Applying Methods from Differential Geometry to Devise Stable and Persistent Air Layers Attached to Objects Immersed in Water

We describe a few mathematical tools which allow to investigate whether air-water interfaces exist(under prescribed conditions)and are mechanically stable and temporally persistent.In terms of physics,air-water interfaces are governed by the Young-Laplace equation.Mathematically they are surfaces of constant mean curvature which represent solutions of a nonlinear elliptic partial differential equation.Although explicit solutions of this equation can be obtained only in very special cases,it is -under moderately special circumstances-possible to establish the existence of a solution without actually solving the differential equation.We also derive criteria for mechanical stability and temporal persistence of an air layer.Furthermore we calculate the lifetime of a non-persistent air layer.Finally,we apply these tools to two examples which exhibit the symmetries of 2D lattices.These examples can be viewed as abstractions of the biological model represented by the aquatic fern Salvinia.

Influence of the Saharan Air Layer on Atlantic Tropical Cyclone Formation during the Period 1-12 September 2003

Atmospheric Infrared Sounder （AIRS） data show that the Saharan air layer （SAL） is a dry, warm, and well-mixed layer between 950 and 500 hPa over the tropical Atlantic, extending westward from the African coast to the Caribbean Sea. The formations of both Hurricane Isabel and Tropical Depression 14 （TD14） were accompanied with outbreaks of SAL air during the period 1-12 September 2003, although TD14 failed to develop into a named tropical cyclone. The influence of the SAL on their formations is investigated by examining data from satellite observations and numerical simulations, in which AIRS data are incorporated into the MM5 model through the nudging technique. Analyses of the AIRS and simulation data suggest that the SAL may have played two roles in the formation of tropical cyclones during the period 1-12 September 2003. First, the outbreaks of SAL air on 3 and 8 September enhanced the transverse-vertical circulation with the rising motion along the southern edge of the SAL and the sinking motion inside the SAL, triggering the development of two tropical disturbances associated with Hurricane Isabel and TD14. Second, in addition to the reduced environmental humidity and enhanced static stability in the lower troposphere, the SAL dry air intruded into the inner region of these tropical disturbances as their cyclonic ？ows became strong. This effect may have slowed down the formation of Isabel and inhibited TD14 becoming a named tropical cyclone, while the enhanced vertical shear contributed little to tropical cyclone formation during this period. The 48-h trajectory calculations confirm that the parcels from the SAL can be transported into the inner region of an incipient tropical cyclone.

Thermal Insulation Distribution Pattern of Layered Clothing Ensemble

With a thermal manikin, the distribution pattern of thermal insulation in multi-layered clothing ensemble is studied. It is found that the thermal insulation of multi-layered clothing ensemble has certain statistical relationship with the thermal insulation of each layer, and the prediction equation has been established.

Wind Wave Growth

A recent formula for the lift force on a low speed wing of circular arc cross-section [1] is adapted to the upward pressure force on the crests of a surface gravity wave propagating in the wind. In both cases, the main feature is the utilization of the air’s compressibility. At and near a wave crest, it is predicted that the air density is increased over the ambient value and that the air density decreases inversely as the square of the upward distance from the radius of curvature of the crest. As a consequence, the air pressure also decreases upward inversely as the square of the same distance. Therefore, an upward pressure force on each crest occurs which presumably will make the crests grow. Growth rates are largest for small wavelengths and large mean slopes of the wave surface. Contrary winds should produce wave growth (not damping) as well as no wind at all.

Transport and Deposition of Saharan Dust Observed from Satellite Images and Ground Measurements

Haboob occurrence strongly impacts the annual variability of airborne desert dust in North Africa.In fact,more dust is raised from erodible surfaces in the early summer(monsoon)season when deep convective storms are common but soil moisture and vegetation cover are low.On 27 June 2018,a large dust storm is initiated over North Africa associated with an intensive westward dust transport.Far away from emission sources,dust is transported over the Atlantic for the long distance.Dust plume is emitted by a strong surface wind and further becomes a type of haboob when it merges with the southwestward deep convective system in central Mali at 0200 UTC(27 June).We use satellite observations to describe and estimate the dust mass concentration during the event.Approximately 93%of emitted dust is removed the dry deposition from the atmosphere between sources(10°N–25°N;1°W–8°E)and the African coast(6°N–21°N;16°W–10°W).The convective cold pool has induced large economic and healthy damages,and death of animals in the northeastern side of Senegal.ERA5 reanalysis has shown that the convective mesoscale impacts strongly the climatological location of the Saharan heat low(SHL).

Numerical study on the wave pattern characteristic of air layer in cavity and the effects of multiple influence factors

Air-layer drag reduction (ALDR) technology for ship energy saving is getting more and more attention in recent years because of the outstanding drag reduction effect. In order to promote practical application, it is necessary to fully understand the two phase flow characteristics of the air layer. Recent experimental studies have shown that the surface of the air layer presents wave pattern, which has an important influence on its damage risk. However, it is difficult to measure the wave pattern quantificationally due to the interference of equipment. The main goal of the present paper is to investigate the wave pattern characteristic of air layer in cavity using numerical simulation method. On this basis, the effect of flow and geometric influence factors are discussed to understand the key control conditions. A computational fluid dynamics (CFD) numerical method based on Reynolds averaged Navier-Stokes (RANS) equations and volume of fluid (VOF) interface capturing method is established, and has been successfully applied in the simulation of air layer wave pattern. Both 2-D and 3-D simulations are carried out, aiming at analyzing air-water interface flow and vortex flow directly. Based on the simulation results, several important conclusions about the mechanism of air layer wave pattern can be obtained. Firstly, it is found to be an inherent characteristic that the wave height of the upstream air layer is higher than that of the downstream. The extremely high wave peak is easy to contact with the flat plate, leading to the breakup of air layer and a “central blank area” phenomenon. With the help of flow analysis, it is found that this characteristic is mainly caused by the strong counterclockwise vortex behind the bow wedge block. Secondly, the air layer stability is reduced with the increase of water flow velocity by affecting the wave height. There is a saturation point of air flow rate to reach maximum thickness of air layer. Thirdly, cavity configuration has obvious influence on air layer stability by influencing vortex flow field. The increase of cavity depth and width can aggravate the unsteady and nonlinear characteristics of air layer. Finally, comprehensive design criteria are concluded from the view of geometrical configuration and flow conditions. A cavity with the moderate depth and width can avoid the upstream damage of air layer. Longitudinal position of air nozzles should be set within the low pressure zone behind the wedge block for stable air layer formation.

Numerical study of air layer drag reduction of an axisymmetric body in oscillatory motions

The air layer drag reduction(ALDR)of an axisymmetric body in oscillatory motions is investigated in this paper with open source toolbox OpenFOAM.The unsteady Reynolds-averaged Navier-Stokes(URANS)equations are used to determine the viscous flow and the volume of fluid(VOF)model is adopted to capture the interface of the air-water two-phase flow.The k-e turbulence model is adopted to simulate the turbulence.The dynamic mesh technique is applied to model the movement of the axisymmetric body.Firstly,the ALDR results are validated by the experimental data.Then,the effects of the movements of the body on the drag reduction during the ALDR state are investigated.Two representative kinds of movements are considered,namely,the pitch and the heave.The numerical results show that the drag reduction varies during the movements and the average drag reduction rates will be reduced.The variation of the drag reduction is related to the morphological change of the air layer.The heave motion is more likely to reduce the effects of the ALDR than the pitch motion.For both oscillatory motions,the large motion amplitude and the low motion period are not conductive to improving the effects of the ALDR.The effects of the oscillatory motion on the ALDR are more sensitive at high water speeds than at low water speeds.Besides,increasing the air flow ratio can be considered as one way to improve the effects of the ALDR.

Underwater Oil Wettability on Nanostructured Superamphiphobic Surface Tuned by Trapped Air Layer Continuity

When the superamphiphobic meshes are immersed in water, the rough structures on steel wires are filled with air. The nanostructured superamphiphobic surfaces were prepared on the stainless-steel mesh. By adjusting the mesh size of the surface, the continuity of trapped air layer on the superamphiphobic surface underwater could be controlled. Then the underwater oil-wetting behavior on the prepared superamphiphobic mesh was investigated. The oil droplet spread out on the superamphiphobic surface without mesh and exhibited an oil contact angle of about 0° under water. But the oil contact angle formed on the superamphiphobic mesh surfaces and extended with increasing mesh size. We thought the discontinuity of trapped air layer on the surface and the entry of water into interval between the steel wires should be responsible for these behaviors.

Characteristics of air flow driven by the free surface of the open channel

Spillway tunnels are a key structure in large-scale water conservancies. The high-head water inlet makes the water surface-velocity extremely high, and the air is driven by the free surface of the water to move downstream. This paper studies the air velocity distribution above the water surface through the model tests, under the assumption that the airflow is a turbulent boundary layer with a rough interface, and the influence of the water depth and the water velocity on the air velocity distribution is analyzed. It is shown that the air velocity is in an exponential distribution. As the measured position moves upward, the air velocity gradually decreases, and the gradient decreases. When the water depth increases, the air velocity increases but with the same distribution form. With the increase of the water surface-velocity, the air velocity at the same measuring point increases, the variation range near the water surface is large, the air boundary layer height increases slightly, and the index coefficient of the air velocity distribution function decreases. Through numerical fitting, the calculation formula of the air boundary layer thickness at different water surface velocities is obtained, along with the numerical value of the index coefficient.

Drying of Flowing Liquid Film on Rotating Disk

Recently,development of high technology has been required for the formation of uniform thin film in manufacturing processes of semiconductor as the precision instruments become more sophisticated.A method called spin coating is often used for spreading photoresist on a wafer surface and drying photoresist film.In spin coating process,photoresist is uniformly spread on the wafer surface by centrifugal force caused by rotating wafer.However,it is a serious concern that streaky lines,which are caused by spiral vortices,appear on the wafer surface and prevent the formation of uniform film in the case of high rotating speed.On the other hand,in the case of low rotating speed,a small hump of the film is formed near the wafer edge.The main purpose of this study is to make clear the drying characteristics of the flowing liquid film on the rotating wafer.Temperature distribution of the flowing liquid film is captured by an infrared thermal video camera and radial gradient of the film temperature is introduced in order to evaluate the drying characteristic of the flowing film under steady state condition.Effects of the flow rate of the liquid film on the film temperature are investigated.The film temperature gradually decreases in the radial direction in all cases.At low rotating speed,the radial gradient of the film temperature is almost constant widely.On the other hand,at high rotating speed,the radial gradient of the film temperature takes a certain maximum value.It is found that the location of the gradient peak corresponds with the transition region of the air boundary layer,in which spiral vortices swirl,and shifts to the inner side of the disk with an increase of the liquid flow rate.