TY - JOUR
T1 - Mean flow generation via non-resonant interactions in two-dimensional forced stratified turbulence
AU - Zoppi, Antonin
AU - Billant, Paul
AU - Demaine, Leo
N1 - Publisher Copyright:
© The Author(s), 2025. Published by Cambridge University Press.
PY - 2025/12/9
Y1 - 2025/12/9
N2 - We perform numerical simulations of two-dimensional strongly stratified flows in a square periodic domain forced by a steady mode with vorticity of the form, where are fixed wavenumbers. It is shown that such deterministic forcing can lead to a transition to turbulence and the emergence of horizontal layers (so-called vertically sheared horizontal flows, VSHFs) similarly as for random stochastic forcing. The flow characteristics are studied depending on the Froude and Reynolds numbers. Furthermore, the mechanisms of layers formation are disentangled. Triadic instabilities first lead to the growth of pairs of wavevectors that resonate with each of the four forced wavevectors. Quadratic interactions between these resonant modes and the forcing also drive the growth of several non-resonant modes at the same growth rate. Since the forcing comprises the wavevectors and their mirror symmetric with respect to the horizontal, there exist enslaved/bound modes with the same horizontal wavenumber and different vertical wavenumbers. Hence, the quadratic interactions between the latter modes force a second generation of modes among which some are VSHFs. Their growth rate is twice the growth rate of the primary resonant modes. Such a mechanism is similar to resonant quartets (Newell, J. Fluid Mech., 1969, vol. 35, no 2, pp. 255-271; Smith & Waleffe, Phys. Fluids, 1999, vol. 11, no 6, pp. 1608-1622). When the forcing is restricted to only the two wavevectors, the second generation of enslaved/bound modes all have a non-zero horizontal wavenumber. However, further quadratic interactions can force VSHF. Thus, horizontal layers also emerge, but with a growth rate equal to the number of quadratic interactions times the growth rate of the primary instability.
AB - We perform numerical simulations of two-dimensional strongly stratified flows in a square periodic domain forced by a steady mode with vorticity of the form, where are fixed wavenumbers. It is shown that such deterministic forcing can lead to a transition to turbulence and the emergence of horizontal layers (so-called vertically sheared horizontal flows, VSHFs) similarly as for random stochastic forcing. The flow characteristics are studied depending on the Froude and Reynolds numbers. Furthermore, the mechanisms of layers formation are disentangled. Triadic instabilities first lead to the growth of pairs of wavevectors that resonate with each of the four forced wavevectors. Quadratic interactions between these resonant modes and the forcing also drive the growth of several non-resonant modes at the same growth rate. Since the forcing comprises the wavevectors and their mirror symmetric with respect to the horizontal, there exist enslaved/bound modes with the same horizontal wavenumber and different vertical wavenumbers. Hence, the quadratic interactions between the latter modes force a second generation of modes among which some are VSHFs. Their growth rate is twice the growth rate of the primary resonant modes. Such a mechanism is similar to resonant quartets (Newell, J. Fluid Mech., 1969, vol. 35, no 2, pp. 255-271; Smith & Waleffe, Phys. Fluids, 1999, vol. 11, no 6, pp. 1608-1622). When the forcing is restricted to only the two wavevectors, the second generation of enslaved/bound modes all have a non-zero horizontal wavenumber. However, further quadratic interactions can force VSHF. Thus, horizontal layers also emerge, but with a growth rate equal to the number of quadratic interactions times the growth rate of the primary instability.
KW - stratified flows
KW - stratified turbulence
KW - transition to turbulence
UR - https://www.scopus.com/pages/publications/105024346833
U2 - 10.1017/jfm.2025.10930
DO - 10.1017/jfm.2025.10930
M3 - Article
AN - SCOPUS:105024346833
SN - 0022-1120
VL - 1024
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
M1 - A59
ER -