flow distortion created by the ship’s hull and superstructure bias wind speed measurements made from anemometers located on ships. Flow distortion must be taken into account if accurate air–sea flux measurements are to be achieved. Little work has been undertaken to examine the wind speed bias due to flow distortion in wind speed reports from voluntary observing ships (VOS). In this first part of a two-part paper the accuracy of the computational fluid dynamics (CFD) code VECTIS in simulating the airflow over VOS is investigated. Simulations of the airflow over a representation of the bridge of a VOS are compared to in situ wind speed measurements made from six anemometers located above the bridge of the RRS Charles Darwin. The ship’s structure was ideal for reproducing the flow over VOS when the wind is blowing onto either beam. The comparisons showed VECTIS was accurate to within 4% in predicting the wind speed over ships, except in extreme cases such as wake regions or the region close to the bridge top where the flow may be stagnant or reverse direction. The study showed that there was little change in the numerically predicted flow pattern above the bridge with change in Reynolds number between 2 × 105 and 1 × 107. The findings showed that the CFD code VECTIS can reliably be used to determine the mean flow above typical VOS.

Corresponding author address: Dr. B. I. Moat, National Oceanography Centre, European Way, Southampton SO14 3ZH, United Kingdom. Email: bim@noc.soton.ac.uk

Abstract

The effects of flow distortion created by the ship’s hull and superstructure bias wind speed measurements made from anemometers located on ships. Flow distortion must be taken into account if accurate air–sea flux measurements are to be achieved. Little work has been undertaken to examine the wind speed bias due to flow distortion in wind speed reports from voluntary observing ships (VOS). In this first part of a two-part paper the accuracy of the computational fluid dynamics (CFD) code VECTIS in simulating the airflow over VOS is investigated. Simulations of the airflow over a representation of the bridge of a VOS are compared to in situ wind speed measurements made from six anemometers located above the bridge of the RRS Charles Darwin. The ship’s structure was ideal for reproducing the flow over VOS when the wind is blowing onto either beam. The comparisons showed VECTIS was accurate to within 4% in predicting the wind speed over ships, except in extreme cases such as wake regions or the region close to the bridge top where the flow may be stagnant or reverse direction. The study showed that there was little change in the numerically predicted flow pattern above the bridge with change in Reynolds number between 2 × 105 and 1 × 107. The findings showed that the CFD code VECTIS can reliably be used to determine the mean flow above typical VOS.

Corresponding author address: Dr. B. I. Moat, National Oceanography Centre, European Way, Southampton SO14 3ZH, United Kingdom. Email: bim@noc.soton.ac.uk

1. Introduction

A proportion of merchant ships routinely report meteorological parameters at the ocean surface as part of the voluntary observing ships (VOS) program. These observations include wind speed and direction, air and sea surface temperature, cloud cover, and sea state. It has long been suspected that wind speed measurements from fixed anemometers on VOS may be affected by the presence of the ship distorting the flow of air (Dobson 1981) to the sensor, but no quantitative results of typical VOS have previously been published.

Physical simulations (Blanc 1986, 1987; Surry et al. 1989; Weill et al. 2003) provided estimates of the airflow distortion at specific anemometer locations. Numerical simulations of the airflow over ships provide a greater opportunity to estimate the flow at a number of different anemometer locations and investigate the flow over the whole of the ship’s structure. Numerical studies have previously been used for studying airflow over research ships (Kahma and Leppäranta 1981; Yelland et al. 1998, 2002; Dupuis et al. 2003; Popinet et al. 2004). Research ship model geometries are very detailed and their anemometers are carefully sited in well-exposed sites, often on a mast in the ship’s bows. In contrast, anemometers on typical tankers and container ships are generally located above the ship’s bridge where the flow distortion may be more severe.

Various experimental studies of the flow over bluff bodies have been published for the purpose of validating computational fluid dynamics (CFD) codes. However, these were either bounded flows (e.g., Martinuzzi and Tropea 1993) or they did not measure the velocity in sufficient detail in the areas of interest to enable a comparison to be made (e.g., Minson et al. 1995; Cheney and Zan 1999). For this application, these studies are not suitable for direct comparison with the CFD code.

This paper provides the first step in deriving a method to determine the possible bias in wind speed measurements for anemometers located on merchant ships. To this end, this paper presents a validation of the CFD code VECTIS. The mean airflow above a surface-mounted block is simulated using VECTIS and the results are compared to in situ wind speed data measured from a number of anemometers located on the RRS Charles Darwin. CFD studies of the airflow over merchant ships are then performed and the results presented in Moat et al. (2006).

Section 2 gives a description of the VECTIS code and the discretization used for the simulations. Although the RRS Charles Darwin (Fig. 1) is not typical of VOS, such as a tanker or container ship, the ship’s structure makes it ideal for studying bluff body flows when the wind is blowing onto either beam (±90°). The instruments used and their locations are described in section 3.

It was not feasible to locate an anemometer far enough from the ship to be certain of measuring the completely undistorted or free streamflow, for example, by using a buoy-mounted anemometer. Therefore, two CFD models of the airflow over a detailed model of the RRS Charles Darwin at ±90° were simulated (section 4). Yelland et al. (2002) validated such detailed models for simulating the flow distortion at well-exposed locations. The results of the models were used to correct the well-exposed foremast anemometer for the effects of flow distortion. The resulting free-stream wind speeds were used to normalize the wind speed measurements from anemometers located above the bridge and the absolute wind speed changes were determined.

Section 5 compares the in situ wind speed measurements with the CFD simulations of the flow over the surface-mounted block. To verify that there was little change in the numerically predicted flow pattern with Reynolds number, a comparison is also made with the CFD wind speed profile from the full-scale simulation of the flow over the detailed model of the ship (performed in section 4).

2. The computational fluid dynamics code

The CFD investigation was carried out using the commercially available VECTIS software package (Ricardo 2001). VECTIS uses the finite-volume method for solving the Reynolds-averaged Navier–Stokes equations on a nonuniform Cartesian grid. The pressure–velocity coupling is achieved with the Pressure Implicit with Splitting of Operators (PISO) algorithm. A second-order-accurate differencing scheme (Zhu and Rodi 1991) is used to approximate the advection and diffusion of the fluid motion. A first-order-accurate upwind differencing scheme (Spalding 1972) was used for the pressure equation, the turbulent kinetic energy (k), and the rate of dissipation of turbulent kinetic energy (ɛ). The RNG kɛ (Yakhot et al. 1992) turbulence closure scheme was used to parameterize the Reynolds stress terms created by the averaging process. Even though the CFD solutions are modeled at sufficiently low wind speeds (<14 m s−1) so that density changes are minimal, a compressible solution is always specified since it produces a more stable solution (B. Carrol 2002, personal communication).

The main benefit of using VECTIS over other commercial CFD codes is the speed at which computational mesh can be created. For complicated ship geometries, typical mesh sizes of 500 000 cells can be created in less than an hour. However, the convergence times of the solutions can be up to 2 weeks depending upon which machine is used. Given that this convergence time is continually reducing with the present increase in computing power, VECTIS will continue to be used to study these types of problems.

All VECTIS simulations presented herein are steady-state solutions and three-dimensional. The simulations were also isothermal; that is, the air, the block sides, and the computational domain walls were set at a constant temperature of 20°C. The number of cells in each simulation can be increased in specific areas of interest such as the region above the bluff body. At large distances from the bluff body, where the flow does not vary a great deal, the number of cells is minimized.

3. The in situ wind speed measurements

RRS Charles Darwin cruises CD140 and CD141 (New et al. 2003) took place in the Indian Ocean (Fig. 2) for 58 days between May and July 2002. The ship was equipped with seven anemometers located on the foremast and above the bridge. The instruments used and their accuracy were as follows: one HS sonic anemometer (<±1% for winds below 45 m s−1), one R2 sonic anemometer (<1% rms), one Windmaster sonic anemometer (1.5% for winds below 20 m s−1), and four Vector cup anemometers (within 1%). The HS, R2, and Windmaster sonics output three-component wind speed measurements at 20, 21, and 0.1 Hz, respectively. The Vector cup anemometers measured the horizontal wind speed component only and were sampled at 0.1 Hz.

The HS sonic anemometer was located on the foremast platform (Fig. 3). A temporary 6-m mast equipped with the R2 sonic anemometer, four Vector anemometers, and the Windmaster sonic anemometer was located above the bridge top (Fig. 4). The anemometers were located 5.2 m back from the bridge front in a region of good exposure for flows over either beam. Normalizing by the height of the bridge above the waterline, H = 13 m, the mast was located x/H = 0.21 from the starboard side and x/H = 0.51 from the port side. The heights of all anemometers above sea level are indicated in Table 1.

The 20-Hz output from the HS sonic and the 21-Hz output from the R2 sonic were logged for 54 and 52 min, respectively (64 sampling periods of 1024 data) every hour. Each sampling period was averaged to produce a mean relative wind speed over a 51-s period. Data from the other anemometers were logged at 0.1 Hz and then averaged over the same 51-s period. The RRS Charles Darwin results contained approximately 1.5 days of wind speed data for flows within ±5° of both beams of the ship. The maximum relative wind speed was 21 m s−1 and the mean was 10 m s−1. Only in situ wind speeds measured above 3 m s−1 were used in the analysis since below this wind speed the data were limited in number and showed a lot of scatter.

Pre- and postcruise calibrations of the HS sonic, R2 sonic, and Windmaster sonic were performed to examine any change in the accuracy of the instrumentation during the cruises. The postcruise HS and Windmaster calibrations showed there was no change in their calibration during the cruise. The postcruise R2 sonic calibration suggested a 2% overestimate of the wind speed for relative wind directions over either beam. A correction was applied to the wind speed data measured by this instrument.

The HS, R2, and the Windmaster sonic anemometers are very accurate at measuring low wind speeds, but could not be used for all the sites on the temporary mast due to the size and weight of the anemometers. Therefore, Vector anemometers were used at four locations above the bridge. The Vector cup anemometers were purchased especially for the cruise. The manufacturer’s calibrations were applied, but no facilities were available to perform a postcruise calibration of these instruments. The Vector anemometers required a cosine correction to calculate the total wind speed:
i1520-0426-23-3-341-e1
where υx is the measured horizontal wind speed component and θ is the angle of the flow to the vertical at the anemometer site. The angle of the flow, θ, was predicted by two CFD models of the flow over either beam of the RRS Charles Darwin (section 4). Cosine corrections of up to 4% were applied to all vector anemometer wind speed data.

4. Determination of an in situ free-stream value

An estimate of the undistorted, or free-stream airflow, is required in order to quantify the biases in the measured wind speed from the in situ ship data. Yelland et al. (1998, 2002) showed that VECTIS simulations of very detailed models of the RRS Charles Darwin geometry reproduced the wind speed at very well exposed anemometer sites to within about 2% for flows within 30° of the bow. The HS sonic anemometer was located on the foremast platform in a well-exposed location and well away from the bridge top, that is, the area under investigation. This section uses two CFD models to produce wind speed corrections for the HS sonic anemometer for flows directly over either beam. These corrected data are then used to calculate the vertical profile of the free-stream wind speed. In addition, wind speed profiles at the vector anemometer locations from these two detailed CFD models of the ship are also compared to the in situ and CFD results above the surface-mounted block in section 5.

Descriptions of the methods used to model the flow over the RRS Charles Darwin are given in detail in Moat and Yelland (1996) and will only be summarized here. The CFD simulations do not take into account the ships pitching or rolling motion and only simulate the airflow over a stationary ship. A commercially available finite-element preprocessor, FEMGEN (Femsys 1999), was used to form the surface geometry of the ship from a digitized set of ship’s plans. The ship geometry was placed in the center of a flow domain with an overall length of 9 ship lengths, width of 23 ship lengths, and a height of 2 ship lengths. The width of the computational domain was chosen to ensure that the blockage of the flow in the domain by the ship was less than 1%. The minimum cell size was 0.007H, where H is the height of the bridge above the waterline. The Reynolds number based on the bridge-to-waterline height was Re = 1.3 × 107. The inlet of the computational domain was defined as a wind speed profile that varied logarithmically with height, z. An open-ocean wind speed of UzN = 14 m s−1 at a height of z = 10 m in neutral atmospheric stability conditions was applied (Stull 1988). Up to 600 000 computational cells of varying size were used to solve the flow field. The RNG kɛ turbulence parameterization was used for both of the models. The time taken for a solution to converge was 2 weeks using an SGI Origin 200 workstation. To check that the ship did not create a significant blockage to the flow, the speed of the flow at points well abeam of the ship was compared to the speed of the flow at the inlet and outlet. Since no significant blockage was found, the speed of the free streamflow was determined using a vertical profile of the wind speed at a point well abeam (more than 700 m) of the anemometer position. It must be noted that smaller structures such as the handrails around the foremast platform and the instruments themselves were too small to be resolved in the model.

CFD corrections of 7% and 4% were applied to the HS sonic wind speed data for flows over the port and starboard beams, respectively. The wind speed along a plane passing through the HS sonic anemometer site is shown in Fig. 5. The presence of the ship causes the air to be deflected in the horizontal plane. Horizontal deflections of 4° and 7° at the HS anemometer site, for flows over the port and starboard beams, were predicted by the CFD models and applied to the in situ wind speed data. Logarithmic wind speed profiles at three different wind speeds in neutrally stable atmospheric conditions were calculated to examine the change in free-stream wind speed with height between the HS sonic and the bridge anemometers. Free-stream wind speeds profiles calculated using Uz = 5, 10, and 15 m s−1 showed an increase in speed of about 2% (about 0.5% m−1) from the HS sonic height at 15.2 m to the R2 sonic at 19.6 m. The free-stream wind speed measured from the HS sonic was corrected for the change in height and used to normalize the wind speed measurements made by anemometers above the bridge. These normalized wind speed profiles for airflows over the port and starboard beams are compared with the bluff body CFD results in section 5.

5. Validation of the CFD code

a. Bluff body simulation used for validation

The CFD-simulated general flow pattern over the bluff body block is presented in this section and will be compared to the in situ measurements from anemometers on the RRS Charles Darwin in section 5b. Simulations of the three-dimensional airflow over the block were performed for flows normal to the geometry. The block was 0.294 m in length (L), 0.595 m in breadth (B), and 0.422 m in height (H) (Fig. 6). It was placed in the center of a flow domain with an overall length of 34L, width of 62L, and a height of 91L. The minimum cell size in the model was 0.008H. The flow over the models was investigated using a uniform inlet wind speed profile of 7 m s−1, leading to a nominal Reynolds number based on the block height of 2.1 × 105. The number of cells in the computational domain was 486 000. All results presented here are from the centerline of the block and have been normalized by the uniform inlet wind speed.

Like all CFD codes the VECTIS simulations are dependent on the mesh density and turbulence closure model applied. For flows over a bluff body ship, Moat (2003) showed VECTIS has possible changes in the normalized wind speed of <1% using minimum cell sizes between 0.018H and 0.04H, <2% between the RNG and kɛ turbulence closure schemes, and <3% in scaling the geometry from H = 13.54 m to H = 0.14 m. The parameter H is defined as the height of the bridge top to the deck. The most important factor was the specification of the inlet wind speed profile. When a boundary layer profile is replaced with a uniform inlet profile, the maximum wind speed above the ship increased in wind by up to 4%. The findings of Moat (2003) were applied to this investigation and resulted in an effectively mesh-independent solution with variations in wind speed of 4% or less.

The CFD-simulated mean wind speed over the block is shown in Fig. 7. The general flow pattern around bluff bodies is well known (Hunt et al. 1978; Murakami et al. 1993) and is reproduced in the VECTIS simulations. A standing vortex is produced in front of the block and there is flow separation at the upwind leading edge. Close to the top of the block the airflow is decelerated and a flow counter to the mean flow direction is present. The depth of the decelerated region increases with distance back from the front edge of the bridge. Above the decelerated region is a line of equality where the wind speed is equal to the free-stream wind speed (normalized wind speed of 1.0). Above the line of equality the wind speed is accelerated and then decreases with increase in height.

b. Comparison of the CFD flow over the block with the in situ ship data

In this section in situ normalized wind speed profiles measured by anemometers above the bridge on the RRS Charles Darwin, for beam-on flows, are compared to the CFD normalized wind speed profiles for a flow directly over the block. The normalized wind speed is defined as the measured wind speed divided by the free-stream wind speed. The CFD profiles above the detailed model of the ship are also compared to determine if the change in the Reynolds number between the bluff body simulation and the full-scale in situ measurements is significant.

Flows over the starboard beam are shown in Fig. 8 and over the port beam in Fig. 9. The height above the bridge, z, was scaled by the step height of the bridge top to the waterline, H = 13 m. Likewise, x, the distance downstream of the leading edge, was scaled by H. Using this step height, the scaled distances of the anemometers from the starboard and port upwind leading edges were x/H = 0.21 and x/H = 0.51, respectively. The upwind leading edge of the bridge is defined as x/H = 0 = z/H. The CFD wind speed profiles were extracted at x/H = 0.21 and x/H = 0.51 back from the front edge of a simulation of the flow over the bluff body cube of height H = 0.422 m. These data were normalized by a free-stream profile obtained from a second CFD simulation with no bluff body present.

Qualitatively, Figs. 8 and 9 show very good agreement with regard to the shape of the profiles from both the CFD simulations of the flow over the block and the in situ results. Both of the in situ profiles predict a decelerated region above the bridge top, which varies in depth with distance back from the upwind leading edge. The normalized wind speed increases to a maximum of 1.17 (at z/H = 0.28; Fig. 8) and then decreases with increase in height. For flows over the starboard beam the agreement between the CFD results and the in situ data is very good at all five anemometer positions (Fig. 8). For flows over the port beam (Fig. 9) the results are also in very good agreement except for the lowest two anemometer sites where the normalized wind speed difference is as large as 0.40. This discrepancy could be due to the vector anemometers measuring only the magnitude of the wind speed and not the direction. The lowest two anemometers are in a region of weak recirculation where the flow is unsteady and a negative normalized velocity, that is, a flow counter to the mean flow, may exist. If this were the case, then it would lead to a better comparison with the CFD studies in this region. In the accelerated region the CFD-simulated wind speed profiles agree to within 0.04 in normalized wind speed with the in situ wind speed measurements for both port and starboard flows. In summary, VECTIS predicts the general flow pattern well above a block and can be used to simulate the airflow above bluff body ships.

c. Variation of the CFD-predicted velocity with Reynolds number

The sensitivity of the numerical model to the variation in Reynolds number was examined. Full-scale CFD simulations of the airflow over both beams of the detailed geometry of the RRS Charles Darwin were compared to the CFD normalized wind speed profiles above the block in Figs. 8 and 9. Based on the bridge-to-waterline height, the Reynolds number of the detailed CFD model of the ship was 1.3 × 107. The Reynolds number of the CFD simulations over the scaled block was 2.1 × 105 based on the block height. The CFD simulations reproduce the general shape of the in situ measurements well. The CFD normalized wind speed profile above the detailed geometry of the ship underestimates the depth of the decelerated region close to the top of the bridge. This can be accounted for by a decrease in the position of the waterline of 0.5 m in the full-scale detailed CFD study of the RRS Charles Darwin. The comparison shows that in the accelerated region there is little variation in the shape and magnitude of the CFD normalized wind speed profiles with change in Reynolds number. This agrees well with Yelland et al. (2002) who used experimental wind speed measurements to show that absolute wind speed errors from the RRS Charles Darwin did not vary with wind speeds in the range 5–25 m s−1.

6. Summary

Simulations of the airflow over a representation of the bridge of VOS were performed using the CFD code VECTIS. The CFD results were compared with beam-on in situ wind speed measurements from anemometers located above the bridge of the RRS Charles Darwin. The comparisons showed VECTIS to be accurate to within 4% in predicting the wind speed over VOS, except in extreme cases such as the region close to the bridge top where the flow may be stagnant or reverse direction.

CFD simulations of the airflow over a detailed model of the RRS Charles Darwin were performed. The simulations were at full scale and were compared to the CFD simulations over a scaled block. The comparison showed that there was little variation in the numerically predicted flow pattern with change in Reynolds number between 2 × 105 and 1 × 107. This suggests that the CFD simulations were not sensitive to changes within this Reynolds number range.

The investigation has demonstrated that VECTIS can be used to determine the general flow pattern. The CFD code will be used to examine the flow over generic bluff body ship shapes in Moat et al. (2006) and a method to determine the bias in the wind speed measurements on voluntary observing ships will be proposed.

Acknowledgments

The authors wish to thank Dr. Peter K. Taylor (National Oceanography Centre, United Kingdom) and Mr. Val Swail (Meteorological Service of Canada) for their support and encouragement. This project was partially funded by the Meteorological Service of Canada and the Woods Hole Oceanographic Institution.

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Fig. 1.
Fig. 1.

A photograph of the RRS Charles Darwin [reproduced with permission from Natural Environment Research Council (NERC) Research Ship Unit, Southampton, United Kingdom].

Citation: Journal of Atmospheric and Oceanic Technology 23, 3; 10.1175/JTECH1858.1

Fig. 2.
Fig. 2.

The ship track of RRS Charles Darwin cruises CD140 (solid line) and CD141 (dotted line).

Citation: Journal of Atmospheric and Oceanic Technology 23, 3; 10.1175/JTECH1858.1

Fig. 3.
Fig. 3.

The position of the HS sonic anemometer (indicated by the arrow) on the foremast platform of the RRS Charles Darwin looking from (a) astern and (b) above.

Citation: Journal of Atmospheric and Oceanic Technology 23, 3; 10.1175/JTECH1858.1

Fig. 4.
Fig. 4.

The temporary mast above the bridge of the RRS Charles Darwin looking toward the starboard side.

Citation: Journal of Atmospheric and Oceanic Technology 23, 3; 10.1175/JTECH1858.1

Fig. 5.
Fig. 5.

The CFD model results for a flow over the port beam of the RRS Charles Darwin. The arrows represent the velocity of the flow at each computational cell, and the variable mesh density can be seen. A vertical plane intersecting the HS sonic anemometer is shown.

Citation: Journal of Atmospheric and Oceanic Technology 23, 3; 10.1175/JTECH1858.1

Fig. 6.
Fig. 6.

The dimensions of the block and the coordinate system used.

Citation: Journal of Atmospheric and Oceanic Technology 23, 3; 10.1175/JTECH1858.1

Fig. 7.
Fig. 7.

Normalized CFD-predicted wind speeds above the block. The mean flow is from left to right.

Citation: Journal of Atmospheric and Oceanic Technology 23, 3; 10.1175/JTECH1858.1

Fig. 8.
Fig. 8.

Comparison of the normalized wind speed profiles at a distance of x/H = 0.21 from the upwind leading edge. The in situ data over the starboard beam of the RRS Charles Darwin (filled squares), CFD wind speed profiles above the surface-mounted block (solid line), and the detailed model of the Darwin (dashed line) are shown. The vertical dashed lines indicate a normalized wind speed of 0.0 and 1.0, respectively. The standard error of the in situ data ranged from 0.001 to 0.003.

Citation: Journal of Atmospheric and Oceanic Technology 23, 3; 10.1175/JTECH1858.1

Fig. 9.
Fig. 9.

As in Fig. 8, but for the flow over the port beam at a distance of x/H = 0.51 from the upwind leading edge. The standard error of the in situ data ranged from 0.003 to 0.006.

Citation: Journal of Atmospheric and Oceanic Technology 23, 3; 10.1175/JTECH1858.1

Table 1.

Location and height above sea level of the anemometers on the RRS Charles Darwin.

Table 1.
Save
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  • Fig. 1.

    A photograph of the RRS Charles Darwin [reproduced with permission from Natural Environment Research Council (NERC) Research Ship Unit, Southampton, United Kingdom].

  • Fig. 2.

    The ship track of RRS Charles Darwin cruises CD140 (solid line) and CD141 (dotted line).

  • Fig. 3.

    The position of the HS sonic anemometer (indicated by the arrow) on the foremast platform of the RRS Charles Darwin looking from (a) astern and (b) above.

  • Fig. 4.

    The temporary mast above the bridge of the RRS Charles Darwin looking toward the starboard side.

  • Fig. 5.

    The CFD model results for a flow over the port beam of the RRS Charles Darwin. The arrows represent the velocity of the flow at each computational cell, and the variable mesh density can be seen. A vertical plane intersecting the HS sonic anemometer is shown.

  • Fig. 6.

    The dimensions of the block and the coordinate system used.

  • Fig. 7.

    Normalized CFD-predicted wind speeds above the block. The mean flow is from left to right.

  • Fig. 8.

    Comparison of the normalized wind speed profiles at a distance of x/H = 0.21 from the upwind leading edge. The in situ data over the starboard beam of the RRS Charles Darwin (filled squares), CFD wind speed profiles above the surface-mounted block (solid line), and the detailed model of the Darwin (dashed line) are shown. The vertical dashed lines indicate a normalized wind speed of 0.0 and 1.0, respectively. The standard error of the in situ data ranged from 0.001 to 0.003.

  • Fig. 9.

    As in Fig. 8, but for the flow over the port beam at a distance of x/H = 0.51 from the upwind leading edge. The standard error of the in situ data ranged from 0.003 to 0.006.

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