TY - JOUR

T1 - Internal wave attractors in three-dimensional geometries

T2 - Trapping by oblique reflection

AU - Pillet, G.

AU - Ermanyuk, E. V.

AU - Maas, L. R.M.

AU - Sibgatullin, I. N.

AU - Dauxois, T.

PY - 2018/6/25

Y1 - 2018/6/25

N2 - We study experimentally the propagation of internal waves in two different three-dimensional (3D) geometries, with a special emphasis on the refractive focusing due to the 3D reflection of obliquely incident internal waves on a slope. Both studies are initiated by ray tracing calculations to determine the appropriate experimental parameters. First, we consider a 3D geometry, the classical set-up to get simple, two-dimensional (2D) parallelogram-shaped attractors in which waves are forced in a direction perpendicular to a sloping bottom. Here, however, the forcing is of reduced extent in the along-slope, transverse direction. We show how the refractive focusing mechanism explains the formation of attractors over the whole width of the tank, even away from the forcing region. Direct numerical simulations confirm the dynamics, emphasize the role of boundary conditions and reveal the phase shifting in the transverse direction. Second, we consider a long and narrow tank having an inclined bottom, to simply reproduce a canal. In this case, the energy is injected in a direction parallel to the slope. Interestingly, the wave energy ends up forming 2D internal wave attractors in planes that are transverse to the initial propagation direction. This focusing mechanism prevents indefinite transmission of most of the internal wave energy along the canal.

AB - We study experimentally the propagation of internal waves in two different three-dimensional (3D) geometries, with a special emphasis on the refractive focusing due to the 3D reflection of obliquely incident internal waves on a slope. Both studies are initiated by ray tracing calculations to determine the appropriate experimental parameters. First, we consider a 3D geometry, the classical set-up to get simple, two-dimensional (2D) parallelogram-shaped attractors in which waves are forced in a direction perpendicular to a sloping bottom. Here, however, the forcing is of reduced extent in the along-slope, transverse direction. We show how the refractive focusing mechanism explains the formation of attractors over the whole width of the tank, even away from the forcing region. Direct numerical simulations confirm the dynamics, emphasize the role of boundary conditions and reveal the phase shifting in the transverse direction. Second, we consider a long and narrow tank having an inclined bottom, to simply reproduce a canal. In this case, the energy is injected in a direction parallel to the slope. Interestingly, the wave energy ends up forming 2D internal wave attractors in planes that are transverse to the initial propagation direction. This focusing mechanism prevents indefinite transmission of most of the internal wave energy along the canal.

KW - geophysical and geological flows

KW - internal waves

KW - stratified flows

KW - ENERGY

KW - INSTABILITY

KW - OCEAN

KW - RECTANGULAR BASIN

KW - ONE SLOPING BOUNDARY

KW - EMPIRICAL MODE DECOMPOSITION

KW - FLUID

KW - SPECTRUM

KW - PROPAGATION

KW - INERTIAL WAVES

UR - http://www.scopus.com/inward/record.url?scp=85045767157&partnerID=8YFLogxK

U2 - 10.1017/jfm.2018.236

DO - 10.1017/jfm.2018.236

M3 - Article

AN - SCOPUS:85045767157

VL - 845

SP - 203

EP - 225

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -