Transition from Geostrophic Flows to Inertia–Gravity Waves in the Spectrum of a Differentially Heated Rotating Annulus Experiment

Inertia–gravity waves (IGWs) play an essential role in the terrestrial atmospheric dynamics as they can lead to energy and momentum flux when propagating upward. An open question is to what extent IGWs contribute to the total energy and to the flattening of the energy spectrum observed at the mesoscale. In this work, we present an experimental investigation of the energy distribution between the large-scale balanced flow and the small-scale imbalanced flow. Weakly nonlinear IGWs emitted from baroclinic jets are observed in the differentially heated rotating annulus experiment. Similar to the atmospheric spectra, the experimental kinetic energy spectra reveal the typical subdivision into two distinct regimes with slopes k−3 for the large scales and k−5/3 for the small scales. By separating the spectra into the vortex and wave components, it emerges that at the large-scale end of the mesoscale the gravity waves observed in the experiment cause a flattening of the spectra and provide most of the energy. At smaller scales, our data analysis suggests a transition toward a turbulent regime with a forward energy cascade up to where dissipation by diffusive processes occurs.

Mechanisms of Mid- to Outer-Shelf Transport of Shoreline-Released Tracers

Transport of shoreline-released tracer from the surfzone across the shelf can be affected by a variety of physical processes from wind-driven to submesoscale, with implications for shoreline contaminant dilution and larval dispersion. Here, a high-resolution wave–current coupled model that resolves the surfzone and receives realistic oceanic and atmospheric forcing is used to simulate dye representing shoreline-released untreated wastewater in the San Diego–Tijuana region. Surfzone and shelf alongshore dye transports are primarily driven by obliquely incident wave breaking and alongshore pressure gradients, respectively. At the midshelf to outer-shelf (MS–OS) boundary (25-m depth), defined as a mean streamline, along-boundary density gradients are persistent, dye is surface enhanced and time and alongshelf patchy. Using baroclinic and along-boundary perturbation dye transports, two cross-shore dye exchange velocities are estimated and related to physical processes. Barotropic and baroclinic tides cannot explain the modeled cross-shore transport. The baroclinic exchange velocity is consistent with the wind-driven Ekman transport. The perturbation exchange velocity is elevated for alongshore dye and cross-shore velocity length scales < 1 km (within the submesoscale) and stronger alongshore density gradient ∂ρ/∂y variability, indicating that alongfront geostrophic flows induce offshore transport. This elevated ∂ρ/∂y is linked to convergent northward surface along-shelf currents (likely due to regional bathymetry), suggesting deformation frontogenesis. Both surfzone and shelf processes influence offshore transport of shoreline-released tracers with key parameters of surfzone and shelf alongcoast currents and alongshelf winds.

Transition from geostrophic flows to inertia-gravity waves in the spectrum of a differentially heated rotating annulus experiment.

&lt;p&gt;Inertia-gravity waves (IGWs) are known to play an essential role in the terrestrial atmospheric dynamics as they can lead to energy and momentum flux when they propagate upwards. An open question is to which extent nearly linear IGWs contribute to the total energy and to flattening of the energy spectrum observed at the mesoscale.&lt;br&gt;In this work, we present an experimental investigation of the energy distribution between the large-scale balanced flow and the small-scale imbalanced flow. Weakly nonlinear IGWs emitted from baroclinic jets are observed in the differentially heated rotating annulus experiment. Similar to the atmospheric spectra, the experimental kinetic energy spectra reveal the typical subdivision into two distinct regimes with slopes &lt;em&gt;k&lt;/em&gt;&lt;sup&gt;-3&lt;/sup&gt; for the large scales and &lt;em&gt;k&lt;sup&gt;-&lt;/sup&gt;&lt;/em&gt;&lt;sup&gt;5/3&lt;/sup&gt; for smaller scales. By separating the spectra into a vortex and wave part, it emerges that at the largest scales in the mesoscale range the gravity waves observed in the experiment cause a flattening of the spectra and provide most of the energy. At smaller scales, our data analysis suggests a transition towards a turbulent regime with a forward energy cascade up to where dissipation by diffusive processes occurs.&lt;/p&gt;

Instability and Convection in Rotating Porous Media: A Review

A review on instability and consequent natural convection in rotating porous media is presented. Taylor-Proudman columns and geostrophic flows exist in rotating porous media just the same as in pure fluids. The latter leads to a tendency towards two-dimensionality. Natural convection resulting from density gradients in a gravity field as well as natural convection induced by density gradients due to the centripetal acceleration are being considered. The former is the result of gravity-induced buoyancy, the latter is due to centripetally-induced buoyancy. The effect of Coriolis acceleration is also discussed. Linear stability analysis as well as weak nonlinear solutions are being derived and presented.

An improved model of near-inertial wave dynamics

The YBJ equation (Young & Ben Jelloul, J. Marine Res., vol. 55, 1997, pp. 735–766) provides a phase-averaged description of the propagation of near-inertial waves (NIWs) through a geostrophic flow. YBJ is obtained via an asymptotic expansion based on the limit $\mathit{Bu}\rightarrow 0$, where $\mathit{Bu}$ is the Burger number of the NIWs. Here we develop an improved version, the YBJ+ equation. In common with an earlier improvement proposed by Thomas, Smith & Bühler (J. Fluid Mech., vol. 817, 2017, pp. 406–438), YBJ+ has a dispersion relation that is second-order accurate in $\mathit{Bu}$. (YBJ is first-order accurate.) Thus both improvements have the same formal justification. But the dispersion relation of YBJ+ is a Padé approximant to the exact dispersion relation and with $\mathit{Bu}$ of order unity this is significantly more accurate than the power-series approximation of Thomas et al. (2017). Moreover, in the limit of high horizontal wavenumber $k\rightarrow \infty$, the wave frequency of YBJ+ asymptotes to twice the inertial frequency $2f$. This enables solution of YBJ+ with explicit time-stepping schemes using a time step determined by stable integration of oscillations with frequency $2f$. Other phase-averaged equations have dispersion relations with frequency increasing as $k^{2}$ (YBJ) or $k^{4}$ (Thomas et al. 2017): in these cases stable integration with an explicit scheme becomes impractical with increasing horizontal resolution. The YBJ+ equation is tested by comparing its numerical solutions with those of the Boussinesq and YBJ equations. In virtually all cases, YBJ+ is more accurate than YBJ. The error, however, does not go rapidly to zero as the Burger number characterizing the initial condition is reduced: advection and refraction by geostrophic eddies reduces in the initial length scale of NIWs so that $\mathit{Bu}$ increases with time. This increase, if unchecked, would destroy the approximation. We show, however, that dispersion limits the damage by confining most of the wave energy to low $\mathit{Bu}$. In other words, advection and refraction by geostrophic flows does not result in a strong transfer of initially near-inertial energy out of the near-inertial frequency band.