# Role of the basin boundary conditions in gravity wave
turbulence

**L. Deike**^{1}, B. Miquel^{2},
P. Gutiérrez^{3}, T. Jamin^{1}, B. Semin^{2},
M. Berhanu^{1}, E. Falcon^{1}, F.
Bonnefoy^{4}

^{1} Univ Paris Diderot, Sorbonne Cité,
MSC, CNRS, UMR 7057, F-75 013 Paris, France

^{2} Ecole Normale Supérieure, LPS, UMR 8550 CNRS, F-75
205 Paris, France

^{3} CEA-Saclay, Sphynx, DSM, URA 2464 CNRS, F-91 191
Gif-sur-Yvette, France

^{4} Ecole Centrale de Nantes, LHEEA, UMR 6598 CNRS, F-44
321 Nantes, France

### Reference: Journal
of Fluid Mechanics 781, 196 - 225 (2015)

**Abstract: **

Gravity wave turbulence
is investigated experimentally in a large wave basin
in which irregular waves are generated unidirectionally. The
roles of the basin boundary conditions (absorbing or reflecting)
and of the forcing properties are investigated. To that purpose,
an absorbing sloping beach opposite the wavemaker can be
replaced by a reflecting vertical wall. We observe that the wave
field properties depend strongly on these boundary
conditions. A quasi-one-dimensional field of nonlinear
waves propagates toward the beach where they are damped whereas
a more multidirectional wave field is observed with the wall. In
both cases, the wave spectrum scales as a frequency-power law
with an exponent that increases continuously with the forcing
amplitude up to a value close to -4. The physical mechanisms
involved most likely differ with the boundary condition used,
but cannot be easily discriminated with only temporal
measurements. We also studied freely decaying gravity wave
turbulence in the closed basin. No self-similar decay of the
spectrum is observed, whereas its Fourier modes decay first as a
time power law due to nonlinear mechanisms, and then
exponentially due to linear viscous damping. We estimate the
linear, nonlinear and dissipative time scales to test the time
scale separation that highlights the important role of a large
scale Fourier mode. By estimation of the mean energy flux from
the initial decay of wave energy, the Kolmogorov-Zakharov
constant of the weak turbulence theory is evaluated and found to
be compatible with a recently obtained theoretical value.

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