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Linear and nonlinear stratified spindown over
Article · October 2010
DOI: 10.1575/1912/3635 · Source: OAI
Australian Institute of Marine Science
15 PUBLICATIONS 56 CITATIONS
Available from: Jessica Benthuysen Retrieved on: 18 October 2016 MIT/WHOI 2010-09 Massachusetts Institute of Technology Woods Hole Oceanographic Institution Joint Program in Oceanography/ Applied Ocean Science and Engineering
DOCTORAL DISSERTATIONLinear and Nonlinear Stratified Spindown over Sloping Topography by Jessica A. Benthuysen June 2010 MITIWHOI 2010-09 Linear and Nonlinear Stratified Spindown over Sloping Topography by Jessica A. Benthuysen Massachusetts Institute of Technology Cambridge, Massachusetts 02139 and Woods Hole Oceanographic Institution Woods Hole, Massachusetts 02543 June 2010
DOCTORAL DISSERTATIONFunding was provided by the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution Academic Programs Office.
Reproduction in whole or in part is permitted for any purpose of the United States Government. This thesis should be cited as: Jessica A. Benthuysen, 2010. Linear and Nonlinear Stratified Spindown over Sloping Topography. Ph.D. Thesis. MIT/WHOI, 2010-09.
Approved for publication; distribution unlimited.
Approved for Distribution:
Robert A. Weller, Chair Department of Physical Oceanography Edward A. Boyle James A. Yoder MIT Director ofJoint Program WHOI Dean of Graduate Studies Linear and Nonlinear Str
Abstract In a stratiﬁed rotating ﬂuid, frictionally driven circulations couple with the buoyancy ﬁeld over sloping topography. Analytical and numerical methods are used to quantify the impact of this coupling on the vertical circulation, spindown of geostrophic ﬂows, and the formation of a shelfbreak jet.
Over a stratiﬁed slope, linear spindown of a geostrophic along-isobath ﬂow induces cross-isobath Ekman ﬂows. Ekman advection of buoyancy weakens the vertical circulation and slows spindown. Upslope (downslope) Ekman ﬂows tend to inject (remove) potential vorticity into (from) the ocean. Momentum advection and nonlinear buoyancy advection are examined in setting asymmetries in the vertical circulation and the vertical relative vorticity ﬁeld. During nonlinear homogeneous spindown over a ﬂat bottom, momentum advection weakens Ekman pumping and strengthens Ekman suction, while cyclonic vorticity decays faster than anticyclonic vorticity. During nonlinear stratiﬁed spindown over a slope, nonlinear advection of buoyancy enhances the asymmetry in Ekman pumping and suction, whereas anticyclonic vorticity can decay faster than cyclonic vorticity outside of the boundary layers.
During the adjustment of a spatially uniform geostrophic current over a shelfbreak, coupling between the Ekman ﬂow and the buoyancy ﬁeld generates Ekman pumping near the shelfbreak, which leads to the formation of a jet. Scalings are presented for the upwelling strength, the length scale over which it occurs, and the timescale for jet formation. The results are applied to the Middle Atlantic Bight shelfbreak.
Thesis Supervisor: Steven J. Lentz Title: Senior Scientist Thesis Supervisor: Leif N. Thomas Title: Assistant Professor Acknowledgments I thank my advisors, Leif Thomas and Steve Lentz, for their scientiﬁc guidance and support. I greatly appreciate the respect that they have shown me throughout the past several years. They have allowed me the freedom to explore new ideas and have helped focus and shape these ideas into feasible projects. With patience, open doors, and constructive criticism, they have set true examples of how to do science as well as how to be a scientist.
I thank Raﬀaele Ferrari who always encouraged me to think about the big picture.
I thank Glen Gawarkiewicz for giving me the opportunity to participate in a cruise to the Middle Atlantic Bight shelfbreak front and the opportunity to learn about autonomous underwater vehicles. Finally, I thank Ken Brink for chairing my defense and helpful discussions ranging from writing to numerical modelling.
Thanks to the students who have helped me along this journey. To my oﬃcemates at MIT and WHOI: Shin Kida, Max Nikurashin, Claude Abiven, Christie Wood, Kjetil V˚ and Rebecca Dell. To my PO classmates for their support: Beatriz Pe˜aage, n Molino and Katie Silverthorne as well as Stephanie Waterman, Hristina Hristova, and Rachel Horwitz. Finally, thanks to Melanie Fewings, Greg Gerbi, and Carlos Moﬀatt for being good mentors who I can always count on for advice.
I thank my parents, Jim and Mei, and my sister, Jackie, for being supportive of all my endeavors. I also thank my undergraduate advisor, Bill Criminale, for introducing me to ﬂuid dynamics and boundary layer theory.
Funding for my research and education was provided by MIT EAPS, the WHOI Academic Programs Oﬃce and the MIT Presidential Fellowship. Financial assistance from the Houghton Fund is also acknowledged.
Chapter 1 Introduction Ocean bottom boundary layers are regions adjacent to topography where turbulence mixes heat, momentum and biogeochemical tracers. These regions serve as a dynamical control on the circulation by dissipating energy and shape the local characteristics of the marine environment by redistributing tracers. Tracers, such as sediment and nutrients, are transported by the lateral circulation near the bottom as well as the vertical circulation into and out of these layers. In order to quantify these momentum and tracer ﬂuxes, an understanding of the strength and structure of this circulation is needed.
Friction plays an important role in driving this lateral and vertical circulation.
The boundary exerts a frictional stress on the ﬂow that reduces the near bottom velocity within a frictional boundary layer, the Ekman layer. This frictional force induces an ageostrophic Ekman ﬂow down the pressure gradient through a subinertial balance between the frictional force, the Coriolis acceleration, and the horizontal pressure gradient. The vertically-integrated Ekman ﬂow, the Ekman transport, is directed to the right (left) of the frictional force in the Northern (Southern) Hemisphere. Convergences and divergences in the Ekman transport eject ﬂuid out of, Ekman pumping, or inject ﬂuid into, Ekman suction, the boundary layer. This process drives an ageostrophic secondary circulation that can accelerate or decelerate the geostrophic ﬂow in the interior.
Observational and theoretical studies have examined the role of cross-isobath Ekman advection of buoyancy in setting the structure of the ocean bottom boundary layer as well as the frictionally driven circulation. Over an insulated stratiﬁed sloping boundary, downslope (upslope) Ekman advection of buoyancy induces a positive (negative) buoyancy anomaly and tilts the isopycnals near the bottom. This isopycnal tilting leads to vertical shear in the geostrophic ﬂow, reducing the bottom stress and hence weakening the Ekman transport (MacCready and Rhines 1991, Trowbridge and Lentz 1991). An arrested Ekman layer occurs when this buoyancy anomaly is suﬃciently large to reduce the bottom stress to zero. This process, known as buoyancy shutdown of the Ekman transport, has important consequences for the interior ﬂow ﬁeld (MacCready and Rhines 1991). By weakening the Ekman transport, buoyancy shutdown also weakens Ekman pumping and suction. When the Ekman ﬂow is arrested, the interior geostrophic ﬂow can evolve unimpeded by frictional forces.
The purpose of this thesis is to examine how coupling between the frictionally driven ﬂow and the buoyancy ﬁeld over sloping topography modiﬁes the vertical circulation and the interior geostrophic ﬂow through feedback by secondary circulations.
Analytical and numerical techniques are used to address how this coupling impacts the temporal evolution and spatial characteristics of the ﬂow. The results of this analysis are applied to observations to determine the extent that cross-isobath Ekman advection of buoyancy can explain the structure of ﬂows over stratiﬁed sloping topography.
In the following sections, an overview of previous research is presented regarding the signiﬁcance of cross-isobath Ekman advection of buoyancy on the structure and dynamics of ﬂows along stratiﬁed boundaries. This overview addresses notable studies, with a primary focus on observations, that have shaped our current understanding of frictionally driven ﬂows over stratiﬁed sloping topography. Then, the goals of this dissertation are presented, with relation to open questions unanswered by previous research, followed by an outline of the thesis chapters.
1.1 Background and Motivation Previous research has identiﬁed cross-isobath Ekman advection of buoyancy as a potentially important mechanism inﬂuencing currents over stratiﬁed shelves and slopes.
Observational and theoretical studies have ranged from examining the one-dimensional bottom boundary layer dynamics to accounting for lateral variations in its structure.
These studies have considered diﬀerent aspects of this mechanism, which can be categorized into the following four questions.
How does cross-isobath Ekman advection of buoyancy:
• inﬂuence the height of the bottom boundary layer?
• impact mixing processes by shear or convective instability?
• couple with the lateral Ekman ﬂow and on what timescales?
• modify the vertical circulation and feedback into the geostrophic ﬂow by secondary circulations?
These questions have been examined in diﬀerent ﬂow regimes along stratiﬁed sloping topography. These regimes include coastal currents along continental shelves and the upper continental slopes oﬀ of the west and east coast of the United States as well as the more weakly stratiﬁed deep western boundary currents along the lower continental slope in the North and South Atlantic ocean. A particular region of interest is the frontal system along the Middle Atlantic Bight shelfbreak, where the gradually sloping continental shelf intersects the steeply sloping continental slope oﬀ of the east coast of the United States. Studies of these regions reveal where cross-isobath Ekman advection of buoyany may or may not be important to the subinertial dynamics over sloping topography.
The overview of past research is presented in three parts. The impact of crossisobath Ekman advection of buoyancy on the structure of bottom boundary layers over the continental shelves and slopes is presented in section 1.1.1. In section 1.1.2, observations of ﬂows near the Middle Atlantic Bight shelfbreak are presented as motivation for studying how these stratiﬁed bottom boundary layer processes over slopes feedback into the coastal currents. Finally, observations supporting or refuting the importance of cross-isobath Ekman advection of buoyancy on bottom boundary layers in deep western boundary currents is presented in section 1.1.3.
1.1.1 Bottom boundary layers over continental shelves and upper continental slopes Over continental shelves and upper continental slopes, characteristics in the near bottom ﬂow and tracer ﬁelds distinguish bottom boundary layers from the overlying ﬂow.
First, currents tend to veer counterclockwise downward, which is consistent with the direction of Ekman veering predicted by a balance between frictional forces and the Coriolis acceleration (e.g. Weatherly 1972, Wimbush and Munk 1970, Kundu 1976, Mercado and Van Leer 1976). Second, small scale measurements of temperature as well as velocity gradients can be used to distinguish the bottom boundary layer as a region with high levels of turbulent kinetic energy dissipation (e.g. Perlin et al.
2005, Moum et al. 2004). Third, temperature, salinity, and density tend to appear vertically well-mixed within a bottom mixed layer (e.g. Weatherly and Niiler 1974, Weatherly and Van Leer 1977, Pak and Zaneveld 1977). Observations indicate that the Ekman layer thickness, determined from Ekman veering, may (e.g. Mercado and Van Leer 1976) or may not (e.g. Perlin et al. 2005) equal the bottom mixed layer thickness.
Observational and numerical studies have shown that coupling between frictionally driven ﬂows and the density ﬁeld can impact the thickness of the frictional bottom boundary layer and the bottom mixed layer. Over a ﬂat bottom, Weatherly and Martin (1978) argued on dimensional grounds that stratiﬁcation reduces the bottom boundary layer height from the unstratiﬁed case. By including stratiﬁcation in the scaling for the frictional boundary layer height, they showed that the revised stratiﬁed scale height was qualitatively consistent with previous estimates of bottom boundary layer thickness over the West Florida continental shelf (Weatherly and Van Leer 1977). From examination of near bottom temperature proﬁles in the Florida current, Weatherly and Niiler (1974) suggested that horizontal advection of buoyancy over sloping topography was key in explaining the formation of bottom mixed layers.
Weatherly and Van Leer (1977) also suggested that patterns of warming (cooling) within the bottom boundary layer may be explained by frictionally driven downslope (upslope) ﬂows due to downwelling (upwelling) favorable along-shelf ﬂows.
Weatherly and Martin (1978) used a numerical model, with the Mellor-Yamada level 2 turbulence closure scheme, to examine how the frictional bottom boundary layer is modiﬁed by upslope or downslope Ekman advection of buoyancy. The thickness of the bottom boundary layer is speciﬁed by the height at which the turbulence vanishes away from the bottom. For upslope Ekman ﬂows, they showed that the bottom boundary layer height tended to remain constant and approximately equal to their stratiﬁed bottom boundary layer height scale. In contrast, for downslope Ekman ﬂows, their model showed a thickening of the bottom boundary layer beyond this scale estimate. Model results compared with Weatherly and Van Leer’s (1977) observations showed qualitative agreement in bottom boundary layer heights.