UC San Diego International Symposium on Stratified Flows Title Experimental study on periodically forced interfacial gravity waves in a rotating cylindrical basin Journal International Symposium on Stratified Flows, 1(1) Publication Date Experimental study on periodically forced interfacial gravi... (original) (raw)
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Experimental study on periodically forced interfacial gravity waves in a rotating cylindrical basin
2016
Experimental study on periodically forced interfacial gravity waves in a rotating cylindrical basin By Pedro Rojas 1 , Hugo Ulloa 1,2 & Yarko Ni˜no 1,3 Departamento de Ingenieria Civil, Universidad de Chile, pedrojas@ing.uchile.cl 1 Mechanical and Aerospace Engineering, University of California, hulloasanchez@eng.ucsd.edu Advanced Mining Technology Center, Universidad de Chile, ynino@ing.uchile.cl 3 Abstract Diurnal wind-driven internal wave resonance regime, observed in stratified rotating lakes, was studied via laboratory experiments. The fundamental Kelvin wave (with a frequency ω K ) res- onance dynamics was forced in a homogeneous water layer, inside a cylindrical basin mounted on a turntable, with a frequency f /2, via a periodic forcing mechanism, ω w . The air-water interface displacement, η ` , simulated the internal interface response of an immiscible two-layer stratified basin forced by Coriolis and a diurnal wind phase. This was achieved by controlling the ratio of the R...
2009
The evolution of internal waves in a two-layer rotating circular lake was studied under nonlinear and weak nonhydrostatic effects. Inclusion of nonlinear acceleration allowed the waves to steepen at the rear of the crest in deep lakes, forming a front with time. The nonhydrostatic acceleration is shown to counteract this wave steeping, leading to wave dispersion, and when the two effects are in balance, solitary-type waves can form. It is shown that a Kelvin wave evolves by imparting energy primarily to submodes of the parent cyclonic wave by steepening and to solitary-type waves. By contrast, a Poincaré wave is shown to evolve without shedding much of its energy to other waves, and only a small fraction of the wave energy goes to other submodes, and this is not lost from the parent wave but rather is periodically transferred back into the parent wave. When both Kelvin and Poincaré waves were present simultaneously in the waterbody, then an interaction was observed when both waves were in phase, which gave rise to additional wave components.
Journal of Fluid Mechanics, 2014
The temporal evolution of nonlinear large-scale internal gravity waves, in a two-layer flow affected by background rotation, is studied via laboratory experiments conducted in a cylindrical tank, mounted on a rotating turntable. The internal wave field is excited by the relaxation of an initial forced tilt of the density interface ($\eta _{i}$), which generates internal waves, such as Kelvin and Poincaré waves, in response to rotation effects. The behaviour of etai\eta _{i}etai, in the shore region, is analysed in terms of the background rotation and the nonlinear steepening of the basin-scale waves. The results show that the degeneration of the fundamental Kelvin wave into a solitary-type wave packet is caused by nonlinear steepening and it is influenced by the background rotation. In addition, the physical scales of the leading solitary-type wave are closer to Korteweg–de Vries theory as the rotation increases. Moreover, the nonlinear interaction between the Kelvin wave and the Poincaré...
Seasonal evolution of the basin-scale internal wave field in a large stratified lake
Limnology and Oceanography, 2000
The response of the water column to varying conditions of stratification and wind forcing was investigated in Lake Kinneret (Israel) using data collected from thermistor chains and acoustic Doppler current profilers during 1997 and 1998. The strong daily sea breeze was found to generate a vertical mode 1 internal Kelvin wave and basin-scale internal Poincaré waves of vertical modes 1, 2, and 3. The Kelvin wave, the dominant component of the internal wave field, was responsible for alongshore velocities in the nearshore regions. In the upwind nearshore regions, velocities were dominated by the forced response to the wind and were cross-shore in nature. In the lake interior, the Kelvin wave effect on the horizontal velocity field was minor compared to the higher vertical mode Poincaré waves. The Kelvin wave is shown to exist in resonant and nonforced states with the wind, whereas the vertical mode 1 Poincaré wave energy remained relatively constant, despite large variability in the forcing conditions. The energy in the higher mode Poincaré waves varied greatly, both on daily and seasonal timescales. The results demonstrate that the wind energy forces multiple basin-scale internal wave modes and that prior motion in the water column must be considered when determining the subsequent internal wave response in periodically forced systems.
The temporal evolution of baroclinic basin-scale waves in a rotating circular basin
Journal of Fluid …, 2005
The temporal evolution of baroclinic basin-scale waves in a rotating circular basin following an initial forcing event is investigated using a laboratory study. Experiments conducted in the circular domain containing a two-layer fluid with a flat bottom and vertical sidewalls demonstrate that the response is essentially linear with frictional effects at the boundaries steadily dissipating wave energy. Experiments conducted in the same configuration but with the addition of simple topographic features, either a radially protruding cape or a bathymetric ridge, exhibit wave/topography interactions that result in the formation of an eddy field and an offshore flow, respectively. The rate of wave decay, as well as the amount of horizontal mixing occurring within the basin, is significantly enhanced by such interactions. The results of this study are then considered in terms of their implications for the baroclinic basin-scale wave energy pathways in large stratified lakes influenced by the Earth's rotation.
The degeneration of large-scale interfacial gravity waves in lakes
Journal of Fluid Mechanics, 2001
Mechanisms for the degeneration of large-scale interfacial gravity waves are identified for lakes in which the effects of the Earth's rotation can be neglected. By assuming a simple two-layer model and comparing the timescales over which each of these degeneration mechanisms act, regimes are defined in which particular processes are expected to dominate. The boundaries of these regimes are expressed in terms of two lengthscale ratios: the ratio of the amplitude of the initial wave to the depth of the thermocline, and the ratio of the depth of the thermocline to the overall depth of the lake. Comparison of the predictions of this timescale analysis with the results from both laboratory experiments and field observations confirms its applicability. The results suggest that, for small to medium sized lakes subject to a relatively uniform windstress, an important mechanism for the degeneration of large-scale internal waves is the generation of solitons by nonlinear steepening. Since...
Earth rotation effects on the internal wave field in a stratified small lake: Numerical simulations
Earth rotation effects on the internal wave field in a stratified small lake: Numerical simulations The Princeton Ocean Model was applied to the Sau Reservoir, a medium-sized Mediterranean reservoir (5.7 km 2) located in Catalonia, Spain, during the summer season, when the water column is continuously stratified and forced by a breeze regime with velocities of up to 3-4 m/s. Based on our simulations, the internal wave field has been analysed and the numerical results compared with the field data previously analysed by other authors. The model adequately reproduces all the significant modes observed. The simulations show the importance of rotational modes on the internal wave field. The Burger number S for all rotating internal waves is on the order of 10 −1 , and the internal Rossby radius R is on the order of 10 2 m, that is, smaller than the width of the lacustrine area of the reservoir (10 3 m). Specifically, two rotating third vertical modes were found during the analysed period: the first, a 24-hour period, was forced by the wind and the phase rotated clockwise; and the second, a 12-hour period, can be interpreted as a second azimuthal horizontal mode of a Poincaré wave. A second vertical mode of 8 hours was observed to rotate counter clockwise, although in this case the Earth's rotation appears not to have been of importance because the same results could be obtained without taking into account the Coriolis force. Finally, two first vertical modes, one of 6 hours and the other of 5 hours, were observed, although with no rotational behaviour. These modes correspond, respectively, to the first and second horizontal stationary modes. Further analysis of the simulated velocities shows the existence of a net clockwise flow along the shore as a consequence of the dominant mode of 24 hours, with a mean velocity of 0.5 m/s that reverses at a distance of about 300 m from the coast. Preliminary results based on the simulated velocity field predict horizontal trajectories of passive particles of up to 1 km per day and vertical displacements of up to 5 m across the entire water column.
Waves in a rotating stratified shallow water
Il Nuovo Cimento B, 1989
In this paper, a study of nonlinear stratified rotating fluids is introduced with the shallow-water theory. The mathematical model for two layers of perfect fluids in a rotating circular cylinder is given as well. A distortion for shallow water and slowly rotating fluids is established. A detailed study of the particular case for progressive waves on both layers is presented and the analytical solution has been obtained; this solution is believed to be new.
Observation of inertia-gravity wave attractors in an axisymmetric enclosed basin
Physical Review Fluids
Internal waves are ubiquitous in the ocean and play an essential role in the transport of energy and mixing. Their peculiar reflection enables the concentration of energy on a limit cycle. With wave beams viewed as rays, this reflection on an inclined slope shrinks its width and generically brings closer two initially different trajectories eventually reaching a limit cycle called an attractor. Following previous studies, a ray-tracing algorithm is used to track the convergence of wave beams onto such a structure in a 3D axisymmetric domain. This information is used to design experiments using a truncated conical shaped tank in order to form an inertia-gravity waves attractor in a 3D axisymmetric geometry. By increasing the amplitude of the forcing, an evolution of the attractor characteristics can be observed. The occurrence of waves at frequencies lower than the forcing frequency ω 0 suggests triadic resonant instability in a rotating or in a stratified case. Experiments performed in a stratification-only or a rotation-only case indicate two distinct behaviors. The existence of easily excited standing waves, resonant modes of the tank, at frequencies lower than the forcing one enables sharp triadic resonance instability for internal gravity waves, which is not possible for inertial waves. The effect of the symmetry axis is also investigated by adding a cylinder of sufficient diameter at the center of the domain for the wave to reflect on and thereby avoid the interaction on the singularity. Without it, the large amplitude of the waves on the axis triggers nonlinear effects and mixing, denying the access to the wave turbulence regime.