An official website of the United States government
Ocean fronts are an important submesoscale feature, yet frontogenesis theory often neglects turbulence – even parameterized turbulence – leaving theory lacking in comparison with observations and models. A perturbation analysis is used to include the effects of eddy viscosity and diffusivity as a first-order correction to existing strain-induced inviscid, adiabatic frontogenesis theory. A modified solution is obtained by using potential vorticity and surface conditions to quantify turbulent fluxes. It is found that horizontal viscosity and diffusivity tend to be readily frontolytic – reducing frontal tendency to negative values under weakly non-conservative perturbations and opposing or reversing front sharpening, whereas vertical viscosity and diffusivity tend to only weaken frontogenesis by slowing the rate of sharpening of the front even under strong perturbations. During late frontogenesis, vertical diffusivity enhances the rate of frontogenesis, although perturbation theory may be inaccurate at this stage. Surface quasi-geostrophic theory – neglecting all injected interior potential vorticity – is able to describe the first-order correction to the along-front velocity and ageostrophic overturning circulation in most cases. Furthermore, local conditions near the front maximum are sufficient to reconstruct the modified solution of both these fields.
more »
« less
Ageostrophic corrections for power spectra and wave–vortex decomposition
We present a method to incorporate weakly nonlinear ageostrophic corrections into a previously developed wave–vortex decomposition algorithm for one-dimensional data obtained along horizontal flight, ship or remote-sensing tracks in the atmosphere or ocean. A new statistical omega equation is derived that links the power spectra of a quasi-geostrophic stream function to the power spectra of the ageostrophic correction. This step assumes mutually independent Fourier components for the quasi-geostrophic stream function. Then this equation is used to estimate the ageostrophic correction from one-dimensional track data under the additional assumptions of horizontal isotropy and the dominance of a single vertical wavenumber scale. A robust and accurate numerical method is designed, tested successfully against synthetic data and then applied to atmospheric flight track data near the tropopause. This probes the robustness of the previous linear wave–vortex decomposition method under the ageostrophic corrections. Preliminary findings indicate that the lower stratospheric flight tracks are very robust whilst the upper tropospheric ones showed some sensitivity to the correction.
more »
« less
- Award ID(s):
- 1813891
- PAR ID:
- 10190870
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 882
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)The energetically independent linear wave and geostrophic (vortex) solutions are shown to be a complete basis for velocity and density variables $$(u,v,w,\rho )$$ in a rotating non-hydrostatic Boussinesq fluid with arbitrary stratification and non-periodic vertical boundaries. This work extends the familiar wave-vortex decomposition for triply periodic domains with constant stratification. As a consequence of the decomposition, the fluid can be unambiguously separated into decoupled linear wave and geostrophic components at each instant in time, without the need for temporal filtering. The fluid can then be diagnosed for temporal changes in wave and geostrophic coefficients at each unique wavenumber and mode, including those that inevitably occur due to nonlinear interactions. We demonstrate that this methodology can be used to determine which physical interactions cause the transfer of energy between modes by projecting the nonlinear equations of motion onto the wave-vortex basis. In the particular example given, we show that an eddy in geostrophic balance superimposed with inertial oscillations at the surface transfers energy from the inertial oscillations to internal gravity wave modes. This approach can be applied more generally to determine which mechanisms are involved in energy transfers between wave and vortices, including their respective scales. Finally, we show that the nonlinear equations of motion expressed in a wave-vortex basis are computationally efficient for certain problems. In cases where stratification profiles vary strongly with depth, this approach may be an attractive alternative to traditional spectral models for rotating Boussinesq flow.more » « less
-
null (Ed.)Abstract Large-eddy simulations are used to investigate the influence of a horizontal frontal zone, represented by a stationary uniform background horizontal temperature gradient, on the wind- and wave-driven ocean surface boundary layers. In a frontal zone, the temperature structure, the ageostrophic mean horizontal current, and the turbulence in the ocean surface boundary layer all change with the relative angle among the wind and the front. The net heating and cooling of the boundary layer could be explained by the depth-integrated horizontal advective buoyancy flux, called the Ekman Buoyancy Flux (or the Ekman-Stokes Buoyancy Flux if wave effects are included). However, the detailed temperature profiles are also modulated by the depth-dependent advective buoyancy flux and submesoscale eddies. The surface current is deflected less (more) to the right of the wind and wave when the depth-integrated advective buoyancy flux cools (warms) the ocean surface boundary layer. Horizontal mixing is greatly enhanced by submesoscale eddies. The eddy-induced horizontal mixing is anisotropic and is stronger to the right of the wind direction. Vertical turbulent mixing depends on the superposition of the geostrophic and ageostrophic current, the depth-dependent advective buoyancy flux, and submesoscale eddies.more » « less
-
We introduce an analytical model that describes the vertical structure of Ekman boundary layer flows coupled to the Monin-Obukhov Similarity Theory (MOST) surface layer repre- sentation, which is valid for conventionally neutral (CNBL) and stable (SBL) atmospheric conditions. The model is based on a self-similar profile of horizontal stress for both CNBL and SBL flows that merges the classic 3/2 power law profile with a MOST-consistent stress profile in the surface layer. The velocity profiles are then obtained from the Ekman momentum balance equation. The same stress model is used to derive a new self-consistent Geostrophic Drag Law (GDL). We determine the ABL height (h) using an equilibrium boundary layer height model and parameterize the surface heat flux for quasi-steady SBL flows as a function of a prescribed surface temperature cooling rate. The ABL height and GDL equations can then be solved together to obtain the friction velocity (u∗) and the cross-isobaric angle (α0) as a function of known input parameters such as the Geostrophic wind speed and surface roughness (z0). We show that the model predictions agree well with simulation data from the literature and newly generated Large Eddy Simulations (LES). These results indicate that the proposed model provides an efficient and relatively accurate self-consistent approach for predicting the mean wind velocity distribution in CNBL and SBL flows.more » « less
-
Abstract The “eddying” ocean, recognized for several decades, has been the focus of much observational and theoretical research. We here describe a generalization for the analysis of eddy energy, based on the use of ensembles, that addresses two key related issues: the definition of an “eddy” and the general computation of energy spectra. An ensemble identifies eddies as the unpredictable component of the flow, and permits the scale decomposition of their energy in inhomogeneous and non‐stationary settings. We present two distinct, but equally valid, spectral estimates: one is similar to classical Fourier spectra, the other reminiscent of classical empirical orthogonal function analysis. Both satisfy Parseval's equality and thus can be interpreted as length‐scale dependent energy decompositions. The issue of “tapering” or “windowing” of the data, used in traditional approaches, is also discussed. We apply the analyses to a mesoscale “resolving” (1/12°) ensemble of the separated North Atlantic Gulf Stream. Our results reveal highly anisotropic spectra in the Gulf Stream and zones of both agreement and disagreement with theoretically expected spectral shapes. In general, we find spectral slopes that fall off faster than the steepest slope expected from quasi‐geostrophic theory.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2019.815
