Michael Spall - Profile on Academia.edu (original) (raw)
Papers by Michael Spall
Ocean Science, Mar 14, 2023
The Chukchi Slope Current is a westward-flowing current along the Chukchi slope, which carries Pa... more The Chukchi Slope Current is a westward-flowing current along the Chukchi slope, which carries Pacific-origin water from the Chukchi shelf into the Canada Basin and helps set the regional hydrographic structure and ecosystem. Using a set of experiments with an idealized primitive equation numerical model, we investigate the energetics of the slope current during the ice-covered period. Numerical calculations show that the growth of surface eddies is suppressed by the ice friction, while perturbations at mid-depths can grow into eddies, consistent with linear instability analysis. However, because the ice stress is spatially variable, it is able to drive Ekman pumping to decrease the available potential energy (APE) and kinetic energy of both the mean flow and mesoscale eddies over a vertical scale of 100 m, well outside the frictional Ekman layer. The rate at which the APE changes is determined by the vertical density flux, which is negative as the ice-induced Ekman pumping advects lighter (denser) water upward (downward). A scaling analysis shows that Ekman pumping will dominate the release of APE for large-scale flows, but the effect of baroclinic instability is also important when the horizontal scale of the mean flow is the baroclinic deformation radius and the eddy velocity is comparable to the mean flow velocity. Our numerical results highlight the importance of ice friction in the energetics of the slope current and eddies, and this may be relevant to other ice-covered regions.
Forward Problem in Numerical Models
Elsevier eBooks, 2019
Journal of Physical Oceanography, Oct 1, 2016
Downfront, or downwelling favorable, winds are commonly found over buoyant coastal plumes. It is ... more Downfront, or downwelling favorable, winds are commonly found over buoyant coastal plumes. It is known that these winds can result in mixing of the plume with the ambient water and that the winds influence the transport, spatial extent, and stability of the plumes. In the present study, the interaction of the Ekman velocity in the surface layer and baroclinic instability supported by the strong horizontal density gradient of the plume is explored with the objective of understanding the potential vorticity and buoyancy budgets. The approach makes use of an idealized numerical model and scaling theory. It is shown that when winds are present the weak stratification resulting from vertical mixing and the strong baroclinicity of the front results in near-zero average potential vorticity q. For weak to moderate winds, the reduction of q by diapycnal mixing is balanced by the generation of q through the geostrophic stress term in the regions of strong horizontal density gradients and stable stratification. However, for very strong winds the wind stress overwhelms the geostrophic stress and leads to a reduction in q, which is balanced by the vertical mixing term. In the absence of winds, the geostrophic stress dominates mixing and the flow rapidly restratifies. Nonlinearity, extremes of relative vorticity and vertical velocity, and mixing are all enhanced by the presence of a coast. Scaling estimates developed for the eddy buoyancy flux, the surface potential vorticity flux, and the diapycnal mixing rate compare well with results diagnosed from a series of numerical model calculations.
The influence of the large scale circulation on an eastern boundary current
AGUFM, Dec 1, 2010
ABSTRACT The wind-driven gyre circulation in the ocean interior varies across large temporal and ... more ABSTRACT The wind-driven gyre circulation in the ocean interior varies across large temporal and spatial scales, while the current along the eastern boundary is concentrated in a narrow jet with smaller temporal and spatial scales. These boundary currents are often hydrodynamically unstable and generate mesoscale and sub-mesoscale variability. In this study, we investigate the influence of the large scale circulation on an unstable eastern boundary current. One example is the influence of the Pacific subtropical gyre on the California current system. We study the problem using both a linear stability analysis and a nonlinear numerical model in a barotropic and quasi-geostrophic framework. The large scale circulation and the boundary current are specified in the linear analysis and are generated by an Ekman forcing in the numerical model. The linear stability analysis shows that to the lowest order the eastward (westward) flow of the large scale circulation stabilizes (destabilizes) the boundary current. Additionally, the meridional flow contributed by the large scale circulation accelerates or decelerates the originally parallel boundary current and modifies the stability of the current through the Doppler effect. Unstable perturbations which can be represented by normal modes for a parallel current then develop streamwise spatial structures. In the nonlinear numerical simulations, the streamwise nonuniformity of the boundary current influenced by the large scale circulation is clearly shown in the eddy kinetic energy. The location of the maximum eddy kinetic energy depends on the relative strength of the large scale circulation and the boundary current. The meridionally nonuniform eddy activities are important in offshore tracer transport. The nonlinear numerical simulation is forced by a wind curl field which generates a southward eastern boundary current and a large scale circulation with double gyres (white contours). The mean eddy kinetic energy of the boundary current (in color) exhibits a meridionally varying structure showing the influence of the large scale circulation on the boundary current stability.
Journal of Physical Oceanography, Jul 1, 2009
A conceptually simple model is presented for predicting the amplitude and periodicity of eddies g... more A conceptually simple model is presented for predicting the amplitude and periodicity of eddies generated by a steady poleward outflow in a 1½-layer b-plane formulation. The prediction model is rooted in linear quasigeostrophic dynamics but is capable of predicting the amplitude of the b plume generated by outflows in the nonlinear range. Oscillations in the plume amplitude are seen to represent a near-zero group velocity response to an adjustment process that can be traced back to linear dynamics. When the plume-amplitude oscillations become large enough so that the coherent b plume is replaced by a robust eddy field, the eddy amplitude is still constrained by the plume-amplitude prediction model. The eddy periodicity remains close to that of the predictable, near-zero group-velocity linear oscillations. Striking similarities between the patterns of variability in the model and observations south of Indonesia's Lombok Strait suggest that the processes investigated in this study may play an important role in the generation of the observed eddy field of the Indo-Australian Basin.
Journal of Physical Oceanography, Sep 1, 2017
The problem of localized dense water formation over a sloping bottom is considered for the genera... more The problem of localized dense water formation over a sloping bottom is considered for the general case in which the topography forms a closed contour. This class of problems is motivated by topography around islands or shallow shoals in which convection resulting from brine rejection or surface heat loss reaches the bottom. The focus of this study is on the large-scale circulation that is forced far from the region of surface forcing. The authors find that a cyclonic current is generated around the topography, in the opposite sense to the propagation of the dense water plume. In physical terms, this current results from the propagation of low sea surface height from the region of dense water formation anticyclonically along the topographic contours back to the formation region. This pressure gradient is then balanced by a cyclonic geostrophic flow. This basic structure is well predicted by a linear quasigeostrophic theory, a primitive equation model, and in rotating tank experiments. For sufficiently strong forcing, the anticyclonic circulation of the dense plume meets this cyclonic circulation to produce a sharp front and offshore advection of dense water at the bottom and buoyant water at the surface. This nonlinear limit is demonstrated in both the primitive equation model and in the tank experiments.
Journal of Physical Oceanography, Jul 1, 2015
Influences of time-dependent precipitation on water mass transformation and heat budgets in an id... more Influences of time-dependent precipitation on water mass transformation and heat budgets in an idealized marginal sea are examined using theoretical and numerical models. The equations proposed by Spall in 2012 are extended to cases with time-dependent precipitation whose form is either a step function or a sinusoidal function. The theory predicts the differences in temperature and salinity between the convective water and the boundary current as well as the magnitudes of heat fluxes into the marginal sea and across the sea surface. Moreover, the theory reveals that there are three inherent time scales: relaxation time scales for temperature and salinity and a precipitation time scale. The relaxation time scales are determined by a steady solution of the theoretical model with steady precipitation. The relaxation time scale for temperature is always smaller than that for salinity as a result of not only the difference in the form of fluxes at the surface but also the variation in the eddy transport from the boundary current. These three time scales and the precipitation amplitude determine the strength of the ocean response to changes in precipitation and the phase relation between precipitation, changes in salinity and temperature, and changes in heat fluxes. It is demonstrated that the theoretical predictions agree qualitatively well with results from the eddy-resolving numerical model. This demonstrates the fundamental role of mesoscale eddies in the ocean response to time-dependent forcing and provides a framework with which to assess the extent to which observed variability in marginal sea convection and water mass transformation are consistent with an external forcing by variations in precipitation.
Journal of Physical Oceanography, May 1, 2013
The circulation induced by the interaction of surface Ekman transport with an island is considere... more 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.
Journal of Physical Oceanography, Dec 1, 2008
A theory for the exchange between a rotating, buoyancy-forced marginal sea and an ocean is develo... more A theory for the exchange between a rotating, buoyancy-forced marginal sea and an ocean is developed and tested numerically. Cooling over the marginal sea leads to sinking and sets up a two-layer exchange flow, with a warm surface layer entering from the ocean and a cool layer exiting at depth. The connecting strait is sufficiently narrow and shallow to cause the exchange flow to be hydraulically controlled. The incoming surface layer forms a baroclinically unstable boundary current that circles the marginal sea in a cyclonic sense and feeds heat to the interior by way of eddies. Consistent with the overall heat and volume balances for the marginal sea, there is a continuous family of hydraulically controlled states with critical flow at the most constricted section of the strait. Included in this family is a limiting "maximal-exchange" solution with two sections of hydraulic control in the strait and with fixed layer depths at the most constricted section. The state of exchange for a given forcing is predicted using a theory that assumes energy conservation over a certain path connecting the strait to the marginal sea or, in some cases, the ocean. Depending on the configuration of the exchange, long-wave information may be blocked from entering the strait from the marginal sea, from the open ocean, or both. The scenario that holds determines what is predicted and what needs to be input. Numerical tests of the prediction for the temperature difference and the state of exchange are carried out for straits with a pure contraction in width and for a constant width strait with a topographic sill. The comparison is reasonable in most cases, though the numerical model is not able to reproduce cases of multiple states predicted by the theory for certain forcing values. The analytical model is an alternative to the Price and Yang and Siddall et al. models of a marginal sea outflow.
Journal of Physical Oceanography, Apr 1, 2017
Mesoscale eddies shape the Beaufort Gyre response to Ekman pumping, but their transient dynamics ... more Mesoscale eddies shape the Beaufort Gyre response to Ekman pumping, but their transient dynamics are poorly understood. Climate models commonly use the Gent-McWilliams (GM) parameterization, taking the eddy streamfunction c* to be proportional to an isopycnal slope s and an eddy diffusivity K. This local-in-time parameterization leads to exponential equilibration of currents. Here, an idealized, eddy-resolving Beaufort Gyre model is used to demonstrate that c* carries a finite memory of past ocean states, violating a key GM assumption. As a consequence, an equilibrating gyre follows a spiral sink trajectory implying the existence of a damped mode of variability-the eddy memory (EM) mode. The EM mode manifests during the spinup as a 15% overshoot in isopycnal slope (2000 km 3 freshwater content overshoot) and cannot be explained by the GM parameterization. An improved parameterization is developed, such that c* is proportional to an effective isopycnal slope s*, carrying a finite memory g of past slopes. Introducing eddy memory explains the model results and brings to light an oscillation with a period 2p ffiffiffiffiffiffiffiffiffi T E g p ' 50 yr, where the eddy diffusion time scale T E ; 10 yr and g ' 6 yr are diagnosed from the eddy-resolving model. The EM mode increases the Ekman-driven gyre variance by g/T E ' 50% 6 15%, a fraction that stays relatively constant despite both time scales decreasing with increased mean forcing. This study suggests that the EM mode is a general property of rotating turbulent flows and highlights the need for better observational constraints on transient eddy field characteristics.
Journal of Physical Oceanography, Aug 1, 2001
A simple, nonlinear, two-layer, planetary geostrophic model of the large-scale circulation forced... more A simple, nonlinear, two-layer, planetary geostrophic model of the large-scale circulation forced by localized mixing over a sloping bottom is discussed. The model is forced by parameterized diapycnal mixing at the density interface and/or by a mass flux downward into (unresolved) deep topographic canyons. Two nondimensional parameters are identified: the ratio of the change in Coriolis parameter over the horizontal mixing length scale to the nominal Coriolis parameter and the ratio of the advective speed to the Rossby wave phase speed. The former controls the strength of horizontal recirculation gyres that are forced by spatially variable diapycnal mixing, while the latter is a measure of the importance of nonlinearity in the density equation. When bottom topography is introduced, bottom pressure torque becomes important and the traditional strong horizontal recirculation gyre found for mixing over a flat bottom (beta plume) is gradually replaced by a zonal flow into or out of the mixing region in the deep ocean. Bottom topography becomes important, and the zonal flow emerges when the topographic Rossby wave speed exceeds the baroclinic planetary Rossby wave speed. Nonlinear effects are shown to enhance the upper-layer recirculation for upwelling and to retard the upper-layer circulation for downwelling. The model is finally configured to represent a region of mixing over the western flank of the Mid-Atlantic Ridge in the deep Brazil Basin. The model upper-layer flow is toward the southwest and the deep flow is very weak, zonal, and toward the east, in reasonable agreement with recent observational and inverse model estimates. The bottom pressure torque is shown to be crucial for maintaining this weak, zonal deep flow in the presence of strong turbulent mixing.
Journal of Physical Oceanography, Apr 1, 2007
The impact of the observed relationship between sea surface temperature and surface wind stress o... more The impact of the observed relationship between sea surface temperature and surface wind stress on baroclinic instability in the ocean is explored using linear theory and a nonlinear model. A simple parameterization of the influence of sea surface temperature on wind stress is used to derive a surface boundary condition for the vertical velocity at the base of the oceanic Ekman layer. This boundary condition is applied to the classic linear, quasigeostrophic stability problem for a uniformly sheared flow originally studied by Eady in the 1940s. The results demonstrate that for a wind directed from warm water toward cold water, the coupling acts to enhance the growth rate, and increase the wavelength, of the most unstable wave. Winds in the opposite sense reduce the growth rate and decrease the wavelength of the most unstable wave. For representative coupling strengths, the change in growth rate can be as large as ϮO(50%). This effect is largest for shallow, strongly stratified, low-latitude flows.
Geophysical Research Letters, Jan 6, 2016
Recently, the Beaufort Gyre has accumulated over 20,000 km 3 of freshwater in response to strong ... more Recently, the Beaufort Gyre has accumulated over 20,000 km 3 of freshwater in response to strong anticyclonic atmospheric winds that have prevailed over the gyre for almost two decades. Here we explore key physical processes affecting the accumulation and release of freshwater within an idealized eddy-resolving model of the Beaufort Gyre. We demonstrate that a realistic halocline can be achieved when its deepening tendency due to Ekman pumping is counteracted by the cumulative action of mesoscale eddies. Based on this balance, we derive analytical scalings for the depth of the halocline and its spin-up time scale and emphasize their explicit dependence on eddy dynamics. Our study further suggests that the Beaufort Gyre is currently in a state of high sensitivity to atmospheric winds. However, an intensification of surface stress would inevitably lead to a saturation of the freshwater content-a constraint inherently set by the intricacies of the mesoscale eddy dynamics.
The Chukchi Slope Current is a westward-flowing current along the Chukchi slope, which carries Pa... more The Chukchi Slope Current is a westward-flowing current along the Chukchi slope, which carries Pacific-origin water from the Chukchi shelf into the Canada Basin and helps set the regional hydrographic structure and ecosystem. Using a set of experiments with an idealized primitive equation numerical model, we investigate the energetics of the slope current during the ice-covered period. Numerical calculations show that the growth of surface eddies is suppressed by the ice friction, while perturbations at mid-depths can grow into eddies, consistent with linear instability analysis. However, because the ice stress is spatially variable, it is able to drive Ekman pumping to decrease the available potential energy (APE) and kinetic energy of both the mean flow and mesoscale eddies over a vertical scale of 100 m, well outside the frictional Ekman layer. The rate at which the APE changes is determined by the vertical density flux, which is negative as the ice-induced Ekman pumping advects lighter (denser) water upward (downward). A scaling analysis shows that Ekman pumping will dominate the release of APE for large-scale flows, but the effect of baroclinic instability is also important when the horizontal scale of the mean flow is the baroclinic deformation radius and the eddy velocity is comparable to the mean flow velocity. Our numerical results highlight the importance of ice friction in the energetics of the slope current and eddies, and this may be relevant to other ice-covered regions.
A Three-Dimensional Inertial Model for Coastal Upwelling along Western Boundaries
Journal of Physical Oceanography, Oct 1, 2022
A three-dimensional inertial model that conserves quasigeostrophic potential vorticity is propose... more A three-dimensional inertial model that conserves quasigeostrophic potential vorticity is proposed for wind-driven coastal upwelling along western boundaries. The dominant response to upwelling favorable winds is a surface-intensified baroclinic meridional boundary current with a subsurface countercurrent. The width of the current is not the baroclinic deformation radius but instead scales with the inertial boundary layer thickness while the depth scales as the ratio of the inertial boundary layer thickness to the baroclinic deformation radius. Thus, the boundary current scales depend on the stratification, wind stress, Coriolis parameter, and its meridional variation. In contrast to two-dimensional wind-driven coastal upwelling, the source waters that feed the Ekman upwelling are provided over the depth scale of this baroclinic current through a combination of onshore barotropic flow and from alongshore in the narrow boundary current. Topography forces an additional current whose characteristics depend on the topographic slope and width. For topography wider than the inertial boundary layer thickness the current is bottom intensified, while for narrow topography the current is wave-like in the vertical and trapped over the topography within the inertial boundary layer. An idealized primitive equation numerical model produces a similar baroclinic boundary current whose vertical length scale agrees with the theoretical scaling for both upwelling and downwelling favorable winds.
Radiating Instability
Cambridge University Press eBooks, Feb 28, 2019
Wind-Driven Freshwater Buildup in the Beaufort Gyre is Inevitably Constrained by Mesoscale Eddies
2015 AGU Fall Meeting, Dec 16, 2015
Forward Problem in Numerical Models
Elsevier eBooks, 2001
Wind-driven variations in an overturning circulation
EGU General Assembly Conference Abstracts, Apr 1, 2017
On the sea-ice cover of the Nordic Seas in an idealized MITgcm-setup
EGU General Assembly Conference Abstracts, Apr 1, 2016
Ocean Science, Mar 14, 2023
The Chukchi Slope Current is a westward-flowing current along the Chukchi slope, which carries Pa... more The Chukchi Slope Current is a westward-flowing current along the Chukchi slope, which carries Pacific-origin water from the Chukchi shelf into the Canada Basin and helps set the regional hydrographic structure and ecosystem. Using a set of experiments with an idealized primitive equation numerical model, we investigate the energetics of the slope current during the ice-covered period. Numerical calculations show that the growth of surface eddies is suppressed by the ice friction, while perturbations at mid-depths can grow into eddies, consistent with linear instability analysis. However, because the ice stress is spatially variable, it is able to drive Ekman pumping to decrease the available potential energy (APE) and kinetic energy of both the mean flow and mesoscale eddies over a vertical scale of 100 m, well outside the frictional Ekman layer. The rate at which the APE changes is determined by the vertical density flux, which is negative as the ice-induced Ekman pumping advects lighter (denser) water upward (downward). A scaling analysis shows that Ekman pumping will dominate the release of APE for large-scale flows, but the effect of baroclinic instability is also important when the horizontal scale of the mean flow is the baroclinic deformation radius and the eddy velocity is comparable to the mean flow velocity. Our numerical results highlight the importance of ice friction in the energetics of the slope current and eddies, and this may be relevant to other ice-covered regions.
Forward Problem in Numerical Models
Elsevier eBooks, 2019
Journal of Physical Oceanography, Oct 1, 2016
Downfront, or downwelling favorable, winds are commonly found over buoyant coastal plumes. It is ... more Downfront, or downwelling favorable, winds are commonly found over buoyant coastal plumes. It is known that these winds can result in mixing of the plume with the ambient water and that the winds influence the transport, spatial extent, and stability of the plumes. In the present study, the interaction of the Ekman velocity in the surface layer and baroclinic instability supported by the strong horizontal density gradient of the plume is explored with the objective of understanding the potential vorticity and buoyancy budgets. The approach makes use of an idealized numerical model and scaling theory. It is shown that when winds are present the weak stratification resulting from vertical mixing and the strong baroclinicity of the front results in near-zero average potential vorticity q. For weak to moderate winds, the reduction of q by diapycnal mixing is balanced by the generation of q through the geostrophic stress term in the regions of strong horizontal density gradients and stable stratification. However, for very strong winds the wind stress overwhelms the geostrophic stress and leads to a reduction in q, which is balanced by the vertical mixing term. In the absence of winds, the geostrophic stress dominates mixing and the flow rapidly restratifies. Nonlinearity, extremes of relative vorticity and vertical velocity, and mixing are all enhanced by the presence of a coast. Scaling estimates developed for the eddy buoyancy flux, the surface potential vorticity flux, and the diapycnal mixing rate compare well with results diagnosed from a series of numerical model calculations.
The influence of the large scale circulation on an eastern boundary current
AGUFM, Dec 1, 2010
ABSTRACT The wind-driven gyre circulation in the ocean interior varies across large temporal and ... more ABSTRACT The wind-driven gyre circulation in the ocean interior varies across large temporal and spatial scales, while the current along the eastern boundary is concentrated in a narrow jet with smaller temporal and spatial scales. These boundary currents are often hydrodynamically unstable and generate mesoscale and sub-mesoscale variability. In this study, we investigate the influence of the large scale circulation on an unstable eastern boundary current. One example is the influence of the Pacific subtropical gyre on the California current system. We study the problem using both a linear stability analysis and a nonlinear numerical model in a barotropic and quasi-geostrophic framework. The large scale circulation and the boundary current are specified in the linear analysis and are generated by an Ekman forcing in the numerical model. The linear stability analysis shows that to the lowest order the eastward (westward) flow of the large scale circulation stabilizes (destabilizes) the boundary current. Additionally, the meridional flow contributed by the large scale circulation accelerates or decelerates the originally parallel boundary current and modifies the stability of the current through the Doppler effect. Unstable perturbations which can be represented by normal modes for a parallel current then develop streamwise spatial structures. In the nonlinear numerical simulations, the streamwise nonuniformity of the boundary current influenced by the large scale circulation is clearly shown in the eddy kinetic energy. The location of the maximum eddy kinetic energy depends on the relative strength of the large scale circulation and the boundary current. The meridionally nonuniform eddy activities are important in offshore tracer transport. The nonlinear numerical simulation is forced by a wind curl field which generates a southward eastern boundary current and a large scale circulation with double gyres (white contours). The mean eddy kinetic energy of the boundary current (in color) exhibits a meridionally varying structure showing the influence of the large scale circulation on the boundary current stability.
Journal of Physical Oceanography, Jul 1, 2009
A conceptually simple model is presented for predicting the amplitude and periodicity of eddies g... more A conceptually simple model is presented for predicting the amplitude and periodicity of eddies generated by a steady poleward outflow in a 1½-layer b-plane formulation. The prediction model is rooted in linear quasigeostrophic dynamics but is capable of predicting the amplitude of the b plume generated by outflows in the nonlinear range. Oscillations in the plume amplitude are seen to represent a near-zero group velocity response to an adjustment process that can be traced back to linear dynamics. When the plume-amplitude oscillations become large enough so that the coherent b plume is replaced by a robust eddy field, the eddy amplitude is still constrained by the plume-amplitude prediction model. The eddy periodicity remains close to that of the predictable, near-zero group-velocity linear oscillations. Striking similarities between the patterns of variability in the model and observations south of Indonesia's Lombok Strait suggest that the processes investigated in this study may play an important role in the generation of the observed eddy field of the Indo-Australian Basin.
Journal of Physical Oceanography, Sep 1, 2017
The problem of localized dense water formation over a sloping bottom is considered for the genera... more The problem of localized dense water formation over a sloping bottom is considered for the general case in which the topography forms a closed contour. This class of problems is motivated by topography around islands or shallow shoals in which convection resulting from brine rejection or surface heat loss reaches the bottom. The focus of this study is on the large-scale circulation that is forced far from the region of surface forcing. The authors find that a cyclonic current is generated around the topography, in the opposite sense to the propagation of the dense water plume. In physical terms, this current results from the propagation of low sea surface height from the region of dense water formation anticyclonically along the topographic contours back to the formation region. This pressure gradient is then balanced by a cyclonic geostrophic flow. This basic structure is well predicted by a linear quasigeostrophic theory, a primitive equation model, and in rotating tank experiments. For sufficiently strong forcing, the anticyclonic circulation of the dense plume meets this cyclonic circulation to produce a sharp front and offshore advection of dense water at the bottom and buoyant water at the surface. This nonlinear limit is demonstrated in both the primitive equation model and in the tank experiments.
Journal of Physical Oceanography, Jul 1, 2015
Influences of time-dependent precipitation on water mass transformation and heat budgets in an id... more Influences of time-dependent precipitation on water mass transformation and heat budgets in an idealized marginal sea are examined using theoretical and numerical models. The equations proposed by Spall in 2012 are extended to cases with time-dependent precipitation whose form is either a step function or a sinusoidal function. The theory predicts the differences in temperature and salinity between the convective water and the boundary current as well as the magnitudes of heat fluxes into the marginal sea and across the sea surface. Moreover, the theory reveals that there are three inherent time scales: relaxation time scales for temperature and salinity and a precipitation time scale. The relaxation time scales are determined by a steady solution of the theoretical model with steady precipitation. The relaxation time scale for temperature is always smaller than that for salinity as a result of not only the difference in the form of fluxes at the surface but also the variation in the eddy transport from the boundary current. These three time scales and the precipitation amplitude determine the strength of the ocean response to changes in precipitation and the phase relation between precipitation, changes in salinity and temperature, and changes in heat fluxes. It is demonstrated that the theoretical predictions agree qualitatively well with results from the eddy-resolving numerical model. This demonstrates the fundamental role of mesoscale eddies in the ocean response to time-dependent forcing and provides a framework with which to assess the extent to which observed variability in marginal sea convection and water mass transformation are consistent with an external forcing by variations in precipitation.
Journal of Physical Oceanography, May 1, 2013
The circulation induced by the interaction of surface Ekman transport with an island is considere... more 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.
Journal of Physical Oceanography, Dec 1, 2008
A theory for the exchange between a rotating, buoyancy-forced marginal sea and an ocean is develo... more A theory for the exchange between a rotating, buoyancy-forced marginal sea and an ocean is developed and tested numerically. Cooling over the marginal sea leads to sinking and sets up a two-layer exchange flow, with a warm surface layer entering from the ocean and a cool layer exiting at depth. The connecting strait is sufficiently narrow and shallow to cause the exchange flow to be hydraulically controlled. The incoming surface layer forms a baroclinically unstable boundary current that circles the marginal sea in a cyclonic sense and feeds heat to the interior by way of eddies. Consistent with the overall heat and volume balances for the marginal sea, there is a continuous family of hydraulically controlled states with critical flow at the most constricted section of the strait. Included in this family is a limiting "maximal-exchange" solution with two sections of hydraulic control in the strait and with fixed layer depths at the most constricted section. The state of exchange for a given forcing is predicted using a theory that assumes energy conservation over a certain path connecting the strait to the marginal sea or, in some cases, the ocean. Depending on the configuration of the exchange, long-wave information may be blocked from entering the strait from the marginal sea, from the open ocean, or both. The scenario that holds determines what is predicted and what needs to be input. Numerical tests of the prediction for the temperature difference and the state of exchange are carried out for straits with a pure contraction in width and for a constant width strait with a topographic sill. The comparison is reasonable in most cases, though the numerical model is not able to reproduce cases of multiple states predicted by the theory for certain forcing values. The analytical model is an alternative to the Price and Yang and Siddall et al. models of a marginal sea outflow.
Journal of Physical Oceanography, Apr 1, 2017
Mesoscale eddies shape the Beaufort Gyre response to Ekman pumping, but their transient dynamics ... more Mesoscale eddies shape the Beaufort Gyre response to Ekman pumping, but their transient dynamics are poorly understood. Climate models commonly use the Gent-McWilliams (GM) parameterization, taking the eddy streamfunction c* to be proportional to an isopycnal slope s and an eddy diffusivity K. This local-in-time parameterization leads to exponential equilibration of currents. Here, an idealized, eddy-resolving Beaufort Gyre model is used to demonstrate that c* carries a finite memory of past ocean states, violating a key GM assumption. As a consequence, an equilibrating gyre follows a spiral sink trajectory implying the existence of a damped mode of variability-the eddy memory (EM) mode. The EM mode manifests during the spinup as a 15% overshoot in isopycnal slope (2000 km 3 freshwater content overshoot) and cannot be explained by the GM parameterization. An improved parameterization is developed, such that c* is proportional to an effective isopycnal slope s*, carrying a finite memory g of past slopes. Introducing eddy memory explains the model results and brings to light an oscillation with a period 2p ffiffiffiffiffiffiffiffiffi T E g p ' 50 yr, where the eddy diffusion time scale T E ; 10 yr and g ' 6 yr are diagnosed from the eddy-resolving model. The EM mode increases the Ekman-driven gyre variance by g/T E ' 50% 6 15%, a fraction that stays relatively constant despite both time scales decreasing with increased mean forcing. This study suggests that the EM mode is a general property of rotating turbulent flows and highlights the need for better observational constraints on transient eddy field characteristics.
Journal of Physical Oceanography, Aug 1, 2001
A simple, nonlinear, two-layer, planetary geostrophic model of the large-scale circulation forced... more A simple, nonlinear, two-layer, planetary geostrophic model of the large-scale circulation forced by localized mixing over a sloping bottom is discussed. The model is forced by parameterized diapycnal mixing at the density interface and/or by a mass flux downward into (unresolved) deep topographic canyons. Two nondimensional parameters are identified: the ratio of the change in Coriolis parameter over the horizontal mixing length scale to the nominal Coriolis parameter and the ratio of the advective speed to the Rossby wave phase speed. The former controls the strength of horizontal recirculation gyres that are forced by spatially variable diapycnal mixing, while the latter is a measure of the importance of nonlinearity in the density equation. When bottom topography is introduced, bottom pressure torque becomes important and the traditional strong horizontal recirculation gyre found for mixing over a flat bottom (beta plume) is gradually replaced by a zonal flow into or out of the mixing region in the deep ocean. Bottom topography becomes important, and the zonal flow emerges when the topographic Rossby wave speed exceeds the baroclinic planetary Rossby wave speed. Nonlinear effects are shown to enhance the upper-layer recirculation for upwelling and to retard the upper-layer circulation for downwelling. The model is finally configured to represent a region of mixing over the western flank of the Mid-Atlantic Ridge in the deep Brazil Basin. The model upper-layer flow is toward the southwest and the deep flow is very weak, zonal, and toward the east, in reasonable agreement with recent observational and inverse model estimates. The bottom pressure torque is shown to be crucial for maintaining this weak, zonal deep flow in the presence of strong turbulent mixing.
Journal of Physical Oceanography, Apr 1, 2007
The impact of the observed relationship between sea surface temperature and surface wind stress o... more The impact of the observed relationship between sea surface temperature and surface wind stress on baroclinic instability in the ocean is explored using linear theory and a nonlinear model. A simple parameterization of the influence of sea surface temperature on wind stress is used to derive a surface boundary condition for the vertical velocity at the base of the oceanic Ekman layer. This boundary condition is applied to the classic linear, quasigeostrophic stability problem for a uniformly sheared flow originally studied by Eady in the 1940s. The results demonstrate that for a wind directed from warm water toward cold water, the coupling acts to enhance the growth rate, and increase the wavelength, of the most unstable wave. Winds in the opposite sense reduce the growth rate and decrease the wavelength of the most unstable wave. For representative coupling strengths, the change in growth rate can be as large as ϮO(50%). This effect is largest for shallow, strongly stratified, low-latitude flows.
Geophysical Research Letters, Jan 6, 2016
Recently, the Beaufort Gyre has accumulated over 20,000 km 3 of freshwater in response to strong ... more Recently, the Beaufort Gyre has accumulated over 20,000 km 3 of freshwater in response to strong anticyclonic atmospheric winds that have prevailed over the gyre for almost two decades. Here we explore key physical processes affecting the accumulation and release of freshwater within an idealized eddy-resolving model of the Beaufort Gyre. We demonstrate that a realistic halocline can be achieved when its deepening tendency due to Ekman pumping is counteracted by the cumulative action of mesoscale eddies. Based on this balance, we derive analytical scalings for the depth of the halocline and its spin-up time scale and emphasize their explicit dependence on eddy dynamics. Our study further suggests that the Beaufort Gyre is currently in a state of high sensitivity to atmospheric winds. However, an intensification of surface stress would inevitably lead to a saturation of the freshwater content-a constraint inherently set by the intricacies of the mesoscale eddy dynamics.
The Chukchi Slope Current is a westward-flowing current along the Chukchi slope, which carries Pa... more The Chukchi Slope Current is a westward-flowing current along the Chukchi slope, which carries Pacific-origin water from the Chukchi shelf into the Canada Basin and helps set the regional hydrographic structure and ecosystem. Using a set of experiments with an idealized primitive equation numerical model, we investigate the energetics of the slope current during the ice-covered period. Numerical calculations show that the growth of surface eddies is suppressed by the ice friction, while perturbations at mid-depths can grow into eddies, consistent with linear instability analysis. However, because the ice stress is spatially variable, it is able to drive Ekman pumping to decrease the available potential energy (APE) and kinetic energy of both the mean flow and mesoscale eddies over a vertical scale of 100 m, well outside the frictional Ekman layer. The rate at which the APE changes is determined by the vertical density flux, which is negative as the ice-induced Ekman pumping advects lighter (denser) water upward (downward). A scaling analysis shows that Ekman pumping will dominate the release of APE for large-scale flows, but the effect of baroclinic instability is also important when the horizontal scale of the mean flow is the baroclinic deformation radius and the eddy velocity is comparable to the mean flow velocity. Our numerical results highlight the importance of ice friction in the energetics of the slope current and eddies, and this may be relevant to other ice-covered regions.
A Three-Dimensional Inertial Model for Coastal Upwelling along Western Boundaries
Journal of Physical Oceanography, Oct 1, 2022
A three-dimensional inertial model that conserves quasigeostrophic potential vorticity is propose... more A three-dimensional inertial model that conserves quasigeostrophic potential vorticity is proposed for wind-driven coastal upwelling along western boundaries. The dominant response to upwelling favorable winds is a surface-intensified baroclinic meridional boundary current with a subsurface countercurrent. The width of the current is not the baroclinic deformation radius but instead scales with the inertial boundary layer thickness while the depth scales as the ratio of the inertial boundary layer thickness to the baroclinic deformation radius. Thus, the boundary current scales depend on the stratification, wind stress, Coriolis parameter, and its meridional variation. In contrast to two-dimensional wind-driven coastal upwelling, the source waters that feed the Ekman upwelling are provided over the depth scale of this baroclinic current through a combination of onshore barotropic flow and from alongshore in the narrow boundary current. Topography forces an additional current whose characteristics depend on the topographic slope and width. For topography wider than the inertial boundary layer thickness the current is bottom intensified, while for narrow topography the current is wave-like in the vertical and trapped over the topography within the inertial boundary layer. An idealized primitive equation numerical model produces a similar baroclinic boundary current whose vertical length scale agrees with the theoretical scaling for both upwelling and downwelling favorable winds.
Radiating Instability
Cambridge University Press eBooks, Feb 28, 2019
Wind-Driven Freshwater Buildup in the Beaufort Gyre is Inevitably Constrained by Mesoscale Eddies
2015 AGU Fall Meeting, Dec 16, 2015
Forward Problem in Numerical Models
Elsevier eBooks, 2001
Wind-driven variations in an overturning circulation
EGU General Assembly Conference Abstracts, Apr 1, 2017
On the sea-ice cover of the Nordic Seas in an idealized MITgcm-setup
EGU General Assembly Conference Abstracts, Apr 1, 2016