Baroclinic turbulence on the polar β-plane in the rotating tank: Down to submesoscale

•Modern laboratory experiments permit investigations of the oceanic submesoscales.•Filaments and eddies dynamically similar to oceanic submesoscale exhibit direct energy cascade.•Energy spectra both in wavenumber and frequency domain are obtained.•Zonal jets, Rossby waves and baroclinic instabilities are identified in the spectra. The energy spectra of the baroclinic turbulence are examined in finely resolved laboratory flows. A wide range of wavenumbers and frequencies is accessible, including those dynamically similar to the oceanic meso- and submesoscales. Oceanographically relevant phenomena observed in the experiments include Rossby waves, alternating zonal jets, baroclinically unstable coastal currents as well as submesoscale filaments and eddies. Independent spectral decomposition methodologies (Fourier and Fourier–Bessel) applied in Cartesian and polar coordinates respectively provide a complementary framework for representing and interpreting the measured flows. Evolution of energy spectra in the wavenumber domain demonstrates that energy concentrates in zonal modes. The spectra in the frequency-wavenumber domain reveal a significant role of the linear dynamics in the form of the Rossby waves and baroclinic instability modes. The spectral analyses are extended to obtain energy fluxes between lengthscales and reveal an inverse cascade at larger (meso-) scales and a direct cascade at smaller (submeso-) scales.