Coastal Baroclinic Two-Dimensional Turbulence. Part 1: Scaling

Coastal two-dimensional (2D) turbulence, driven by buoyant coastal currents and responsible for most cross-shelf eddy buoyancy transport, exhibits consistant spatial and temporal scalings that remain largely insensitive to variations in gentle-to-moderate slope, typical coastal drag coefficients, lateral density contrast and cross-shelf buoyancy flux in idealize experiments.This robustness arises because the strong bottom drag characteristic of coastal regions drives the system toward an equivalent-barotropic state.Using a novel "pseudo-current" numerical setup, we examine the equilibrium state of coastal 2D turbulence in an along-shelf periodic domain.The coastal ocean is found to be in a moderate-drag regime, leading the dynamics toward an equivalent-barotropic state (i.e., weak near-bottom flow), and the turbulent timescale approximates the Ekman timescale.Consequently, turbulent activity is concentrated near the surface like a twolayer model and interacts only with the upper-layer background potential vorticity (PV) gradient, which is determined by the mean isopycnal slope.Because the turbulence is regulated by the PV gradient and dissipated on the Ekman timescale, the inverse cascade remains weak, and the energy containing scale approximates the Rhines scale, scale, frictional scale, linearly most unstable wavelength, and deformation radius.Moreover, the mixing length is comparable to both the deformation radius and the product of turbulent velocity and the Ekman timescale.Scaling estimates from the pseudo-current simulations are consistent with results from more realistic buoyant outflow simulations.