Rotating shallow water turbulence: Experiments with altimetry

Abstract

Results from a new series of experiments on turbulent flows in a rotating circular container are presented. Electromagnetic forcing is applied to induce flow in a layer of fluid of constant depth. Continuously forced and decaying flows are investigated. Optical altimetry is used to measure the gradient of the surface elevation field and to obtain the velocity and vorticity fields with high temporal and spatial resolution. Spectral analysis of the flows demonstrates the formation of dual cascade with energy and enstrophy intervals although the corresponding spectral fluxes of energy and enstrophy are not uniform in these intervals. The energy interval is characterized by the slope of ∼−5/3 in terms of wavenumber and is limited in extent by the finite radius of deformation effect. In the enstrophy range, the slope is steeper than −3 due to the presence of long-lived coherent vortices. The spatial patterns of fluxes to large or small scales in the flow indicate that inverse energy transfer and direct enstrophy transfer occur mainly in elongated vorticity patches. Cyclone/anticyclone asymmetry in favor of anticyclones is observed in our flows. Dominance of anticyclones is most clear during the decay phase of turbulence. The anticyclones remain circular, while cyclonic vorticity is stretched into elongated patches. Measurements show that skewness of vorticity distribution increases with increasing Froude number of the flow.

Complex environmental <i>β</i>-plane turbulence: laboratory experiments with altimetric imaging velocimetry

“…Note that although in our experiments one can infer the direction of the energy cascade from the form of the spectrum assuming that the forcing wavenumber is known, direct evidence of the cascade direction can only be provided by the analyses of the spectral energy flux. Such evidence was provided for shallow water rotating turbulence (without β-effect) in the laboratory investigation by Afanasyev and Craig (2013). The analysis of the energy flux for the large-scale oceanic turbulence by Scott and Wang (2005) revealed the existence of the inverse cascade in agreement with the two-dimensional turbulence theory.…”

“…The steeper slope in the second experiment is, perhaps, due to the fact that this two-layer, statically stable flow is significantly baroclinic. Note that a steeper than −3 slope was also measured in the experiments with shallow water, f -plane turbulence by Afanasyev and Craig (2013) and in the numerical simulations by Yuan and Hamilton (1994).…”

“…Since the size of the domain was large, the scale separation was large enough for the development of the inverse cascade of energy. A recent study on two-dimensional turbulence (in the absence of β-effect) by Afanasyev and Craig (2013) gave the experimental evidence of dual cascade with the spectral slopes of −5/3 and −3. Further experiments with barotropic turbulence on the β-plane by Zhang and Afanasyev (2014) demonstrated the dual cascade in the presence of β-effect as well as the figure-of-eight energy spectrum in the wavenumber space.…”

Multiple Zonal Jets in a Differentially Heated Rotating Annulus

“…The assumption that barotropization is rapid relative to other processes has led to a host of laboratory (Afanasyev and Wells 2005;Afanasyev and Craig 2013;Di Nitto et al 2013a,b; and references therein) and numerical (e.g., Dritschel and Scott 2011;Scott and Tissier 2012;Scott and Dritschel 2012) studies that focus on 2D turbulence with stochastic forcing at a given scale, representing the injection of barotropic energy at L D . This work has established an alternate formulation of the Rhines parameter (e.g., Scott and Dritschel 2012; and references therein):…”

Rossby wave radiation by an eddy on a beta-plane: Experiments with laboratory altimetry

“…TheorySuppose we have a turbulent flow on an f-plane (e.g. Afanasyev and Craig 201323 ). Energy distribution between motions of different spatial scale is established by nonlinear (triad) interactions.…”