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Register a new userOn stratification, barotropic tides, and secular changes in surface tidal elevations: Two-layer analytical model
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In this study the influence of stratification on surface tidal elevations in a two-layer analytical model is examined. The model assumes linearized, non-rotating, shallow-water dynamics in one dimension with astronomical forcing and allows for arbitrary topography. Using a natural modal separation, both large scale (barotropic) and small scale (baroclinic) components of the surface tidal elevation are shown to be comparably affected by stratification. It is also shown that the topography and basin boundaries affect the sensitivity of the barotropic surface tide to stratification significantly. This paper, therefore, provides a framework to understand how the presence of stratification impacts barotropic as well as baroclinic tides, and how climatic perturbations to oceanic stratification contribute to secular variations in tides. Results from a realistic-domain global numerical two-layer tide model are briefly examined and found to be qualitatively consistent with the analytical model results.
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A theoretical framework is developed for understanding the transient growth and propagation characteristics of thermodynamically coupled, meridional mode-like structures in the tropics. The model consists of a Gill-Matsuno type steady atmosphere under the longwave approximation coupled via a wind-evaporation-sea surface temperature (WES) feedback to a slab ocean model. When projected onto basis functions for the atmosphere the system simplifies to a non-normal set of equations that describes the evolution of individual sea surface temperature (SST) modes, with clean separation between symmetric and anti-symmetric modes. The following major findings result from analysis of the system: (i) a transient growth process exists whereby specific SST modes propagate toward lower order modes at the expense of the higher-order modes; (ii) the same dynamical mechanisms govern the evolution of symmetric and anti-symmetric SST modes except for the lowest-order wave number, where for symmetric structures the atmospheric Kelvin wave plays a critically different role in enhancing decay; and (iii) the WES feedback is positive for all modes (with a maximum for the most equatorially confined antisymmetric structure) except for the most equatorially confined symmetric mode where the Kelvin wave generates a negative WES feedback. Taken together, these findings explain why equatorially anti-symmetric dipole-like structures may dominate thermodynamically coupled ocean / atmosphere variability in the tropics. The role of non-normality as well as the role of realistic mean states in meridional mode variability are discussed.
A framework is introduced to compare moist `potential temperatures. The equivalent potential temperature, $theta_e,$ the liquid water potential temperature, $theta_ell,$ and the entropy potential temperature, $theta_s$ are all shown to be potential temperatures in the sense that they measure the temperature moist-air, in some specified state, must have to have the same entropy as the air-parcel that they characterize. They only differ in the choice of reference state composition: $theta_ell$ describes the temperature a condensate-free state, $theta_e$ a vapor-free state, and $theta_s$ a water-free state would require to have the same entropy as the given state. Although in this sense $theta_e,$ $theta_ell,$ and $theta_s$ are all different flavors of the same thing, only $theta_ell$ satisfies the stricter definition of a `potential temperature, as corresponding to a reference temperature accessible by an isentropic and closed transformation of a system in equilibrium; only $theta_e$ approximately measures the ability of moist-air to do work; and only $theta_s$ measures air-parcel entropy. None mix linearly, but all do so approximately, and all reduce to the dry potential temperature, $theta$ in the limit as the water mass fraction goes to zero. As is well known, $theta$ does mix linearly and inherits all the favorable (entropic, enthalpic, and potential temperature) properties of its various -- but descriptively less rich -- moist counterparts. All, involve quite complex expressions, but admit relatively simple and useful approximations. Of the three moist `potential temperatures, $theta_s$ is the least familiar, but the most well mixed in the broader tropics, a property that merits further study as a basis for constraining mixing processes.
We explore the possibility to identify areas of intense patch formation from floating items due to systematic convergence of surface velocity fields by means of a visual comparison of Lagrangian Coherent Structures (LCS) and estimates of areas prone to patch formation using the concept of Finite-Time Compressibility (FTC, a generalisation of the notion of time series of divergence). The LCSs are evaluated using the Finite Time Lyapunov Exponent (FTLE) method. The test area is the Gulf of Finland (GoF) in the Baltic Sea. A basin-wide spatial average of backward FTLE is calculated for the GoF for the first time. This measure of the mixing strength displays a clear seasonal pattern. The evaluated backward FTLE features are linked with potential patch formation regions with high FTC levels. It is shown that areas hosting frequent upwelling or downwelling have consistently stronger than average mixing intensity. The combination of both methods, FTC and LCS, has the potential of being a powerful tool to identify the formation of patches of pollution at the sea surface.
Eddy saturation is the regime in which the total time-mean volume transport of an oceanic current is relatively insensitive to the wind stress forcing and is often invoked as a dynamical description of Southern Ocean circulation. We revisit the problem of eddy saturation using a primitive-equations model in an idealized channel setup with bathymetry. We apply only mechanical wind stress forcing; there is no diapycnal mixing or surface buoyancy forcing. Our main aim is to assess the relative importance of two mechanisms for producing eddy saturated states: (i) the commonly invoked baroclinic mechanism that involves the competition of sloping isopycnals and restratification by production of baroclinic eddies, and (ii) the barotropic mechanism, that involves production of eddies through lateral shear instabilities or through the interaction of the barotropic current with bathymetric features. Our results suggest that the barotropic flow-component plays a crucial role in determining the total volume transport.
Eddy saturation describes the nonlinear mechanism in geophysical flows whereby, when average conditions are considered, direct forcing of the zonal flow increases the eddy kinetic energy, while the energy associated with the zonal flow does not increase. Here we present a minimal baroclinic model that exhibits complete eddy saturation. Starting from Phillips classical quasi-geostrophic two-level model on the beta channel of the mid-latitudes, we derive a reduced order model comprising of six ordinary differential equations including parameterised eddies. This model features two physically realisable steady state solutions, one a purely zonal flow and one where, additionally, finite eddy motions are present. As the baroclinic forcing in the form of diabatic heating is increased, the zonal solution loses stability and the eddy solution becomes attracting. After this bifurcation, the zonal components of the solution are independent of the baroclinic forcing, and the excess of heat in the low latitudes is efficiently transported northwards by finite eddies, in the spirit of baroclinic adjustment.
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