[Paper Review] Zonal jets at the laboratory scale: hysteresis and Rossby waves resonance

Daphné Lemasquerier, Benjamin Favier+1 more|St Andrews Research Repository (St Andrews Research Repository)|Aug 24, 2020

Oceanographic and Atmospheric Processes112 references20 citations

TL;DR

This experimental study investigates zonal jet formation in a rotating tank with a strong, uniform topographic β-effect and small-scale turbulent forcing. Using time-resolved PIV, it identifies a subcritical bifurcation between two jet regimes: weak, steady jets at low forcing and strong, dynamic, wide jets at high forcing, driven by resonance between forced Rossby waves and the background zonal flow.

ABSTRACT

The dynamics, structure and stability of zonal jets in planetary flows are still poorly understood, especially in terms of coupling with the small-scale turbulent flow. Here, we use an experimental approach to address the questions of zonal jets formation and long-term evolution. A strong and uniform topographic $β$-effect is obtained inside a water-filled rotating tank thanks to the paraboloidal fluid free upper surface combined with a specifically designed bottom plate. A small-scale turbulent forcing is performed by circulating water through the base of the tank. Time-resolving PIV measurements reveal the self-organization of the flow into multiple zonal jets with strong instantaneous signature. We identify a subcritical bifurcation between two regimes of jets depending on the forcing intensity. In the first regime, the jets are steady, weak in amplitude, and directly forced by the local Reynolds stresses due to our forcing. In the second one, we observe highly energetic and dynamic jets of width larger than the forcing scale. An analytical modeling based on the quasi-geostrophic approximation reveals that this subcritical bifurcation results from the resonance between the directly forced Rossby waves and the background zonal flow.

Motivation & Objective

• To understand the self-organization of zonal jets in planetary-scale flows under controlled laboratory conditions.
• To investigate the coupling between small-scale turbulent forcing and large-scale zonal jet dynamics.
• To determine the mechanisms behind the transition between distinct jet regimes, particularly the emergence of strong, wide jets.
• To test the role of Rossby wave resonance in amplifying zonal flows beyond direct forcing.

Proposed method

• A water-filled rotating tank with a paraboloidal free surface and specially designed bottom plate generates a strong, uniform topographic β-effect.
• Small-scale turbulent forcing is applied via controlled water circulation through six rings at the tank base, simulating localized energy input.
• Time-resolved particle image velocimetry (PIV) measures the full velocity field to capture jet formation and evolution.
• A quasi-geostrophic analytical model is used to interpret the bifurcation behavior, incorporating Reynolds stresses and Rossby wave dynamics.
• Forcing calibration is performed in situ using RMS velocity measurements in defined regions of interest to quantify forcing amplitude.
• Sensitivity analysis of model parameters (friction, β, forcing wavenumber) is conducted to validate the model's predictive power.

Experimental results

Research questions

• RQ1 What mechanisms drive the formation of zonal jets in a laboratory-scale rotating flow with small-scale forcing?
• RQ2 How does the system transition between distinct jet regimes as forcing intensity increases?
• RQ3 What is the role of Rossby wave resonance in amplifying zonal flows beyond direct forcing?
• RQ4 To what extent do nonlinear interactions between turbulent eddies and the zonal mean flow govern jet stability and amplitude?

Key findings

• A subcritical bifurcation is observed between two jet regimes: weak, steady jets at low forcing and strong, dynamic, wide jets at high forcing.
• The transition is driven by resonance between directly forced Rossby waves and the background zonal flow, as confirmed by the quasi-geostrophic model.
• In the high-forcing regime, jets exhibit amplitudes and widths significantly larger than the forcing scale, indicating nonlinear energy transfer.
• The zonostrophy index $ R_{\beta} \approx 2.84 $ in the high-forcing regime indicates a zonostrophic regime where jets are well-defined and stable.
• The low-forcing regime has $ R_{\beta} \approx 2.26 $, indicating a regime near the threshold of strong anisotropization.
• Model sensitivity analysis shows that the bistable zone and jet amplitude are most sensitive to the friction coefficient and β-effect, with experimental values falling within the observed range.