Internal gravity waves versus inertial waves in the laboratory

Density-stratified and/or rotating fluids are very common in geophysical and astrophysical flows and enable the propagation of respectively internal gravity waves and inertial waves. Their peculiar dispersion relation has the same mathematical form for both classes of waves and can lead to unexpected outcomes through amplification, resonance or non-linearities. Even though their dispersion relation is very similar, internal gravity waves and inertial waves have different structural characteristics and arise from distinct physical mechanisms. Understanding the analogies and the differences in their behaviors is crucial for studying their respective roles. In this review, we will describe laboratory experiments that have studied either inertial waves in rotating homogeneous fluids or internal gravity waves in non-rotating density stratified fluids to highlight both the similarities and the differences between these two types of waves. We will focus on linear and non-linear phenomena occurring for three different configurations: wave beams in 2D and in 3D geometry, axisymmetric waves, as well as wave attractors, a specific feature for these waves. In particular, we will describe the influence of these various configurations on the Triadic Resonant Instability (TRI).