**Speaker**: Vincent Labarre

**Abstract**: Internal gravity waves propagating in stratified flows are an important

component of geophysical and astrophysical systems, encompassing a wide range of

scales. In the weakly nonlinear regime, these waves interact through nonlinear resonant

triadic interactions, leading to a mixing of density, momentum, and energy. Representing

such wave dynamics is of paramount importance, particularly in climate modelling.

We present a new derivation of the kinetic equation for weak internal gravity wave

turbulence. This equation aligns with the one obtained by Caillol and Zeitlin, but it is

expressed in a more compact form. We demonstrate that it conserves energy without

relying on the frequency resonance condition, and we investigate steady, scale-invariant

solutions.

We parameterize the resonant manifold, corresponding to the set of resonant triadic

interactions among internal gravity waves. It enables us to numerically verify that the

interaction coefficients are fully symmetric under the permutation of wave vectors on the

resonant manifold, simplify the collision integral, and evaluate the transfer coefficients of

all triadic interactions.

In the hydrostatic limit, our equation is equivalent to the Hamiltonian description of Lvov

and Tabak. The steady, bi-homogeneous, nonequilibrium spectrum associated with

energy conservation, the Pelinovsky-Raevsky spectrum, is derived without employing the

frequency resonance condition, an uncommon approach in Weak Wave Turbulence

theory. We also present preliminary results from the numerical simulation of the kinetic

equation.