Baroclinic instability over topography : unstable at any wave number

Author Posting. © Sears Foundation for Marine Research, 2016. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 74 (2016): 1-19, doi:10.1357/002224016818377595.The instability of an inviscid, baroclinic vertically sheared current of uniform potential vorticity, flowing along a uniform topographic slope, becomes linearly unstable at all wave numbers if the flow is in the direction of propagation of topographic waves. The parameter region of instability in the plane of scaled topographic slope versus wave number then extends to arbitrarily large wave numbers at large slopes. The weakly nonlinear treatment of the problem reveals the existence of a nonlinear enhancement of the instability close to one of the two boundaries of this parametrically narrow unstable region. Because the domain of instability becomes exponentially narrow for large wave numbers, it is unclear how applicable the results of the asymptotic, weakly nonlinear theory are given that it must be limited to a region of small supercriticality. This question is pursued in that parameter domain through the use of a truncated model in which the approximations of weakly nonlinear theory are avoided. This more complex model demonstrates that the linearly most unstable wave in the narrow wedge in parameter space is nonlinearly stable and that the region of nonlinear destabilization is limited to a tiny region near one of the critical curves rendering both the linear and nonlinear growth essentially negligible

A note on interior pathways in the meridional overturning circulation

Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 48 (2018): 643-646, doi:10.1175/JPO-D-17-0240.1.A simple oceanic model is presented for source–sink flow on the β plane to discuss the pathways from source to sink when transport boundary layers have large enough Reynolds numbers to be inertial in their dynamics. A representation of the flow as a Fofonoff gyre, suggested by prior work on inertial boundary layers and eddy-driven circulations in two-dimensional turbulent flows, indicates that even when the source and sink are aligned along the same western boundary the flow must intrude deep into the interior before exiting at the sink. The existence of interior pathways for the flow is thus an intrinsic property of an inertial circulation and is not dependent on particular geographical basin geometry.2018-09-1

Symmetric instability of cross-stream varying currents

Author Posting. © Sears Foundation for Marine Research, 2014. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 72 (2014): 31-45, doi:10.1357/002224014812655206.The symmetric instability of a simple shear flow in which the velocity is a linear function of the vertical coordinate but which varies slowly in the cross-stream direction is studied using an asymptotic analytical method. Explicit analytical solutions are found for the evolution of the envelope of the developing linear instability. Although the problem with no lateral variation yields cell-like instabilities growing in place, the lateral variation of the shear produces time dependence and cross-stream propagation of the envelope and accompanying cells. A similar solution is derived for the case of laterally uniform shear in a current whose depth slowly varies exponentially in the cross-stream direction producing similar time dependence to the otherwise stationary cell pattern

Laminated Wave Turbulence: Generic Algorithms III

Model of laminated wave turbulence allows to study statistical and discrete layers of turbulence in the frame of the same model. Statistical layer is described by Zakharov-Kolmogorov energy spectra in the case of irrational enough dispersion function. Discrete layer is covered by some system(s) of Diophantine equations while their form is determined by wave dispersion function. This presents a very special computational challenge - to solve Diophantine equations in many variables, usually 6 to 8, in high degrees, say 16, in integers of order $10^{16}$ and more. Generic algorithms for solving this problem in the case of {\it irrational} dispersion function have been presented in our previous papers. In this paper we present a new generic algorithm for the case of {\it rational} dispersion functions. Special importance of this case is due to the fact that in wave systems with rational dispersion the statistical layer does not exist and the general energy transport is governed by the discrete layer alone.Comment: submitted to IJMP

An inertial model of the interaction of Ekman layers and planetary islands

Author Posting. © American Meteorological Society, 2013. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 43 (2013): 1398–1406, doi:10.1175/JPO-D-13-028.1.An adiabatic, inertial, and quasigeostrophic model is used to discuss the interaction of surface Ekman transport with an island. The theory extends the recent work of Spall and Pedlosky to include an analytical and nonlinear model for the interaction. The presence of an island that interrupts a uniform Ekman layer transport raises interesting questions about the resulting circulation. The consequential upwelling around the island can lead to a local intake of fluid from the geostrophic region beneath the Ekman layer or to a more complex flow around the island in which the fluid entering the Ekman layer on one portion of the island's perimeter is replaced by a flow along the island's boundary from a downwelling region located elsewhere on the island. This becomes especially pertinent when the flow is quasigeostrophic and adiabatic. The oncoming geostrophic flow that balances the offshore Ekman flux is largely diverted around the island, and the Ekman flux is fed by a transfer of fluid from the western to the eastern side of the island. As opposed to the linear, dissipative model described earlier, this transfer takes place even in the absence of a topographic skirt around the island. The principal effect of topography in the inertial model is to introduce an asymmetry between the circulation on the northern and southern sides of the island. The quasigeostrophic model allows a simple solution to the model problem with topography and yet the resulting three-dimensional circulation is surprisingly complex with streamlines connecting each side of the island.This research was supported in part by NSF Grant OCE Grant 0925061

Interaction of Ekman layers and islands

Author Posting. © American Meteorological Society, 2013. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 43 (2013): 1028–1041, doi:10.1175/JPO-D-12-0159.1.The circulation induced by the interaction of surface Ekman transport with an island is considered using both numerical models and linear theory. The basic response is similar to that found for the interaction of Ekman layers and an infinite boundary, namely downwelling (upwelling) in narrow boundary layers and deformation-scale baroclinic boundary layers with associated strong geostrophic flows. The presence of the island boundary, however, allows the pressure signal to propagate around the island so that the regions of upwelling and downwelling are dynamically connected. In the absence of stratification the island acts as an effective barrier to the Ekman transport. The presence of stratification supports baroclinic boundary currents that provide an advective pathway from one side of the island to the other. The resulting steady circulation is quite complex. Near the island, both geostrophic and ageostrophic velocity components are typically large. The density anomaly is maximum below the surface and, for positive wind stress, exhibits an anticyclonic phase rotation with depth (direction of Kelvin wave propagation) such that anomalously warm water can lie below regions of Ekman upwelling. The horizontal and vertical velocities exhibit similar phase changes with depth. The addition of a sloping bottom can act to shield the deep return flow from interacting with the island and providing mass transport into/out of the surface Ekman layer. In these cases, the required transport is provided by a pair of recirculation gyres that connect the narrow upwelling/downwelling boundary layers on the eastern and western sides of the island, thus directly connecting the Ekman transport across the island.This study was supported by the National Science Foundation under Grants OCE-0826656 and OCE-0959381 (MAS), and OCE-0925061 (JP).2013-11-0

Shelf–open ocean exchange forced by wind jets

Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 48 (2018): 163-174, doi:10.1175/JPO-D-17-0161.1.The general problem of exchange from a shallow shelf across sharp topography to the deep ocean forced by narrow, cross-shelf wind jets is studied using quasigeostrophic theory and an idealized primitive equation numerical model. Interest is motivated by katabatic winds that emanate from narrow fjords in southeast Greenland, although similar topographically constrained wind jets are found throughout the world’s oceans. Because there is no net vorticity input by the wind, the circulation is largely confined to the region near the forcing. Circulation over the shelf is limited by bottom friction for weakly stratified flows, but stratification allows for much stronger upper-layer flows that are regulated by weak coupling to the lower layer. Over the sloping topography, the topographic beta effect limits the deep flow, while, for sufficient stratification, the upper-layer flow can cross the topography to connect the shelf to the open ocean. This can be an effective transport mechanism even for short, strong wind events because damping of the upper-layer flow is weak. A variety of transients are generated for an abrupt onset of winds, including short topography Rossby waves, long topographic Rossby waves, and inertial waves. Using parameters representative of southeast Greenland, katabatic wind events will force an offshore transport of O(0.4) Sv (1 Sv ≡ 106 m3 s−1) that, when considered for 2 days, will result in an offshore flux of O(5 × 1010) m3.MAS was supported by the National Science Foundation under Grant OCE-1533170.2018-07-1

Ensemble inequivalence, bicritical points and azeotropy for generalized Fofonoff flows

We present a theoretical description for the equilibrium states of a large class of models of two-dimensional and geophysical flows, in arbitrary domains. We account for the existence of ensemble inequivalence and negative specific heat in those models, for the first time using explicit computations. We give exact theoretical computation of a criteria to determine phase transition location and type. Strikingly, this criteria does not depend on the model, but only on the domain geometry. We report the first example of bicritical points and second order azeotropy in the context of systems with long range interactions.Comment: 4 pages, submitted to Phys. Rev. Let

Rossby waves with continuous stratification and bottom friction

Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 48 (2018): 2209-2219, doi:10.1175/JPO-D-18-0070.1.Published observations of subinertial ocean current variability show that the vertical structure is often well described by a vertical mode that has a node of horizontal velocity at the bottom rather than the traditional node of vertical velocity. The theory of forced and free linear Rossby waves in a continuously stratified ocean with a sloping bottom and bottom friction is treated here to see if frictional effects can plausibly contribute to this phenomenon. For parameter values representative of the mesoscale, bottom dissipation by itself appears to be too weak to be an explanation, although caution is required because the present approach uses a linear model to address a nonlinear phenomenon. One novel outcome is the emergence of a short-wave, bottom-trapped, strongly damped mode that is present even with a flat bottom.Partial funding for this article is provided by the National Science Foundation Physical Oceanography section through Award OCE-1433953.2019-03-1

Reply to “Comments on ‘The interaction of an eastward-flowing current and an island : sub- and supercritical flow’”

Author Posting. © American Meteorological Society, 2016. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 46 (2016): 2267–2268, doi:10.1175/JPO-D-16-0057.1.The original article that was the subject of this comment/reply can be found at http://journals.ametsoc.org/doi/abs/10.1175/JPO-D-15-0061.1.2017-01-1