The Influence of Sea Sprays on Drag Coefficient at High Wind Speed

Field and laboratory observations indicate that the variation of drag coefficient with wind speed at high winds is different from that under low-to-moderate winds.By taking the effects of wave development and sea spray into account,a new parameterization of drag coefficient applicable from low to extreme winds is proposed.It is shown that,under low-to-moderate wind conditions so that the sea spray effects could be neglected,the nondimensional aerodynamic roughness first increases and then decreases with the increasing wave age;whereas under high wind conditions,the drag coefficient decreases with the increasing wind speed due to the modification of the logarithmic wind profile by the effect of sea spray droplets produced by bursting bubbles or wind tearing breaking wave crests.The drag coefficients and sea surface aerodynamic roughnesses reach their maximum values vary under different wave developments.Correspondingly,the reduction of drag coefficient under high winds reduces the increasing rate of friction velocity with increasing wind speed.

Drag Coefficient of a Non-Convex Polygonal Plate during Free Fall

Waterside creatures or aquatic organisms use a fin or web to generate a thrust force. These fins or webs have a non-convex section, referred to as a non-convex shape. We investigate the drag force acting on a non-convex plate during unsteady motion. We perform the experiment in a water tank during free fall. We fabricate the non-convex plate by cutting isosceles triangles from the side of a convex hexagonal plate. The base angle of the triangle is between 0° to 45°. The base angle is 0 indicates the convex hexagonal thin plate. We estimate the drag coefficient with the force balance acting on the model based on the image analysis technique. The results indicate that increasing the base angle by more than 30° increased the drag coefficient. The drag coefficient during unsteady motion changed with the growth of the vortex behind the model. The vortex has small vortices in the shear layer, which is related to the Kelvin-Helmholtz instabilities.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Relevance of zero lift drag coefficient and lift coefficient to Mach number for large aspect ratio winged rigid body

Synthetic analysis is conducted to the wind tunnel experiment results of zero lift drag coefficient and lift coefficient for large aspect ratio winged rigid body.By means of wind tunnel experiment data,the dynamics model of the zero lift drag coefficient and lift coefficient for the large aspect ratio winged rigid body is amended.The research indicates that the change trends of zero lift drag coefficient and lift coefficient to Mach number are similar.The calculation result and wind tunnel experiment data all verify the validity of the amended dynamics model by which to estimate the zero lift drag coefficient and lift coefficient for the large aspect ratio winged rigid body,and thus providing some technical reference to aerodynamics character analysis of the same types of winged rigid body.

Projected area and drag coefficient of high velocity irregular fragments that rotate or tumble

3 degrees of freedom(DOF)exterior ballistic computer models are used in fragment studies to calculate individual trajectories of each fragment based on drag coefficient and the projected(presented)area in the direction of velocity of center of mass.The expectation of a randomly distributed projected area is commonly used for fragments that tumble(random rotation)during flight.We forecast a model where the expected drag coefficient is dependent of shape and Mach number.Rotation or tumbling only affects the expected projected area.Models of projected areas during tumbling and rotation are presented.An examination of the data by Mc Cleskey(1988)indicates that the volume of the fragment to the power of2/3 is a better parameter to characterize the drag coefficient of the fragments than the maximum projected area.Hydrocode simulations are used to verify results and to study projected area and drag coefficient of fragments.

Dependence of sea surface drag coefficient on wind-wave parameters

The relationships between sea surface roughness z 0 and wind-wave parameters are analyzed,and spurious self-correlations are found in all of the parameterization schemes.Sea surface drag coefficient C D is fitted by four wind-wave parameters that are wave age,wave steepness,windsea Reynolds number R B and R H ,and the analyzed data are divided into laboratory,field and combined data sets respectively.Comparison and analysis of dependence of C D on wind-wave parameters show that R B can fit the C D most appropriately.Wave age and wave steepness are not suitable to fit C D with a narrow range data set.When the value of wave age has a board range,R H is not suitable to fit C D either.Three relationships between C D and R B are integrated into the bulk algorithm COARE to calculate the observational friction velocity,and the results show that the relationship between C D and R B which is fitted with field data set can describe the momentum transfer in the open ocean,under low-moderate wind speed condition,most appropriately.

Parametric study on smoothed particle hydrodynamics for accurate determination of drag coefficient for a circular cylinder

Simulations of two-dimensional(2D) flow past a circular cylinder with the smoothed particle hydrodynamics(SPH) method were conducted in order to accurately determine the drag coefficient. The fluid was modeled as a viscous liquid with weak compressibility. Boundary conditions,such as a no-slip solid wall, inflow and outflow, and periodic boundaries, were employed to resemble the physical problem. A sensitivity analysis, which has been rarely addressed in previous studies, was conducted on several SPH parameters. Hence, the effects of distinct parameters, such as the kernel choices and the domain dimensions, were investigated with the goal of obtaining highly accurate results. A range of Reynolds numbers(1-500) was simulated, and the results were compared with existing experimental data. It was observed that the domain dimensions and the resolution of SPH particles, in comparison to the obstacle size, affected the obtained drag coefficient significantly. Other parameters, such as the background pressure, influenced the transient condition, but did not influence the steady state at which the drag coefficient was determined.

Analysis of Flow Structure and Calculation of Drag Coefficient for Concurrent-up Gas-Solid Flow

This study investigates the heterogeneous structure and its influence on drag coefficient for concurrent-up gas-solid flow. The energy-minimization multi-scale (EMMS) model is modified to simulate the variation of structure parameters with solids concentration, showing the tendency for particles to aggregate to form clusters and for fluid to pass around clusters. The global drag coefficient is resolved into that for the dense phase, for the dilute phase and for the so-called inter-phase, all of which can be obtained from their respective phase-specific structure parameters. The computational results show that the drag coefficients of the different phases are quite different, and the global drag coefficient calculated from the EMMS approach is much lower than that from the correlation of Wen and Yu. The simulation results demonstrate that the EMMS approach can well describe the heterogeneous flow structure, and is very promising for incorporation into the two-fluid model or the discrete particle model as the closure law for drag coefficient.

Introduction of parameterized sea ice drag coefficients into ice free-drift modeling

Many interesting characteristics of sea ice drift depend on the atmospheric drag coefficient （Ca） and oceanic drag coefficient （Cw）. Parameterizations of drag coefficients rather than constant values provide us a way to look insight into the dependence of these characteristics on sea ice conditions. In the present study, the parameterized ice drag coefficients are included into a free-drift sea ice dynamic model, and the wind factor a and the deflection angle θ between sea ice drift and wind velocity as well as the ratio of Ca to Cw are studied to investigate their dependence on the impact factors such as local drag coefficients, floe and ridge geometry. The results reveal that in an idealized steady ocean, Ca/Cw increases obviously with the increasing ice concentration for small ice floes in the marginal ice zone, while it remains at a steady level （0.2-0.25） for large floes in the central ice zone. The wind factor a increases rapidly at first and approaches a steady level of 0.018 when A is greater than 20%. And the deflection angle ~ drops rapidly from an initial value of approximate 80° and decreases slowly as A is greater than 20% without a steady level like a. The values of these parameters agree well with the previously reported observations in Arctic. The ridging intensity is an important parameter to determine the dominant contribution of the ratio of skin friction drag coefficient （Cs＇/Cs） and the ratio of ridge form drag coefficient （Cr＇/Cr） to the value of Ca/Cw, a, and 8, because of the dominance of ridge form drag for large ridging intensity and skin friction for small ridging intensity among the total drag forces. Parameterization of sea ice drag coefficients has the potential to be embedded into ice dynamic models to better account for the variability of sea ice in the transient Arctic Ocean.

On the parameterization of drag coefficient over sea surface

Six parameterization schemes of roughness or drag coefficient are evaluated on the basis of the data from six experiments. They present great consistency with measurement when friction velocity u＊〈0.5 m/s （ap- proximately corresponding to 10 m wind speed U10〈 12 m/s） and large deviation from measurement when u＊≥0.5 m/s （approximately U10 ≥ 12 m/s）. In order to improve the deviation, a new parameterization of drag coefficient is derived on the basis of the similarity theory, Charnock relationship and Toba 3/2 power law. Wave steepness and wind-sea Reynolds number are considered in the new parameterization. Then it is test- ed on the basis of the measurements and shows significant improvement when u＊≥0.5 m/s. Its standard errors are much smaller than the ones of the other six parameterizations. However, the new parameteriza- tion still needs more tests especially for high winds.

Impacts of Surface Exchange Coefficients on Simulations of Super Typhoon Megi(2010)Using a Coupled Ocean-Atmosphere-Wave Model

In this study,the effects of surface exchange coefficients on simulations of Super Typhoon Megi(2010)are investigated using a fully coupled ocean-atmosphere-wave model.Several experiments are conducted using different parameterization schemes for the drag(C_(D))and enthalpy exchange(C_(K))coefficients.For the selected case,considering only the leveling-off of C_(D)at high wind speeds does not effectively improve the simulated typhoon track,intensity,or size.We found that increasing C_(K)monotonically with wind speed(Komori et al.,2018)yields stronger winds and deeper pressures by enhancing latent and sensible heat fluxes,but typhoon intensity remains underestimated.We propose a new higher C_(K)than that from Komori et al.(2018)based on the theory of Emanuel(1995).This approach produces a greater modeled typhoon intensity that is in good agreement with the best track data and effectively improves the track error for the simulation.Improved accuracy for modeled typhoon intensity is achieved with the new coefficient because C_(K)/C_(D)reaches the threshold of about 0.75 predicted by Emanuel(1995).The new proposed C_(K)also results in a reasonably accurate modeled sea surface temperature.However,typhoon size and surface wave height are overestimated.This finding implies that more numerical tests for tropical cyclones of different nature(such as strong,weak,dissipating,rapidly intensifying,or weakening tropical cyclones)should be studied,and more physical processes should be explored in future coupled models.

Determination of the Drag Coefficient over the Tibetan Plateau

In this paper,a preliminary study is given on the drag (i.e.bulk transfer for momentum) coefficient,on the basis of data from four sets of AWS in Tibet during the first observational year from July 1993 to July 1994 according to China Japan Asian Monsoon Cooperative Research Program.The results show that the drag coefficient over the Tibetan Plateau is 3.3 to 4.4×103.In addition,monthly and diurnal variations of drag coefficient and the relationship among the drag coefficients and the bulk Richardson number,surface roughness length and wind speed at 10 m height are discussed in detail.

Observation and Numerical Experiments for Drag Coefficient Under Typhoon Wind Forcing

This paper presents a study on drag coefficients under typhoon wind forcing based on observations and numerical experiments. The friction velocity and wind speed are measured at a marine observation platform in the South China Sea. Three typhoons: SOULIK(2013), TRAMI(2013) and FITOW(2013) are observed at a buoy station in the northeast sea area of Pingtan Island. A new parameterization is formulated for the wind drag coefficient as a function of wind speed. It is found that the drag coefficient(Cd) increases linearly with the slope of 0.083′10^(-3) for wind speed less than 24 m s^(-1). To investigate the drag coefficient under higher wind conditions, three numerical experiments are implemented for these three typhoons using SWAN wave model. The wind input data are objective reanalysis datasets, which are assimilated with many sources and provided every six hours with the resolution of 0.125?×0.125?. The numerical simulation results show a good agreement with wave observation data under typhoon wind forcing. The results indicate that the drag coefficient levels off with the linear slope of 0.012′10^(-3) for higher wind speeds(less than 34 m s^(-1)) and the new parameterization improvese the simulation accuracy compared with the Wu(1982) default used in SWAN.

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

Effect of the drag coefficient on a typhoon wave model

The effect of the drag coefficient on a typhoon wave model is investigated.Drag coefficients for Pingtan Island are derived from the progress of nine typhoons using COARE 3.0 software.The wind parameters are obtained using the Weather Research and Forecasting model.The simulation of wind agrees well with observations.Typhoon wave fields are then simulated using the third-generation wave model SWAN.The wave model includes exponential and linear growths of the wind input,which determine the wave-growth mode.A triple triangular mesh is adopted with spatial resolution as fine as 100 m nearshore.The SWAN model performs better when using the new drag coefficient rather than the original coefficient.

Assessment of surface drag coefficient parametrizations based on observations and simulations using the Weather Research and Forecasting model

The drag coefficient is important in meteorological studies of the boundary layer because it describes the air-sea momentum flux. Eight drag coefficient schemes were assessed. These parametrizations were compared taking into account data from in situ and laboratory observations.The drag coefficients determined using three schemes were consistent with the level-off phenomenon, supported by the results of laboratory studies. The drag coefficient determined using one scheme decreased at wind speeds higher than approximately 30 m s-1, in agreement with indirect measurements under typhoon conditions. In contrast, the drag coefficients determined using the other four schemes increased with wind speed, even under high wind regimes. Sensitivity tests were performed using simulations of two super typhoons in the Weather Research and Forecasting model. While the typhoon tracks were negligibly sensitive to the parametrization used, the typhoon intensities （the maximum lO-m wind speed and the minimum sea level pressure）, sizes, and structure, were very sensitive to it.

Wind speed scaling and the drag coefficient

Wind speed scaling in similarity law in wind-generated waves and the drag coefficient are studied. In analyzing the data in the wind wave channel, it is found that the u＊ scaling greatly reduces the scatter in the U10 scaling. The u＊ scaling has much less scatter than the scaling using other wind speeds. The friction velocity seems to play a distinctive role in wave growth. The result is important in the applications of the similarity law and in wave modeling. In theory it gives an insight into the mechanism of wind wave interaction. It is found that wave steepness is important in influencing the drag coefficient. The variability of the coefficients in the currently widely used drag form can be explained by the differences in wave steepness in the observations. A drag coefficient model with wind speed and wave steepness as parameters is proposed. An explanation for Kahma＇s result that the u, scaling does not reduce the scatter in the U10 scaling is given.

The Influence of Wave State and Sea Spray on Drag Coefficient from Low to High Wind Speeds

Ocean waves alter the roughness of sea surface,and sea spray droplets redistribute the momentum flux at the air-sea interface.Hence,both wave state and sea spray influence sea surface drag coefficient.Based on the new sea spray generation function which depends on sea surface wave,a wave-dependent sea spray stress is obtained.According to the relationship between sea spray stress and the total wind stress on the sea surface,a new formula of drag coefficient at high wind speed is acquired.With the analysis of the new drag coefficient,it is shown that the drag coefficient reduces at high wind speed,indicating that the sea spray droplets can limit the increase of drag coefficient.However,the value of high wind speed corresponding to the initial reduced drag coefficient is not fixed,and it depends on the wave state,which means the influence of wave cannot be ignored.Comparisons between the theoretical and measured sea surface drag coefficients in field and laboratory show that under different wave ages,the theoretical result of drag coefficient could include the measured data,and it means that the new drag coefficient can be used properly from low to high wind speeds under any wave state condition.

Numerical Investigation of Mooring Line Damping and the Drag Coefficients of Studless Chain Links

The chain/wire rope/chain combination is a common choice for mooring offshore floating platforms. However, data of the drag coefficients of chain links are rather limited, resulting in uncertainties with the calculations of the drag force, and hence the damping of the mooring system. In this paper, the importance of the selection of the drag coefficient is first investigated. The computational fluid dynamics(CFD) method is then used to determine the drag coefficients of a studless chain under steady flows. Numerical model validation is first completed by simulating a smooth circular cylinder under steady flows. In particular, the performance of different turbulence models is assessed through the comparisons between the calculations and the experimental results. The large eddy simulation(LES) model is finally selected for the simulation of steady flows past a chain. The effects of the Reynolds number on the drag coefficient of a stud-less chain is also studied. The results show that the calculated drag coefficients of a stud-less chain are fairly consistent with the available experimental data.