Direct numerical simulations of interface dynamics to link capillary pressure and total surface energy

The flow of two immiscible fluids through a porous medium depends on the complex interplay between gravity, capillarity, and viscous forces. The interaction between these forces and the geometry of the medium gives rise to a variety of complex flow regimes that are difficult to describe using continuum models. Although a number of pore-scale models have been employed, a careful investigation of the macroscopic effects of pore-scale processes requires methods based on conservation principles in order to reduce the number of modeling assumptions. In this work we perform direct numerical simulations of drainage by solving Navier-Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid-fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and model the transition from stable flow to viscous fingering, we focus on the macroscopic capillary pressure and we compare different definitions of this quantity under quasi-static and dynamic conditions. We show that the difference between the intrinsic phase-average pressures, which is commonly used as definition of Darcy-scale capillary pressure, is subject to several limitations and it is not accurate in presence of viscous effects or trapping. In contrast, a definition based on the variation of the total surface energy provides an accurate estimate of the macroscopic capillary pressure. This definition, which links the capillary pressure to its physical origin, allows a better separation of viscous effects and does not depend on the presence of trapped fluid clusters.

Gravity-driven slug motion in capillary tubes

The velocity of a liquid slug falling in a capillary tube is lower than predicted for Poiseuille flow due to presence of menisci, whose shapes are determined by the complex interplay of capillary, viscous, and gravitational forces. Due to the presence of menisci, a capillary pressure proportional to surface curvature acts on the slug and streamlines are bent close to the interface, resulting in enhanced viscous dissipation at the wedges. To determine the origin of drag-force increase relative to Poiseuille flow, we compute the force resultant acting on the slug by integrating Navier-Stokes equations over the liquid volume. Invoking relationships from differential geometry we demonstrate that the additional drag is due to viscous forces only and that no capillary drag of hydrodynamic origin exists (i.e., due to hydrodynamic deformation of the interface). Requiring that the force resultant is zero, we derive scaling laws for the steady velocity in the limit of small capillary numbers by estimating the leading order viscous dissipation in the different regions of the slug (i.e., the unperturbed Poiseuille-like bulk, the static menisci close to the tube axis and the dynamic regions close to the contact lines). Considering both partial and complete wetting, we find that the relationship between dimensionless velocity and weight is, in general, nonlinear. Whereas the relationship obtained for complete-wetting conditions is found in agreement with the experimental data of Bico and Quere [J. Bico and D. Quere, J. Colloid Interface Sci. 243, 262 (2001)], the scaling law under partial-wetting conditions is validated by numerical simulations performed with the Volume of Fluid method. The simulated steady velocities agree with the behavior predicted by the theoretical scaling laws in presence and in absence of static contact angle hysteresis. The numerical simulations suggest that wedge-flow dissipation alone cannot account for the entire additional drag and that the non-Poiseuille dissipation in the static menisci (not considered in previous studies) has to be considered for large contact angles.

Sea state effect on the sea surface emissivity at L-band

In May 1999, the European Space Agency (ESA) selected the Earth Explorer Opportunity Soil Moisture and Ocean Salinity (SMOS) mission to obtain global and frequent soil moisture and ocean salinity maps. SMOS' single payload is the Microwave Imaging Radiometer by Aperture Synthesis (MIRAS), an L-band two-dimensional aperture synthesis radiometer with multiangular observation capabilities. At L-band, the brightness temperature sensitivity to the sea surface salinity (SSS) is low, approximately 0.5 K/psu at 20/spl deg/C, decreasing to 0.25 K/psu at 0/spl deg/C, comparable to that to the wind speed /spl sim/0.2 K/(m/s) at nadir. However, at a given time, the sea state does not depend only on local winds, but on the local wind history and the presence of waves traveling from far distances. The Wind and Salinity Experiment (WISE) 2000 and 2001 campaigns were sponsored by ESA to determine the impact of oceanographic and atmospheric variables on the L-band brightness temperature at vertical and horizontal polarizations. This paper presents the results of the analysis of three nonstationary sea state conditions: growing and decreasing sea, and the presence of swell. Measured sea surface spectra are compared with the theoretical ones, computed using the instantaneous wind speed. Differences can be minimized using an "effective wind speed" that makes the theoretical spectrum best match the measured one. The impact on the predicted brightness temperatures is then assessed using the small slope approximation/small perturbation method (SSA/SPM).

A model of the wind direction signature in the Stokes emission vector from the ocean surface at microwave frequencies

This paper presents a model of the Stokes emission vector from the ocean surface. The ocean surface is described as an ensemble of facets with Cox and Munk's (1954) Gram-Charlier slope distribution. The study discusses the impact of different up-wind and cross-wind rms slopes, skewness, peakedness, foam cover models and atmospheric effects on the azimuthal variation of the Stokes vector, as well as the limitations of the model. Simulation results compare favorably, both in mean value and azimuthal dependence, with SSM/I data at 53° incidence angle and with JPL's WINDRAD measurements at incidence angles from 30° to 65°, and at wind speeds from 2.5 to 11 m/s.

The role of surface vertical mixing in phytoplankton distribution in a stratified reservoir

We investigated convection caused by surface cooling and mixing attributable to wind shear stress and their roles as agents for the transport of phytoplankton cells in the water column by carrying out two daily surveys during the stratified period of the Sau reservoir. Green algae, diatoms, and cryptophyceae were the dominant phytoplankton communities during the surveys carried out in the middle (July) and end (September) of the stratified period. We show that a system with a linear stratification and that is subject to weak surface forcing, with weak winds , < 4 m S (-1) and low energy dissipation rate values of the order of 1028 m2 s23 or lower, enables the formation of thin phytoplankton layers. These layers quickly disappear when water parcels mix because there is a medium external forcing (convection) induced by the night surface cooling, which is characterized by energy dissipation rates on the order of , 5x10(-8)m2s(-3). During both surveys the wind generated internal waves during the entire diurnal cycle. During the day, and because of the weak winds, phytoplankton layers rise in the water column up to a depth determined by both solar heating and internal waves. In contrast, during the night phytoplankton mixes down to a depth determined by both convection and internal waves. These internal waves, together with the wind-driven current generated at the surface, seem to be the agents responsible for the horizontal transport of phytoplankton across the reservoir.

The seasonal evolution of high vertical–mode internal waves in a deep reservoir

The causal mechanism and seasonal evolution of the internal wave field in a deep, warm, monomictic reservoirare examined through the analysis of field observations and numerical techniques. The study period extends fromthe onset of thermal stratification in the spring until midsummer in 2005. During this time, wind forcing wasperiodic, with a period of 24 h (typical of land–sea breezes), and the thermal structure in the lake wascharacterized by the presence of a shallow surface layer overlying a thick metalimnion, typical of small to mediumsized reservoirs with deep outtakes. Basin-scale internal seiches of high vertical mode (ranging from mode V3 toV5) were observed in the metalimnion. The structure of the dominant modes of oscillation changed asstratification evolved on seasonal timescales, but in all cases, their periods were close to that of the local windforcing (i.e., 24 h), suggesting a resonant response. Nonresonant oscillatory modes of type V1 and V2 becamedominant after large frontal events, which disrupted the diurnal periodicity of the wind forcing

Surface Circulation in the Tropical Indian Ocean Using Multi-Mission Altimeter Data

In the present study the availability of satellite altimeter sea level data with good spatial and temporal resolution is explored to describe and understand circulation of the tropical Indian Ocean. The derived geostrophic circulations showed large variability in all scales. The seasonal cycle described using monthly climatology generated using 12 years SSH data from 1993 to 2004 revealed several new aspects of tropical Indian Ocean circulation. The interannual variability presented in this study using monthly means of SSH data for 12 years have shown large year-to-year variability. The EOF analysis has shown the influence of several periodic signals in the annual and interannual scales where the relative strengths of the signals also varied from year to year. Since one of the reasons for this kind of variability in circulation is the presence of planetary waves. This study discussed the influence of such waves on circulation by presenting two cases one in the Arabian Sea and other in the Bay of Bengal.

Studies on ocean surface layer responses to atmospheric forcing in the North Indian Ocean

The present study on upper ocean responses to atmospheric forcing (associated with cyclone passage) in North Indian Ocean revealed significant variability between AS and BoB. The analysis of cyclone frequency during 1947 to 2006 exhibited lesser frequency of cyclones in AS than that of BoB. The analysis also revealed significant reduction in cyclone frequency after the year 1976 with substantial reduction during monsoon season. The long term SST data at selected points in AS and BoB could not reveal any relation with reduction in cyclone frequency. However the SLP at same locations exhibited considerable increase during mid 1970’s, which could have contributed to the observed reduction in cyclone frequency after the year 1976.The response in waves during cyclone passage exhibited significant asymmetry on either side of the track in AS and BoB and the response is observed at 100’s of kilometers away from the track. The significant clockwise rotation in wave direction is observed on the right side of the track starting from near the track to far away locations, which existed for a longer duration. However, the anticlockwise rotation in wave direction is observed over a shorter distance on the left side of the track and dissipated immediately.Inertial oscillation is observed in surface current and in the mixed layer temperature associated with cyclone passage, which revealed the role of relative location(s) on either side of the track. The inertial peak closer to the local inertial period indicates maximum transfer of energy during the cyclone passage in both AS and BoB. The absence of strong inertial oscillation even with clockwise rotation in surface current and wind indicates the dominant role of duration of strong wind in generating inertial oscillation.The oceanic response associated with cyclone passage reveal the variable response(s) which depends on cyclone intensity, the proximity to track and cyclone translation speed. It is observed that resonance with wind generates higher response in surface current, wave and SST on the right side of the track and it lasts for a longer duration. The maximum oceanic response is observed at a few kilometers away on right side of the track. However lesser rightward bias in the location of maximum cooling is observed for cyclones with low cyclone translation speed. The response on the left side of the track is less and is limited over a shorter distance and dissipates immediately. It is observed that the ocean response, in general, increases with intensity of cyclones. However the differential cooling produced by the same intensity cyclones in AS and in BoB indicates the dominant role of low cyclone translation speed in oceanic response.The surface cooling exhibited strikingly differential responses between AS and BoB. The TMI-SST and buoy observations exhibited significant cooling for a longer duration in AS compared to that of BoB. The spatial extent of cooling is also much higher in AS than that of BoB. The wide spread cooling associated with cyclone passage in AS indicates the dominant role of thermal structure in oceanic response in AS than that of BoB.

Seasonal and interannual variability of sea level and associated surface meteorological parameters at Cochin

This thesis entitled seasonal and interannual variability of sea level and associated surface meteorological parameters at cochin.The interesting aspect of studying sea level variability on different time scales can be attributed to the diversity of its applications.Study of tides could perhaps be the oldest branch of physical oceanography.The thesis is presented in seven chapters. The first chapter gives, apart from a general introduction, a survey of literature on sea level variability on different time scales - tidal, seasonal and interannual (geological scales excluded), with particular emphasis on the work carried out in the Indian waters. The second chapter is devoted to the study of observed tides at Cochin on seasonal and interannual time scales using hourly water level data for the period 1988-1993. The third chapter describes the long-term climatology of some important surface oceanographic and meteorological parameters (at Cochin) which are supposed to affect the sea level. The fourth chapter addresses the problem of seasonal forecasting of the meteorological and oceanographic parameters at Cochin using autoregressive, sinusoidal and exponentially weighted moving average techniques and testing their accuracy with the observed data for the period 1991-1993. The fifth chapter describes the seasonal cycles of sea level and the driving forces at 16 stations along the Indian subcontinent. It also addresses the observed interannual variability of sea level at 15 stations using available multi-annual data sets. The sixth chapter deals with the problem of coastal trapped waves between Cochin and Beypore off the Kerala coast using sea level and atmospheric pressure data sets for the year 1977. The seventh and the last chapter contains the summary and conclusions and future outlook based on this study.

Fluid mechanics-non-linear waves studies on korteweg-de vries equations

In this thesis the author has presented qualitative studies of certain Kdv equations with variable coefficients. The well-known KdV equation is a model for waves propagating on the surface of shallow water of constant depth. This model is considered as fitting into waves reaching the shore. Renewed attempts have led to the derivation of KdV type equations in which the coefficients are not constants. Johnson's equation is one such equation. The researcher has used this model to study the interaction of waves. It has been found that three-wave interaction is possible, there is transfer of energy between the waves and the energy is not conserved during interaction.

Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.

A High Order Finite Volume Scheme for the 2D Shallow Water Equations Including Topography

Inhalt dieser Arbeit ist ein Verfahren zur numerischen Lösung der zweidimensionalen Flachwassergleichung, welche das Fließverhalten von Gewässern, deren Oberflächenausdehnung wesentlich größer als deren Tiefe ist, modelliert. Diese Gleichung beschreibt die gravitationsbedingte zeitliche Änderung eines gegebenen Anfangszustandes bei Gewässern mit freier Oberfläche. Diese Klasse beinhaltet Probleme wie das Verhalten von Wellen an flachen Stränden oder die Bewegung einer Flutwelle in einem Fluss. Diese Beispiele zeigen deutlich die Notwendigkeit, den Einfluss von Topographie sowie die Behandlung von Nass/Trockenübergängen im Verfahren zu berücksichtigen. In der vorliegenden Dissertation wird ein, in Gebieten mit hinreichender Wasserhöhe, hochgenaues Finite-Volumen-Verfahren zur numerischen Bestimmung des zeitlichen Verlaufs der Lösung der zweidimensionalen Flachwassergleichung aus gegebenen Anfangs- und Randbedingungen auf einem unstrukturierten Gitter vorgestellt, welches in der Lage ist, den Einfluss topographischer Quellterme auf die Strömung zu berücksichtigen, sowie in sogenannten \glqq lake at rest\grqq-stationären Zuständen diesen Einfluss mit den numerischen Flüssen exakt auszubalancieren. Basis des Verfahrens ist ein Finite-Volumen-Ansatz erster Ordnung, welcher durch eine WENO Rekonstruktion unter Verwendung der Methode der kleinsten Quadrate und eine sogenannte Space Time Expansion erweitert wird mit dem Ziel, ein Verfahren beliebig hoher Ordnung zu erhalten. Die im Verfahren auftretenden Riemannprobleme werden mit dem Riemannlöser von Chinnayya, LeRoux und Seguin von 1999 gelöst, welcher die Einflüsse der Topographie auf den Strömungsverlauf mit berücksichtigt. Es wird in der Arbeit bewiesen, dass die Koeffizienten der durch das WENO-Verfahren berechneten Rekonstruktionspolynome die räumlichen Ableitungen der zu rekonstruierenden Funktion mit einem zur Verfahrensordnung passenden Genauigkeitsgrad approximieren. Ebenso wird bewiesen, dass die Koeffizienten des aus der Space Time Expansion resultierenden Polynoms die räumlichen und zeitlichen Ableitungen der Lösung des Anfangswertproblems approximieren. Darüber hinaus wird die wohlbalanciertheit des Verfahrens für beliebig hohe numerische Ordnung bewiesen. Für die Behandlung von Nass/Trockenübergangen wird eine Methode zur Ordnungsreduktion abhängig von Wasserhöhe und Zellgröße vorgeschlagen. Dies ist notwendig, um in der Rechnung negative Werte für die Wasserhöhe, welche als Folge von Oszillationen des Raum-Zeit-Polynoms auftreten können, zu vermeiden. Numerische Ergebnisse die die theoretische Verfahrensordnung bestätigen werden ebenso präsentiert wie Beispiele, welche die hervorragenden Eigenschaften des Gesamtverfahrens in der Berechnung herausfordernder Probleme demonstrieren.

Numerical simulation of baroclinic waves with a parameterized boundary layer

A dry three-dimensional baroclinic life cycle model is used to investigate the role of turbulent fluxes of heat and momentum within the boundary layer on mid-latitude cyclones. Simulations are performed of life cycles for two basic states, both with and without turbulent fluxes. The different basic states produce cyclones with contrasting frontal and mesoscale-flow structures. The analysis focuses on the generation of potential-vorticity (PV) in the boundary layer and its subsequent transport into the free troposphere. The dynamic mechanism through which friction mitigates a barotropic vortex is that of Ekman pumping. This has often been assumed to be also the dominant mechanism for baroclinic developments. The PV framework highlights an additional, baroclinic mechanism. Positive PV is generated baroclinically due to friction to the north-east of a surface low and is transported out of the boundary layer by a cyclonic conveyor belt flow. The result is an anomaly of increased static stability in the lower troposphere which restricts the growth of the baroclinic wave. The reduced coupling between lower and upper levels can be sufficient to change the character of the upper-level evolution of the mature wave. The basic features of the baroclinic damping mechanism are robust for different frontal structures, with and without turbulent heat fluxes, and for the range of surface roughness found over the oceans.

Surface wave processes in air-sea interaction

We review briefly recent progress on understanding the role of surface waves on the marine atmospheric boundary layer and the ocean mixed layer and give a global perspective on these processes by analysing ERA-40 data. Ocean surface waves interact with the marine atmospheric boundary layer in two broad regimes: (i) the conventional wind-driven wave regime, when fast winds blow over slower moving waves, and (ii) a wave-driven wind regime when long wavelength swell propagates under low winds, and generates a wave-driven jet in the lower part of the marine boundary layer. Analysis of ERA-40 data indicates that the wave-driven wind regime is as prevalent as the conventional wind-driven regime. Ocean surface waves also change profoundly mixing in the ocean mixed layer through generation of Langmuir circulation. Results from large-eddy simulation are used here to develop a scaling for the resulting Langmuir turbulence, which is a necessary step in developing a parametrization of the process. ERA-40 data is then used to show that the Langmuir regime is the predominant regime over much of the global ocean, providing a compelling motivation for parameterising this process in ocean general circulation models.

Convectively coupled equatorial waves in high resolution Hadley centre climate models

Current global atmospheric models fail to simulate well organised tropical phenomena in which convection interacts with dynamics and physics. A new methodology to identify convectively coupled equatorial waves, developed by NCAS-Climate, has been applied to output from the two latest models of the Met Office/Hadley Centre which have fundamental differences in dynamical formulation. Variability, horizontal and vertical structures, and propagation characteristics of tropical convection and equatorial waves, along with their coupled behaviour in the models are examined and evaluated against a previous comprehensive study of observations. It is shown that, in general, the models perform well for equatorial waves coupled with off-equatorial convection. However they perform poorly for waves coupled with equatorial convection. The vertical structure of the simulated wave is not conducive to energy conversion/growth and does not support the correct physical-dynamical coupling that occurs in the real world. The following figure shows an example of the Kelvin wave coupled with equatorial convection. It shows that the models fail to simulate a key feature of convectively coupled Kelvin wave in observations, namely near surface anomalous equatorial zonal winds together with intensified equatorial convection and westerly winds in phase with the convection. The models are also not able to capture the observed vertical tilt structure and the vertical propagation of the Kelvin wave into the lower stratosphere as well as the secondary peak in the mid-troposphere, particularly in HadAM3. These results can be used to provide a test-bed for experimentation to improve the coupling of physics and dynamics in climate and weather models.