What is the apparent angle of a Kelvin ship wave pattern?

While the half-angle which encloses a Kelvin ship wave pattern is commonly accepted to be 19.47 degrees, recent observations and calculations for sufficiently fast-moving ships suggest that the apparent wake angle decreases with ship speed. One explanation for this decrease in angle relies on the assumption that a ship cannot generate wavelengths much greater than its hull length. An alternative interpretation is that the wave pattern that is observed in practice is defined by the location of the highest peaks; for wakes created by sufficiently fast-moving objects, these highest peaks no longer lie on the outermost divergent waves, resulting in a smaller apparent angle. In this paper, we focus on the problems of free surface flow past a single submerged point source and past a submerged source doublet. In the linear version of these problems, we measure the apparent wake angle formed by the highest peaks, and observe the following three regimes: a small Froude number pattern, in which the divergent waves are not visible; standard wave patterns for which the maximum peaks occur on the outermost divergent waves; and a third regime in which the highest peaks form a V-shape with an angle much less than the Kelvin angle. For nonlinear flows, we demonstrate that nonlinearity has the effect of increasing the apparent wake angle so that some highly nonlinear solutions have apparent wake angles that are greater than Kelvin's angle. For large Froude numbers, the effect on apparent wake angle can be more dramatic, with the possibility of strong nonlinearity shifting the wave pattern from the third regime to the second. We expect our nonlinear results will translate to other more complicated flow configurations, such as flow due to a steadily moving closed body such as a submarine.

Propagation of ship waves on a sloping bottom

The numerical model FUNWAVE was adapted in order to simulate the generation and propagation of ship waves to shore, including phenomena such as refraction, diffraction, currents and breaking of waves. Results are shown for Froude numbers equal to 0.8, 1.0 and 1.1, in order to verify the refraction of the wave pattern, identify breaking conditions and to investigate the wave generation scheme as a moving pressure at the free surface. © 2009 World Scientific Publishing Co. Pte. Ltd.

Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

Wake angle for surface gravity waves on a finite depth fluid

Linear water wave theory suggests that wave patterns caused by a steadily moving disturbance are contained within a wedge whose half-angle depends on the depth-based Froude number $F_H$. For the problem of flow past an axisymmetric pressure distribution in a finite-depth channel, we report on the apparent angle of the wake, which is the angle of maximum peaks. For moderately deep channels, the dependence of the apparent wake angle on the Froude number is very different to the wedge angle, and varies smoothly as $F_H$ passes through the critical value $F_H=1$. For shallow water, the two angles tend to follow each other more closely, which leads to very large apparent wake angles for certain regimes.

On the linkage of mesospheric planetary waves with those of the lower atmosphere and ionosphere: A case study from Indian low latitudes

In this paper we study the planetary-scale wave features using concurrent observations of mesospheric wind and temperature, ionospheric h'F, and tropospheric wind from Tirunelveli, Gadanki, and Kolhapur, all located in the Indian low latitudes, made during February 2009. Our investigations reveal that 3 to 5 day periodicity, characterized as ultrafast Kelvin (UFK) waves, was persistent throughout the atmosphere during this period. These waves show clear signatures of upward wave propagation from troposphere to the upper mesosphere, linking the ionosphere through a clear correlation between mesospheric winds and h'F variations. We also note that the amplitude of this wave decreased as we moved away from the equator. These results are the first of their kind from Indian sector, portraying the vertical as well as latitudinal characteristics of the 3 to 5 day UFK waves simultaneously from the troposphere to the ionosphere.

Waves generated by two or more ships in a channel

The numerical model FUNWAVE+Ship simulates the generation and propagation of ship waves to shore, including phenomena such as refraction, diffraction, currents and breaking of waves. The interaction of two wave trains, generated by ships moving either in the same direction at different speeds or in opposite directions, is studied. Focus is given to the wave orbital velocities and to the free surface pattern.

Dynamic auroral structure in the vicinity of the polar cusp - multipoint observations during southward and northward IMF

The low- and high-latitude boundary layers of the earth's magnetosphere [low-latitude boundary layer (LLBL) and mantle] play important roles in transferring momentum and energy from the solar wind to the magnetosphere-ionosphere system. Particle precipitation, field-aligned current, auroral emission, ionospheric ion drift and ground magnetic perturbations are among the low-altitude parameters that show signatures of various plasma processes in the LLBL and the magnetopause current layer. Magnetic merging events, Kelvin-Helmholtz waves, and pressure pulses excited by the variable solar wind/magnetosheath plasma are examples of boundary phenomena that may be coupled to the ionosphere via field-aligned currents. Optical auroral observation, by photometry and all-sky TV cameras, is a unique technique for investigating the spatial and temporal structure of the electron precipitation associated with such phenomena. However, the distinction between the different boundary layer plasma populations cannot in general be unambiguously determined by optics alone. Additional information, such as satellite observations of particle boundaries and field-aligned currents, is needed in order to identify the plasma source(s) and the magnetosphere-ionosphere coupling mode(s). Two categories of auroral activity/structure in the vicinity of the polar cusp are discussed in this paper, based on combined ground and satellite data. In one case, the quasi-periodic sequence of auroral events at the polar cap boundary involves accelerated electrons (< 1 keV) moving poleward (< 1 km s-1) and azimuthally along the persistent cusp/cleft arc poleward boundary with velocities (< 4 km s-1), comparable to the local ionospheric ion drift during periods of southward IMF. A critical question is whether or not the optical events signify a corresponding plasma flow across the open/closed field line boundary in such cases. Near-simultaneous observations of magnetopause flux transfer events (FTEs) and such optical/ion drift events are reported. The reverse pattern of motion of discrete auroral forms is observed during positive interplanetary magnetic field (IMF) B(Z), i.e. equatorward motion into the cusp/cleft background arc from the poleward edge. Combined satellite and ground-based information for the latter cases indicate a source mechanism, poleward of the cusp at the high-latitude magnetopause or plasma mantle, giving rise to strong momentum transfer and electron precipitation structures within a approximately 200 km-wide latitudinal zone at the cusp/cleft poleward boundary. The striking similarities of auroral electrodynamics in the cleft/mantle region during northward and southward IMF indicate that a qualitatively similar solar wind-magnetosphere coupling mode is operating. It is suggested that, in both cases, the discrete auroral forms represent temporal/spatial structure of larger-scale convection over the polar magnetosphere.

Impacts of the Madden-Julian oscillation on intraseasonal precipitation over northeast Brazil

Este estudo tem como objetivo investigar os impactos da oscilação de Madden-Julian (OMJ) na precipitação da região Nordeste do Brasil (NEB). Para tanto foram utilizados dados diários de precipitação baseados em 492 pluviômetros distribuídos na região e cobrindo um período de 30 anos (1981 − 2010). As análises através de composições de anomalias de precipitação, radiação de onda longa e fluxo de umidade, foram obtidas com base no índice da OMJ desenvolvido por Jones-Carvalho. Para distinguir o sinal da OMJ de outros padrões de variabilidade climática, todos os dados diários foram filtrados na escala de 20 − 90 dias; portanto somente dias classificados como eventos da OMJ foram considerados nas composições. Uma análise preliminar baseada apenas nos dados de precipitação foi feita para uma pequena área localizada no interior semiárido do NEB, conhecida como Seridó. Essa microrregião é uma das áreas mais secas do NEB e foi reconhecida pela Convenção das Nações Unidas para o Combate à Desertificação e Mitigação dos Efeitos das Secas como particularmente vulnerável à desertificação. Composições de anomalias de precipitação foram feitas para cada uma das oito fases da OMJ durante Fevereiro-Maio (principal período chuvoso da microrregião). Os resultados mostraram a existência de variações significativas nos padrões de precipitação (de precipitação excessiva à deficiente) associados à propagação da OMJ. A combinação dos sinais de precipitação obtidos durantes as fases úmidas e secas da OMJ mostrou que a diferença corresponde cerca de 50 − 150% de modulação das chuvas na microrregião. Em seguida, uma investigação abrangente sobre o papel da OMJ sobre toda a região Nordeste foi feita considerando-se as quatro estações do ano. Os resultados mostraram que os impactos da OMJ na precipitação intrassazonal do NEB apresentam forte sazonalidade. A maior coerência espacial dos sinais de precipitação ocorreram durante o verão austral, quando cerca de 80% das estações pluviométricas apresentaram anomalias positivas de precipitação durante as fases 1 − 2 da OMJ e anomalias negativas de precipitação nas fases 5 − 6 da oscilação. Embora impactos da OMJ na precipitação intrassazonal tenham sido encontrados na maioria das localidades e em todas as estações do ano, eles apresentaram variações na magnitude dos sinais e dependem da fase da oscilação. As anomalias de precipitação do NEB observadas são explicadas através da interação existente entre as ondas de Kelvin-Rossby acopladas convectivamente e as características climáticas predominantes sobre a região em cada estação do ano. O aumento de precipitação observado sobre a maior parte do NEB durante o verão e primavera austrais encontra-se associado com o fluxo de umidade de oeste (regime de oeste), o qual favorece a atividade convectiva em amplas áreas da América do Sul tropical. Por outro lado, as anomalias de precipitação durante o inverno e outono austrais apresentaram uma variabilidade espacial mais complexa. Durante estas estações, as anomalias de precipitação observadas nas estações localizadas na costa leste do NEB dependem da intensidade do anticiclone do Atlântico Sul, o qual é modulado em grande parte por ondas de Rossby. As características topográficas do NEB parecem desempenhar um papel importante na variabilidade observada na precipitação, principalmente nestas áreas costeiras. A intensificação do anticiclone aumenta a convergência dos ventos alísios na costa contribuindo para a ocorrência de precipitação observada à barlavento do planalto da Borborema. Por outro lado, o aumento da subsidência parece ser responsável pelos déficits de precipitação observados à sotavento. Tais condições mostraram-se típicas durante o predomínio do regime de leste sobre a região tropical da América do Sul e o NEB, durante o qual ocorre uma diminuição no fluxo de umidade proveniente da Amazônia.

The role of the Indian Ocean sector and sea surface salinity for prediction of the coupled Indo-Pacific system

The purpose of this dissertation is to evaluate the potential downstream influence of the Indian Ocean (IO) on El Niño/Southern Oscillation (ENSO) forecasts through the oceanic pathway of the Indonesian Throughflow (ITF), atmospheric teleconnections between the IO and Pacific, and assimilation of IO observations. Also the impact of sea surface salinity (SSS) in the Indo-Pacific region is assessed to try to address known problems with operational coupled model precipitation forecasts. The ITF normally drains warm fresh water from the Pacific reducing the mixed layer depths (MLD). A shallower MLD amplifies large-scale oceanic Kelvin/Rossby waves thus giving ~10% larger response and more realistic ENSO sea surface temperature (SST) variability compared to observed when the ITF is open. In order to isolate the impact of the IO sector atmospheric teleconnections to ENSO, experiments are contrasted that selectively couple/decouple the interannual forcing in the IO. The interannual variability of IO SST forcing is responsible for 3 month lagged widespread downwelling in the Pacific, assisted by off-equatorial curl, leading to warmer NINO3 SST anomaly and improved ENSO validation (significant from 3-9 months). Isolating the impact of observations in the IO sector using regional assimilation identifies large-scale warming in the IO that acts to intensify the easterlies of the Walker circulation and increases pervasive upwelling across the Pacific, cooling the eastern Pacific, and improving ENSO validation (r ~ 0.05, RMS~0.08C). Lastly, the positive impact of more accurate fresh water forcing is demonstrated to address inadequate precipitation forecasts in operational coupled models. Aquarius SSS assimilation improves the mixed layer density and enhances mixing, setting off upwelling that eventually cools the eastern Pacific after 6 months, counteracting the pervasive warming of most coupled models and significantly improving ENSO validation from 5-11 months. In summary, the ITF oceanic pathway, the atmospheric teleconnection, the impact of observations in the IO, and improved Indo-Pacific SSS are all responsible for ENSO forecast improvements, and so each aspect of this study contributes to a better overall understanding of ENSO. Therefore, the upstream influence of the IO should be thought of as integral to the functioning of ENSO phenomenon.

Equatorial Kelvin waves as revealed by EOS Microwave Limb Sounder observations and European Centre for Medium-Range Weather Forecasts analyses: Evidence for slow Kelvin waves of zonal wave number 3

[1] Temperature and ozone observations from the Microwave Limb Sounder (MLS) on the EOS Aura satellite are used to study equatorial wave activity in the autumn of 2005. In contrast to previous observations for the same season in other years, the temperature anomalies in the middle and lower tropical stratosphere are found to be characterized by a strong wave-like eastward progression with zonal wave number equal to 3. Extended empirical orthogonal function (EOF) analysis reveals that the wave 3 components detected in the temperature anomalies correspond to a slow Kelvin wave with a period of 8 days and a phase speed of 19 m/s. Fluctuations associated with this Kelvin wave mode are also apparent in ozone profiles. Moreover, as expected by linear theory, the ozone fluctuations observed in the lower stratosphere are in phase with the temperature perturbations, and peak around 20–30 hPa where the mean ozone mixing ratios have the steepest vertical gradient. A search for other Kelvin wave modes has also been made using both the MLS observations and the analyses from one experiment where MLS ozone profiles are assimilated into the European Centre for Medium-Range Weather Forecasts (ECMWF) data assimilation system via a 6-hourly 3D var scheme. Our results show that the characteristics of the wave activity detected in the ECMWF temperature and ozone analyses are in good agreement with MLS data.

ENSO impact on Kelvin waves and associated tropical convection

The impact of El Nino–Southern Oscillation (ENSO) on atmospheric Kelvin waves and associated tropical convection is investigated using the ECMWF Re-Analysis, NOAA outgoing longwave radiation (OLR), and the analysis technique introduced in a previous study. It is found that the phase of ENSO has a substantial impact on Kelvin waves and associated convection over the equatorial central-eastern Pacific. El Nino (La Nina) events enhance (suppress) variability of the upper-tropospheric Kelvin wave and the associated convection there, both in extended boreal winter and summer. The mechanism of the impact is through changes in the ENSO-related thermal conditions and the ambient flow. In El Nino years, because of SST increase in the equatorial central-eastern Pacific, variability of eastward-moving convection, which is mainly associated with Kelvin waves, intensifies in the region. In addition, owing to the weakening of the equatorial eastern Pacific westerly duct in the upper troposphere in El Nino years, Kelvin waves amplify there. In La Nina years, the opposite occurs. However, the stronger westerly duct in La Nina winters allows more NH extratropical Rossby wave activity to propagate equatorward and force Kelvin waves around 200 hPa, partially offsetting the in situ weakening effect of the stronger westerlies on the waves. In general, in El Nino years Kelvin waves are more convectively and vertically coupled and propagate more upward into the lower stratosphere over the central-eastern Pacific. The ENSO impact in other regions is not clear, although in winter over the eastern Indian and western Pacific Oceans Kelvin waves and their associated convection are slightly weaker in El Nino than in La Nina years.

Origin of Convectively Coupled Kelvin Waves over South America

Convectively coupled Kelvin waves over the South American continent are examined through the use of temporal and spatial filtering of reanalysis, satellite, and gridded rainfall data. They are most prominent from November to April, the season analyzed herein. The following two types of events are isolated: those that result from preexisting Kelvin waves over the eastern Pacific Ocean propagating into the continent, and those that apparently originate over Amazonia, forced by disturbances propagating equatorward from central and southern South America. The events with precursors in the Pacific are mainly upper-level disturbances, with almost no signal at the surface. Those events with precursors over South America, on the other hand, originate as upper-level synoptic wave trains that pass over the continent and resemble the ""cold surges`` documented by Garreaud and Wallace. As the wave train propagates over the Andes, it induces a southerly low-level wind that advects cold air to the north. Precipitation associated with a cold front reaches the equator a few days later and subsequently propagates eastward with the characteristics of a Kelvin wave. The structures of those waves originating over the Pacific are quite similar to those originating over South America as they propagate to eastern South America and into the Atlantic. South America Kelvin waves that originate over neither the Pacific nor the midlatitudes of South America can also be identified. In a composite sense, these form over the eastern slope of the Andes Mountains, close to the equator. There are also cases of cold surges that reach the equator yet do not form Kelvin waves. The interannual variability of the Pacific-originating events is related to sea surface temperatures in the central-eastern Pacific Ocean. When equatorial oceanic conditions are warm, there tends to be an increase in the number of disturbances that reach South America from the Pacific.

Reproduction of recorded ocean waves in a ship model towing tank.

Mode of access: Internet.

Oceanic internal waves from ship, aircraft, and spacecraft : a report on the New York-to-Bermuda remote sensing experiment /

Mode of access: Internet.

Interaction of Kelvin waves and nonlocality of energy transfer in superfluids

We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.