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| Titel |
Inertial Wave Excitation and Wave Attractors in an Annular Tank: DNS |
| VerfasserIn |
Marten Klein, Abouzar Ghasemi, Uwe Harlander, Andreas Will |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250099769
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| Publikation (Nr.) |
 EGU/EGU2014-15585.pdf |
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| Zusammenfassung |
| Rotation is the most relevant aspect of geophysical fluid dynamics, manifesting itself by the
Coriolis force. Small perturbations to the state of rigid body rotation can excite inertial waves
(waves restored by Coriolis force) with frequencies in the range 0 < Ïă < 2Ω0. We can
restrict our attention to an incompressible fluid so that inertial waves remain the only waves
in the mathematical model, which can transport kinetic energy and angular momentum. In
geophysics, inertial waves have received a lot attention over the last decades. A
spherical shell, for instance, is already non-simple in a sense that its inertial mode’s
spatial structures are complex, forming so-called wave attractors [1]. But also other
containers have been investigated, e.g., cylinders and boxes from the viewpoints of
normal mode excitation [2,3], mean flow generation and boundary layer flow [4]. A
simple wave attractor was found in a prism, which can be seen as idealized ocean
basin [5]. However, local mechanisms of wave excitation are still not very well
understood.
In order to contribute to the ongoing discussion, we consider an annular geometry. Its
rectangular symmetry was broken by replacing the inner cylinder with a frustum of apex
half-angle α = 5.7°. The annular gap is filled with a fluid of kinematic viscosityν. The
whole vessel rotates with a mean angular velocityΩ0 around its axis of symmetry. Ekman
numbers investigated are 1 -« E = ν(Ω0H2)-1 ≥ 10-5. Similarly to [1–5] we perturb the
system by longitudinal libration, Ω(t) = Ω0(1 + ÉsinÏt), where Ï > 0 denotes the
frequency and 0 < É < 1 the amplitude of libration.
Three-dimensional direct numerical simulations (3-D DNS) of the set-up were conducted
in order to resolve different excitation mechanisms. We used an incompressible
Navier–Stokes solver with the equations formulated for volume fluxes in generalized
curvilinear coordinates. Under some constraints the scheme conserves three quantities of
Hamiltonian mechanics: mass, momentum and kinetic energy. To separate between possible
excitation mechanisms we investigated configurations that cannot be accessed in the
laboratory, e.g., axially periodic geometries and cases with libration of different
walls.
For É -¤ 0.3 we found qualitative agreement of wave attractor patterns obtained by
numerical simulations, ray tracing and measurements in the laboratory for all libration
frequencies investigated. We adapted boundary layer theory for the librating walls to
estimate inertial wave excitation, in particular, the relation to libration frequency and
amplitude, as well as the effect of the inclination angle α of the frustum. By comparison
with numerical simulations we found that wave energy in the bulk obeys a similar
dependency on frequency as the energy in the boundary layer over the librating
wall.
References
[1] A.Tilgner, Phys.Rev.E (1999), vol.59(2), pp.1769–1794.
[2] J.Boisson, C.Lamriben, L.R.M.Maas, P.-P.Cortet and F.Moisy, Phys.Fluids
(2012), vol.24, 076602.
[3] A.Sauret, D.Cébron, M.LeBars and S.LeDizès, Phys.Fluids (2012), vol.24,
026603.
[4] F.H.Busse, PhysicaD, vol.240 (2011), pp.208—211.
[5] L.R.M.Maas, J.FluidMech. (2001), vol.437, pp.13–28. |
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