This study concerns on trapped Rossby waves and local Rossby wave packets in zonal basic flows with two or more prominent extreme values (so called multiple-jet flows). For simplicity, most of the calculations are performed on the f-plane, but an extension to the ß-plane is also discussed. Under the assumption that the basic fiow is a solution to a special type of second order ordinary differential equation, we show that then the amplitudes of stationary trapped Rossby waves are solutions to an equation of the same type. We investigate the occurrence of trapped modal waves as well as the rays of wave action radiation in a particular multiple-jet flow. Further we consider the development of the local wavenumbers of Rossby wave packets in such a flow, with and without a zonally oriented reflective boundary. lt is found that wave action can propagate in the zonal direction only when the boundary is present. Otherwise the rays of wave action radiation form a closed curve. / Diese Studie beschäftigt sich mit gefangenen Rossby Wellen und lokalen gefangenen Rossbywellenpaketen in einer zonalen Strömung mit zwei oder mehreren ausgeprägten Extrema (sog. Strömungen mit mehrfachen Jets). Der Einfachheit halber werden die meisten Berechnungen auf der f-Ebene angestellt, eine Erweiterung auf die ß-Ebene wird allerdings auch diskutiert. Wenn man annimmt, dass der Grundstrom die Lösung einer bestimmten gewöhnlichen Differentialgleichung zweiter Ordnung ist, kann man zeigen, dass die Amplituden gefangener Wellen Lösungen des gleichen Gleichungstypes sind. Wir betrachten die Bedingungen für das Auftreten gefangener modaler Wellen, als auch die Pfade der Wellenenergie-Abstrahlung in einer bestimmten Mehrfach-Jet-Strömung. Ferner untersuchen wir die Entwicklung der lokalen Wellenzahlen von Wellenpaketen in einer solchen Strömung, mit und ohne eines zonal orientierten reflektierenden Randes. Wir finden, dass sich Wellenenergie auf der f-Ebene nur dann in zonaler Richtung ausbreiten kann, falls eine solcher Rand vorhanden ist. Anderenfalls ergeben die Strahlen der Wellenenergie Ausbreitung eine geschlossene Kurve.

This study concerns on trapped Rossby waves and local Rossby wave packets in zonal basic flows with two or more prominent extreme values (so called multiple-jet flows). For simplicity, most of the calculations are performed on the f-plane, but an extension to the ß-plane is also discussed. Under the assumption that the basic fiow is a solution to a special type of second order ordinary differential equation, we show that then the amplitudes of stationary trapped Rossby waves are solutions to an equation of the same type. We investigate the occurrence of trapped modal waves as well as the rays of wave action radiation in a particular multiple-jet flow. Further we consider the development of the local wavenumbers of Rossby wave packets in such a flow, with and without a zonally oriented reflective boundary. lt is found that wave action can propagate in the zonal direction only when the boundary is present. Otherwise the rays of wave action radiation form a closed curve. / Diese Studie beschäftigt sich mit gefangenen Rossby Wellen und lokalen gefangenen Rossbywellenpaketen in einer zonalen Strömung mit zwei oder mehreren ausgeprägten Extrema (sog. Strömungen mit mehrfachen Jets). Der Einfachheit halber werden die meisten Berechnungen auf der f-Ebene angestellt, eine Erweiterung auf die ß-Ebene wird allerdings auch diskutiert. Wenn man annimmt, dass der Grundstrom die Lösung einer bestimmten gewöhnlichen Differentialgleichung zweiter Ordnung ist, kann man zeigen, dass die Amplituden gefangener Wellen Lösungen des gleichen Gleichungstypes sind. Wir betrachten die Bedingungen für das Auftreten gefangener modaler Wellen, als auch die Pfade der Wellenenergie-Abstrahlung in einer bestimmten Mehrfach-Jet-Strömung. Ferner untersuchen wir die Entwicklung der lokalen Wellenzahlen von Wellenpaketen in einer solchen Strömung, mit und ohne eines zonal orientierten reflektierenden Randes. Wir finden, dass sich Wellenenergie auf der f-Ebene nur dann in zonaler Richtung ausbreiten kann, falls eine solcher Rand vorhanden ist. Anderenfalls ergeben die Strahlen der Wellenenergie Ausbreitung eine geschlossene Kurve.

Unconfined multiple interacting confluent round jets are interesting from a purely scientific point of view, as interaction between neighboring jets brings additional complexity to the flow field. Unconfined confluent round jets also exist in various engineering applications, such as ventilation supply devices, sewage disposal systems, combustion burners, chemical mixing or chimney stacks. Even so, little scientific attention has been paid to unconfined confluent round jets. The present work uses both advanced measurement techniques and computational models to provide deeper understanding of the turbulent flow field development of unconfined confluent round jets. Both Laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV) have been used to measure mean velocity and turbulence properties within two setups, consisting of a single row of 1×6 jets and a square array of 6×6 confluent jets. Simulations using computational fluid dynamics (CFD) of the 6×6 setup were conducted using three different Reynolds Averaged Navier-Stokes (RANS) turbulence models: the standard k-ε, the RNG k-ε and the Reynolds Stress model (RSM). The results from the CFD simulations were compared with experimental data. The employed RANS turbulence models were all capable of accurately predicting mean velocities and turbulent properties in the investigated confluent jet array. In general the RSM and k-ε std. models provided smaller deviations between numerical and experimental results than the RNG k-ε model. In terms of mean velocity the second-order closure model (RSM) was not found to be superior to the less complex standard k-ε model. The validated CFD model was employed in a parametrical investigation, including five independent variables: inlet velocity, nozzle diameter, nozzle edge-to-edge spacing, nozzle height and the number of jets in the array. The parametrical investigations made use of statistical methods in the form of response surface methodology. The derived response surface models provided information on the principal influence and relative importance of the investigated parameters within the investigated design space. The positions of the jets within the array strongly influence both mean velocity and turbulence. In all investigated setups the jets experience merging and combining. Square arrays also include considerable jet convergence, which was not present in the 1×6 jet array. Due to the jet convergence in square arrays the turbulent flow field, especially for jets far away from the array center, is affected by mean flow curvature. Jets located along the sides of square jet arrays experience strong jet-to-jet interactions that result in considerable jet deformation, shorter potential core, higher turbulent kinetic energy and faster velocity decay compared to other jets. Jets located at the corners of the array do not interact as strongly with neighboring jets as do the jets along the sides. The locations of merging and combined points differ considerably between different jets and different jet configurations. As the jets combine a zone with uniform stream-wise velocity and low turbulence intensity forms in the center of square jet arrays. This zone has been called Confluent Core Zone (CCZ) due to its similarities with the potential core zone of a single jet. Within the CCZ the appropriate scaling length changes from nozzle diameter to the effective source diameter. The parametrical investigation showed that nozzle diameter and edge-to-edge nozzle spacing were the most important of the investigated parameters, reflecting a strong dependence on dimensionless jet spacing, S/d0. Higher S/d0 delays both merging and combining of the jets and leads to a CCZ with lower velocity and longer downstream extension. Increasing the array size leads to a reduced combined point distance, a stronger inwards displacement of jets in the outer part of the array, and reduced entrainment near the nozzles. A higher inlet velocity was found to increase the jet convergence in the investigated square confluent jet arrays. Nozzle height generally has minor impact on the investigated response variables.

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