Boundary Conditions for Momentum and Vorticity at an Interface between Two Fluids

Boundary conditions for momentum and vorticity have been precisely derived, paying attention to the physical meaning of each mathematical expression of terms rigorously obtained from the basic equations: Navier-Stokes equation and the equation of vorticity transport. It has been shown first that a contribution of fluid molecules crossing over a conceptual surface moving with fluid velocity due to their fluctuating motion is essentially important to understanding transport phenomena of momentum and vorticity. A notion of surface layers, which are thin layers at both sides of an interface, has been introduced next to elucidate the transporting mechanism of momentum and vorticity from one phase to the other at an interface through which no fluid molecules are crossing over. A fact that a size of δV, in which reliable values of density, momentum, and velocity of fluid are respectively defined as a volume-averaged mass of fluid molecules, a volume-averaged momentum of fluid molecules and a mass-averaged velocity of fluid molecules, is not infinitesimal but finite has been one of the key factors leading to the boundary conditions for vorticity at an interface between two fluids. The most distinguished characteristics of the boundary conditions derived here are the zero-value conditions for a normal component of momentum flux and tangential components of vorticity flux, at an interface.

DISTRIBUTION OF WAVE INDUCED EXCESS MOMENTUM FLUXES OVER DEPTH AND APPLICATION TO THREE DIMENSIONAL NUMERICAL MODELING OF WAVE CURRENT INTERACTIONS

Using the linear wave theory, the distributions of the wave induced excess momentum fluxes over depth at the arbitrary wave angle and their asymptotic forms for deep and shallow water are developed. Results indicate that the distribution of the wave induced excess momentum fluxes over depth is non uniform and the contributions of the component below the wave trough to the total momentum fluxes become considerable in shallow water. On the basis of the Navier Stokes equations, the simplified three dimensional mathematical model is established by taking a phase average over a wavelength. It is found that there are the terms of the wave induced excess momentum fluxes varying over depth in the model, which illustrates the situation of wave current interactions and the vertical structure of current velocity are changed because of different wave induced excess momentum fluxes at various vertical location. The finite difference method is employed to solve the simplified model. Performances of the two dimensional vertically integrated equations are evaluated against available numerical and experimental results including the cases of wave set up on a plane beach, longshore current due to an oblique wave, wave induced nearshore circulation in a semi enclosed seas, and wave current interactions. All cases yield satisfactory agreements. The three dimensional mathematical model is applied to the numerical simulation of wave current interactions, and it performs well in predicting the vertical velocity structure and the plane flow field.

Observation Research of the Turbulent Fluxes of Momentum, Sensible Heat and Latent Heat over the West Pacific Tropical Ocean Area

This paper describes results of the fluxes of momentum , sensible heat and latent heat for the West Pacific Tropical Ocean Area ( 127 ° E - 150 ° E , 5 ° N -3 ° S ). The data were collected by the small tethered balloon sounding system over this ocean area including 6 continuous stations (140 ° E. 0 ° ; 145 ° E, 0 ° ; 150 ° E, 0 ° ; 140° E, 5 ° N; 145 ° E, 5° N and 150 ° E, 5 ° N) from 11 October to 15 December, 1986 . These fluxes were calculated by the semiempirical flux-profile relationships of Monin-Obukhov similarity theory using these observed data. The results show that for this tropical ocean area the drag coefficient CD is equal to (1.53 ± 0.25) × 10 3 and the daily mean latent flux Hl is greater than its daily mean sensible flux HV by a factor of about 9.

Air-sea fluxes of heat and momentum over the Yellow Sea during cold air outbreaks

The impact of sea surface waves on air-sea fluxes of heat and momentum over the Yellow Sea caused by cold fronts during cold air outbreak(CAO)events is investigated through numerical experiments with a FVCOM-SWAVE(Finite-Volume Coastal Ocean Model-Surface WAVE)wave-current coupled model.Two typical types of cold fronts,i.e.,those respectively from the north and from the west,are simulated and compared to each other and with monthly mean.During cold seasons,currents in the Yellow Sea are weaker than that during warm seasons.As a result,waves show a more prominent impact.The numerical simulations suggested that both the heat and momentum fluxes are significantly enhanced during CAO events;and they could be a few times larger than the monthly average of a five-year mean.The enhancement is highly sensitive to the features of CAOs.Specifically,it depends on the cold front orientation,intensity and evolution.One mechanism that strengthens the two fluxes is via sea waves.For the CAOs that are studied,an increase in sea wave height by 50%can double the maximal momentum flux,and cause an increase in heat flux by 10-160 W/m^2.

Tower-based observation of air-sea momentum flux:comparisons between onshore and offshore winds

We investigate the air-sea momentum flux in the marine atmospheric boundary layer using a tower-based direct measurement method.First,we compare the collected data with previous observations,and the results are roughly consistent.Next,in the low-to-moderate winds,the exchange coefficients(or drag coefficients)deviate between onshore and offshore winds,which exhibits the influence of surface wave on the momentum flux.Furthermore,we use a surface-wave-involved parameterization scheme to explain the dependence of momentum flux on surface wave.The results consolidate the influence of surface wave on momentum flux on the one hand,and validate the surface-wave-involved parameterization scheme on the other hand.

Analysis of atmospheric turbulence in the upper layers of sea fog

Atmospheric turbulence plays a vital role in the formation and dissipation of fog. However,studies of such turbulence are typically limited to observations with ultrasonic anemometers less than 100 m above ground. Thus,the turbulence characteristics of upper fog layers are poorly known. In this paper,we present 4-layers of data,measured by ultrasonic anemometers on a wind tower about 400 m above the sea surface; we use these data to characterize atmospheric turbulence atop a heavy sea fog. Large differences in turbulence during the sea fog episode were recorded. Results showed that the kinetic energy,momentum flux,and sensible heat flux of turbulence increased rapidly during the onset of fog. After onset,high turbulence was observed within the uppermost fog layer. As long as this turbulence did not exceed a critical threshold,it was crucial to enhancing the cooling rate,and maintaining the fog. Vertical momentum flux and sensible heat flux generated by this turbulence weakened wind speed and decreased air temperature during the fog. Towards the end of the fog episode,the vertical distribution of sensible heat flux reversed,contributing to a downward momentum flux in all upper layers. Spatial and temporal scales of the turbulence eddy were greater before and after the fog,than during the fog episode. Turbulence energy was greatest in upper levels,around 430 m and 450 m above mean sea level(AMSL),than in lower levels of the fog(390 m and 410 m AMSL); turbulence energy peaked along the mean wind direction. Our results show that the status of turbulence was complicated within the fog; turbulence caused fluxes of momentum and sensible heat atop the fog layer,affecting the underlying fog by decreasing or increasing average wind speed,as well as promoting or demoting air temperature stratification.

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.

Large eddy simulation of turbulence in ocean surface boundary layer at Zhangzi Island offshore

This study uses a large eddy simulation （LES） model to investigate the turbulence processes in the ocean surface boundary layer at Zhangzi Island offshore. Field measurements at Zhangzi Island （39°N, 122°E） during July 2009 are used to drive the LES model. The LES results capture a clear diurnal cycle in the oceanic turbulence boundary layer. The process of the heat penetration and heat distribution characteristics are analyzed through the heat flux results from the LES and their differences between two diurnal cycles are discussed as well. Energy balance and other dynamics are investigated which show that the tide-induced shear production is the main source of the turbulence energy that balanced dissipation. Momentum flux near the surface shows better agreement with atmospheric data computed by the eddy correlation method than those computed by bulk formula.

Reexamination of the Relationship between Tropical Cyclone Size and Intensity over the Western North Pacific

This study reexamines the correlation between the size and intensity of tropical cyclones(TCs) over the western North Pacific from the perspective of individual TCs, rather than the previous large-sample framework mixing up all TC records.Statistics show that the positive size-intensity correlation based on individual TCs is relatively high. However, this correlation is obscured by mixing large samples. The weakened correlation based on all TC records is primarily due to the diversity in the size change relative to the same intensity change among TCs, which can be quantitatively measured by the linear regression coefficient(RC) of size against intensity. To further explore the factors that cause the variability in RCs that weakens the size-intensity correlation when considering all TC records, the TCs from 2001 to 2020 are classified into two groups according to their RC magnitudes, within which the high-RC TCs have a larger size expansion than the low-RC TCs given the same intensity change. Two key mechanisms responsible for the RC differences are proposed. First, the highRC TCs are generally located at higher latitudes than the low-RC TCs, resulting in higher planetary vorticity and thus higher planetary angular momentum import at low levels. Second, the high-RC TCs are susceptible to stronger environmental vertical wind shear, leading to more prolific outer convection than the low-RC TCs. The positive feedback between outer diabatic heating and boundary layer inflow favors the inward import of absolute angular momentum in the outer region, thereby contributing to a larger size expansion in the high-RC TCs.

Gustiness and coherent structure under weak wind period in atmospheric boundary layer

Statistical analysis of turbulent and gusty characteristics in the atmospheric boundary layer under weak wind period has been carried out.The data used in the analysis were from the multilevel ultrasonic anemometer-thermometers at 47 m,120 m,and 280 m levels on Beijing 325 m meteorological tower.The time series of 3D atmospheric velocity were analyzed by using conventional Fourier spectral analysis and decompose into three parts:basic mean flow(period > 10 min),gusty disturbances(1 min < period < 10 min)and turbulence fluctuations(period < 1 min).The results show that under weak mean wind condition:1)the gusty disturbances are the most strong fluctuations,contribute about 60% kinetic energy of eddy kinetic energy and 80% downward flux of momentum,although both the eddy kinetic energy and momentum transport are small in comparison with those in strong mean wind condition;2)the gusty wind disturbances are anisotropic;3)the gusty wind disturbances have obviously coherent structure,and their horizontal and vertical component are negatively correlated and make downward transport of momentum more effectively;4)the friction velocities related to turbulence and gusty wind are approximately constant with height in the surface layer.

Barotropic Processes Associated with the Development of the Mei-yu Precipitation System

The barotropic processes associated with the development of a precipitation system are investigated through analysis of cloud-resolving model simulations of Mei-yu torrential rainfall events over eastern China in mid-June 2011. During the model integration period, there were three major heavy rainfall events： 9–12, 13–16 and 16–20 June. The kinetic energy is converted from perturbation to mean circulations in the first and second period, whereas it is converted from mean to perturbation circulations in the third period. Further analysis shows that kinetic energy conversion is determined by vertical transport of zonal momentum. Thus, the prognostic equation of vertical transport of zonal momentum is derived, in which its tendency is associated with dynamic, pressure gradient and buoyancy processes. The kinetic energy conversion from perturbation to mean circulations in the first period is mainly associated with the dynamic processes. The kinetic energy conversion from mean to perturbation circulations in the third period is generally related to the pressure gradient processes.

Upper-Tropospheric Environment–Tropical Cyclone Interactions over the Western North Pacific:A Statistical Study

Based on 25-year（1987–2011） tropical cyclone（TC） best track data, a statistical study was carried out to investigate the basic features of upper-tropospheric TC–environment interactions over the western North Pacific. Interaction was defined as the absolute value of eddy momentum flux convergence（EFC） exceeding 10 m s^（-1）d^（-1）. Based on this definition, it was found that 18% of all six-hourly TC samples experienced interaction. Extreme interaction cases showed that EFC can reach^120 m s^（-1）d^（-1） during the extratropical-cyclone（EC） stage, an order of magnitude larger than reported in previous studies.Composite analysis showed that positive interactions are characterized by a double-jet flow pattern, rather than the traditional trough pattern, because it is the jets that bring in large EFC from the upper-level environment to the TC center. The role of the outflow jet is also enhanced by relatively low inertial stability, as compared to the inflow jet. Among several environmental factors, it was found that extremely large EFC is usually accompanied by high inertial stability, low SST and strong vertical wind shear（VWS）. Thus, the positive effect of EFC is cancelled by their negative effects. Only those samples during the EC stage, whose intensities were less dependent on VWS and the underlying SST, could survive in extremely large EFC environments, or even re-intensify. For classical TCs（not in the EC stage）, it was found that environments with a moderate EFC value generally below ~25 m s^（-1）d^（-1） are more favorable for a TC＇s intensification than those with extremely large EFC.

Impact of Cyclone Nilam on Tropical Lower Atmospheric Dynamics

A deep depression formed over the Bay of Bengal on 28 October 2012, and developed into a cyclonic storm. After landfall near the south coast of Chennai, cyclone Nilam moved north-northwestwards. Coordinated experiments were conducted from the Indian stations of Gadanki（13.5？N, 79.2？E） and Hyderabad（17.4？N, 78.5？E） to study the modification of gravity-wave activity and turbulence by cyclone Nilam, using GPS radiosonde and mesosphere–stratosphere–troposphere radar data. The horizontal velocities underwent large changes during the closest approach of the storm to the experimental sites. Hodograph analysis revealed that inertia gravity waves（IGWs） associated with the cyclone changed their directions from northeast（control time） to northwest following the path of the cyclone. The momentum flux of IGWs and short-period gravity waves（1–8 h） enhanced prior to, and during, the passage of the storm（±0.05 m2s-2and ±0.3 m2s-2, respectively）, compared to the flux after its passage. The corresponding body forces underwent similar changes, with values ranging between ±2–4m s-1d-1and ±12–15 m s-1d-1. The turbulence refractivity structure constant（C2n） showed large values below 10 km before the passage of the cyclone when humidity in the region was very high. Turbulence and humidity reduced during the passage of the storm when a turbulent layer at ～17 km became more intense. Turbulence in the lower troposphere and near the tropopause became weak after the passage of the cyclone.

Three-Dimensional Wave-Induced Current Model Equations and Radiation Stresses

After the approach by Mellor （2003, 2008）, the present paper reports on a repeated effort to derive the equations for three-dimensional wave-induced current. Via the vertical momentum equation and a proper coordinate transformation, the phase-averaged wave dynamic pressure is well treated, and a continuous and depth-dependent radiation stress tensor, rather than the controversial delta Dirac function at the surface shown in Mellor （2008）, is provided. Besides, a phase-averaged vertical momentum flux over a sloping bottom is introduced. All the inconsistencies in Mellor （2003, 2008）, pointed out by Ardhuin et al. （2008） and Bennis and Ardhuin （2011）, are overcome in the presently revised equations. In a test case with a sloping sea bed, as shown in Ardhuin et al. （2008）, the wave-driving forces derived in the present equations are in good balance, and no spurious vertical circulation occurs outside the surf zone, indicating that Airy’s wave theory and the approach of Mellor （2003, 2008） are applicable for the derivation of the wave-induced current model.

Spatiotemporal spectrum and momentum flux of the stratospheric gravity waves generated by a typhoon

The simulation results of Typhoon Matsa （2005） by using the Weather Research and Forecasting （WRF） model show that pro- nounced stratospheric gravity waves （GWs） are generated in the vicinity of the typhoon. Using the model output, we investi- gate the spatial structures and the temporal variations of the GWs through a three dimensional （3-d） spectral analysis, i.e. the spectrum with respect to two horizontal wavenumbers and frequency. We further derive the momentum flux carried by the GWs. Spectral investigation results show that the power spectral density （PSD） of the GWs exhibits a single-peaked spectrum, which consists primarily of a distinct spectrum at horizontal wavelength of -1000 km, time period of 12-18 h, and vertical wavelength of 7-9 kin. This spectrum is different from the spectra of GWs generated by deep convections disclosed by the previous researches. Both the PSD and momentum flux spectrum are prominent in positive kh portion, which is consistent with the fact that the GWs propagate in the upstream of mean flow. Large momentum flux is found to be associated with the GWs, and the net zonal momentum flux is 0.7845×10-3 Pa at 20 km height, which can account for -26% of the momentum flux that is required in driving the QBO phenomenon.

Breakup Structure of Two-phase Jets with Various Momentum Flux from a Porous Injector

Spray structure and atomization characteristics were investigated through a comparison of a porous and a shear coaxial injector. The porous injector shows better atomization performance than the shear coaxial injector. To in- crease atomization performance and mixing efficiency of two-phase jets, a coaxial porous injector which can be applicable to liquid rocket combustors was designed and tested. The characteristics of atomization and spray from a porous and a shear coaxial injector were characterized by the momentum flux ratio. The breakup mechanism of the porous injector is governed by Taylor-Culick flow and axial shear forces. Momentum of injected gas flow through a porous material which is composed of sintered metal is radically transferred to the center of the liquid column, and then liquid column is effectively broken up. Although the shapes of spray from porous and shear co- axial jets were similar for various momentum ratio, spray structures such as spray angle and droplet sizes were different. As increasing the momentum flux ratio, SMD from the porous injector showed smaller value than the shear coaxial injector

CONCENTRATION AND FLUX OF CO_2, TURBULENCE FLUXES AND RADIATION BALANCE IN THE NEAR SURFACE LAYER OVER WHEAT FIELD

The gradient of CO_2 concentration, photosynthetically active radiation (PAR). net radiation. soil heat flux, profiles of wind speed, and air temperature and humidity were measured above a wheat field during May and June 1985 at Beijing Agro-Ecosystems Experimental Station. Beijing, China. Fluxes of carbon dioxide, sensible heat, latent heat and momentum were calculated by using the aerodynamic method. The observation site. equipment, calibration techniques, the errors associated with the measurement, and the computational procedures are described. The results show that the diurnal variations of amplitude of CO_2 concentrations were 103.8 to 27. 0. 86. 3 to 22.8 and 69.8 to 11.6 ppm: the average CO_2 concentrations were 331.5. 339.9 and 364.6 ppm for the photosynthesis type, and 369.6. 364.0 and 375.2 ppm for the respiration type at 1. 2 and 10 m above surface, respectively, from May 14 to June 15. In the daytime, transfer direction of the CO_2 fluxes and gradients is from air to crop canopy, and at noon (1100 to 1300 BT (Beijing Time)) the transfer rate reaches negative maximum value. At night, transfer of CO_2 fluxes and gradients is in the reversed direction and reaches positive maximum in the early morning (0400 to 0600 BT). There are strong negative correlations between CO_2 flux and the net radiation (Rn), available energy (H+LE). photosynthetically active radiation (PAR) and momentum flux (τ).

On the surface fluxes characteristics and roughness lengths at Zhongshan station,Antarctica

Over Antarctica,surface fluxes play an important role in the local atmospheric dynamical processes.To reveal the surface fluxes characteristics and aerodynamic and thermal roughness lengths over Zhongshan station,Antarctica,this paper analyzes the data observed at the station during 3 March 2008 through 15 February 2009.It is found that easterlies dominated this site throughout the whole year,with a maximum(average)speed of 25(5.6)m s−1 at 3.9 m height,and the annual maximum(minimum)surface temperature reached 291.05(230.05)K,while the annual maximum(minimum)air-specific humidity was 4.1(0.05)g/kg at 3.9 m height.The maximum(minimum)values of seasonal mean temperature,humidity,each radiation components,sensible and latent heat flux occurred in summer(winter),while for the seasonal averaged wind speed andτthe minimums(maximums)appeared in summer(autumn).After comparing with a partially linear regression method for aerodynamic roughness length and four previous equations that derive thermal roughness length from surface Reynolds number,constant values of aerodynamic roughness length as 3.6×10^(−3)m and thermal roughness length as 1.2×10^(−4)m at this site were validated by using the other three level observations and suggested for future studies.

On the Pressure Drop and the Velocity Distribution in the Cylindrical Vortex Chamber with Two Inlet Pipes for the Control of Vortex Flow

Vortex flow is applied to a cyclone dust collector, a vortex combustion chamber, and a vortex diode for vortex control. In order to apply the vortex flow to the industries, it is necessary to keep the stable flow condition and to estimate the response time of the transient flow process and also the intensity of the vortex flow. For control vortex flow, two types of vortex chamber with two inlet pipes were designed. One of them is to promote the vortex flow named as Co-Rotating Flow System and another one is to hinder the vortex flow named as Counter-Rotating Flow System. The pressure drops and the velocity distributions were measured for these vortex chambers. The estimation of the tangential velocity by the application of the angular momentum flux is compared with the measured velocity by a cylindrical Pitot-tube. The characteristics of the total pressure drop could be explained by introducing the circulation.

Estimation of the Radial Distribution of the Tangential Velocity in a Vortex Chamber

The estimation of maximum tangential velocity becomes a very important factor for the estimation of performancesof the vortex chamber. In this paper, a proposed flow model of how to estimate the maximum tangential velocity inthe special form of the vortex chamber is described in detail. The pressure drop basing upon the rapid expansion byflowing from the inlet pipe into the cyclone body is estimated as half of the dynamic pressure in the inlet pipe.