Open Access

This study investigates convection in a non-isothermal spherical Taylor–Couette flow (sTC) under the influence of the dielectrophoretic (DEP) force. The convective flow is driven by differential rotation of the inner and outer boundaries rotating with Ω and ΔΩ in combination of an electric tension applied between both shells to induce thermo-electrohydrodynamic (TEHD) convection. To understand the interaction between DEP force-driven and rotation-driven mechanisms, we first analysed TEHD convection and non-isothermal sTC flow independently. For the TEHD case, we establish scaling relations for heat transport by expressing the Nusselt number, Nu, as a function of the electric Rayleigh number, RaE , and the kinetic energy density, ˜Ek. These relations are evaluated against classical models of convection to assess consistency and deviations. A similar approach was applied to the non-isothermal sTC flow in the absence of the DEP force, where we identified axisymmetric and non-axisymmetric flow regimes which were classified by Nu, ˜Ek and ΔΩ, and developed corresponding scaling relations. When both mechanisms were active, Nu generally increased, however, the DEP force locally suppressed angular momentum transport, especially near the equator. This interplay revealed three distinct regimes: (A) DEP force-dominated TEHD convection, (C) rotation-dominated non-isothermal sTC flow and (B) a transitional regime with reduced heat transport. A decomposition of a derived inflow Nusselt number, Nuq , based on conductive and convective contributions, further elucidated the underlying heat transport mechanism.

We investigate surface waves in an oscillating circular channel with local topography. The focus is on spatially or temporally breaking this dynamic system’s symmetry. Asymmetrical wave dynamics and a mean flux excitation are detected to varying degrees, depending on the two input parameters, fluid depth and the tank’s oscillation frequency. The fluid resonates around multiples of the fundamental eigenfrequency of the channel. The development of solitary wave-trains (undular bores) is observed in these resonance bands. A particle image velocimetry system measures the velocity field in the vertical plane of the free surface flow. Moreover, we are using 17 evenly distributed ultrasonic sensors to measure the surface displacement. This makes it possible to find out how strongly the mean flux depends on the resonance frequencies and to study the influence of the surface waves on the symmetry breaking. A numerical long-wave model helps to isolate the various factors influencing the mean flux.

The transport and waves in parametrically excited fluid layers play a significant role in an understanding of non-linear surface wave phenomena and tidal resonances. In this thesis, we study resonant waves occurring in a circular channel with various obstacles under external oscillatory excitation. Typically, such sloshing experiments are conducted in rectangular, straight channels. The external excitation is implemented using a rotating table on which the entire experiment, including measurement equipment, is mounted. The excitation is either sinusoidal or ratched motion. The obstacles include a fully blocking barrier and a symmetric or asymmetric hill. The channel circumference is 4.76 m, with water depths ranging from 2 cm to 6 cm. Wave displacements within the channel are measured using 17 ultrasonic sensors equidistantly distributed along half of the channel. Particle Image Velocimetry (PIV) is employed to measure the flow. We also consider a simplified numerical model capable of reproducing the experimental results. This model is based on a long-wave approximation and vertical integration using a profile function (Kármán-Pohlhausen approach). Additionally, we use a wave attractor model to quantitatively explain the development of resonances. These resonances are distributed in bands of the excitation frequency around the linear eigenfrequency. The experimental wave attractor and numerical results are consistent with each other. The waves observed within these resonant frequency bands appear as undular bores or solitary waves. In the fully blocking case, bands of constructive and destructive interference are observed, while in the presence of hills, all eigenfrequencies exhibit resonances of varying intensity. These non-linear wave phenomena are characterized by strong transport properties, which can be studied here due to the fact that the circular channel is not fully blocked. The ratched excitation generated asymmetric wave fields, which also induced asymmetric transport in the channel, leading to the emergence of a mean flow in the channel. A similar mean channel flow is observed for the asymmetric hill; however, wave-induced transport played a lesser role in this case. This is attributed to a large separation vortex on the steep side of the hill, which created a valve effect that rectified part of the oscillatory flow. These results are of interest not only for engineering applications but also for the understanding of tidal flows over seabed topography.