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- Author or Editor: David Brickman x

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## Abstract

Cold air blowing out over a warm ocean leads to convection over an isolated region of the ocean basin. This phenomenon, known as open-ocean convection, is often simulated by convective forcing from a circular disk much smaller than the dimension of the domain. An important feature of these simulations is the development of eddies at the edge of the disk that serve to transport heat horizontally. This has sparked interest in the heat-flux characteristics of such a system.

This paper deals with the thermodynamic properties of this type of convective flow, using a rotating tank with bottom-mounted hotplate as the experimental apparatus. Experiments are performed, in an initially unstratified fluid, for a set of values of the nondimensional forcing parameter *R _{c}
* =

*B*

^{1/2}/(

*Hf*

^{3/2}), where

*B*is the buoyancy flux,

*H*is the fluid depth, and

*f*is the Coriolis parameter. The ratio of the frontal eddy size to the hotplate radius, Îµ, is shown to be an important parameter. The experiments reported are for the regime Îµ âˆ¼ O(1), consistent with those of other researchers. The author shows that Îµ â‰ª 1 is the more relevant case oceanographically, a fact that is likely more important thermodynamically than dynamically. The evolution of the mean temperature (difference) above the heating region is determined, from which can he deduced the vertical/horizontal heat flux partitioning as a function of time and

*R*.

_{c}The average behavior of the mean temperature field (*TÌ„*) above the plate follows a relation: *TÌ„*(*t*) = *T _{e}
* tanh(

*t*/Ï„), where

*t*is time and

*T*and Ï„ are functions of

_{e}*R*. The nondimensional adjustment timescale is found to be Ï„

_{c}*f*= 4.27

*R*

_{c}^{âˆ’2/3}, which implies that the dimensional timescale Ï„ is, remarkably, independent of the rotation rate. The equilibrium temperature scale

*T*, expressed as a buoyancy deficit and nondimensionalized, is well described by

_{e}*g*Î±

*T*/

_{e}*H*

^{1/3}= (4.67)

*R*

_{c}^{âˆ’0.075}and is thus also effectively independent of

*f*.

A heton-type model for the mean temperature field is developed with *TÌ„*(t) as solution to its associated differential equation. The physical model, the differential equation, plus the (determined) properties of its solution constitute a parameterized thermodynamic model of this form of convection with potential use in meso-scale ocean climate models. Ideas are presented on how this could be done.

## Abstract

Cold air blowing out over a warm ocean leads to convection over an isolated region of the ocean basin. This phenomenon, known as open-ocean convection, is often simulated by convective forcing from a circular disk much smaller than the dimension of the domain. An important feature of these simulations is the development of eddies at the edge of the disk that serve to transport heat horizontally. This has sparked interest in the heat-flux characteristics of such a system.

This paper deals with the thermodynamic properties of this type of convective flow, using a rotating tank with bottom-mounted hotplate as the experimental apparatus. Experiments are performed, in an initially unstratified fluid, for a set of values of the nondimensional forcing parameter *R _{c}
* =

*B*

^{1/2}/(

*Hf*

^{3/2}), where

*B*is the buoyancy flux,

*H*is the fluid depth, and

*f*is the Coriolis parameter. The ratio of the frontal eddy size to the hotplate radius, Îµ, is shown to be an important parameter. The experiments reported are for the regime Îµ âˆ¼ O(1), consistent with those of other researchers. The author shows that Îµ â‰ª 1 is the more relevant case oceanographically, a fact that is likely more important thermodynamically than dynamically. The evolution of the mean temperature (difference) above the heating region is determined, from which can he deduced the vertical/horizontal heat flux partitioning as a function of time and

*R*.

_{c}The average behavior of the mean temperature field (*TÌ„*) above the plate follows a relation: *TÌ„*(*t*) = *T _{e}
* tanh(

*t*/Ï„), where

*t*is time and

*T*and Ï„ are functions of

_{e}*R*. The nondimensional adjustment timescale is found to be Ï„

_{c}*f*= 4.27

*R*

_{c}^{âˆ’2/3}, which implies that the dimensional timescale Ï„ is, remarkably, independent of the rotation rate. The equilibrium temperature scale

*T*, expressed as a buoyancy deficit and nondimensionalized, is well described by

_{e}*g*Î±

*T*/

_{e}*H*

^{1/3}= (4.67)

*R*

_{c}^{âˆ’0.075}and is thus also effectively independent of

*f*.

A heton-type model for the mean temperature field is developed with *TÌ„*(t) as solution to its associated differential equation. The physical model, the differential equation, plus the (determined) properties of its solution constitute a parameterized thermodynamic model of this form of convection with potential use in meso-scale ocean climate models. Ideas are presented on how this could be done.

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## Abstract

Lagrangian stochastic (LS) modeling is a common technique in atmospheric boundary layer modeling but is relatively new in coastal oceanography. This paper presents some fundamental aspects of LS modeling as they pertain to oceanography. The theory behind LS modeling is reviewed and an introduction to the substantial atmospheric literature on the subject is provided.

One of the most important properties of an LS model is that it maintains an initially uniform distribution of particles uniform for all timeâ€”the well-mixed condition (WMC). Turbulent data for use in an oceanic LS model (LSM) are typically output at discrete positions by a general circulation model. Tests for the WMC are devised, and it is shown that for inhomogeneous turbulence the data output by an oceanic general circulation model is such that the WMC cannot be demonstrated. It is hypothesized that this is due to data resolution problems. To test this hypothesis analytical turbulence data are constructed and output at various resolutions to show that the WMC can only be demonstrated if the resolution is high enough (the required resolution depending on the inhomogeneity of the turbulence data). The output of an LSM represents one trial of possible ensemble and this paper seeks to learn the ensemble average properties of the dispersion. This relates to the number of particles or trials that are performed. Methods for determining the number of particles required to have statistical certainty in one's results are demonstrated, and two possible errors that can occur when using too few particles are shown.

## Abstract

Lagrangian stochastic (LS) modeling is a common technique in atmospheric boundary layer modeling but is relatively new in coastal oceanography. This paper presents some fundamental aspects of LS modeling as they pertain to oceanography. The theory behind LS modeling is reviewed and an introduction to the substantial atmospheric literature on the subject is provided.

One of the most important properties of an LS model is that it maintains an initially uniform distribution of particles uniform for all timeâ€”the well-mixed condition (WMC). Turbulent data for use in an oceanic LS model (LSM) are typically output at discrete positions by a general circulation model. Tests for the WMC are devised, and it is shown that for inhomogeneous turbulence the data output by an oceanic general circulation model is such that the WMC cannot be demonstrated. It is hypothesized that this is due to data resolution problems. To test this hypothesis analytical turbulence data are constructed and output at various resolutions to show that the WMC can only be demonstrated if the resolution is high enough (the required resolution depending on the inhomogeneity of the turbulence data). The output of an LSM represents one trial of possible ensemble and this paper seeks to learn the ensemble average properties of the dispersion. This relates to the number of particles or trials that are performed. Methods for determining the number of particles required to have statistical certainty in one's results are demonstrated, and two possible errors that can occur when using too few particles are shown.

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## Abstract

This paper discusses the energetics of the internal waves generated by the tide on the northern edge of Georges Bank in the outer Gulf of Maineâ€“-a region of strong tidal flow, a density/temperature front, and abrupt topography. A series of bank-edge cross sections in early July 1988, using the towed vertically profiling Batfish, shows that during off-bank flow a large internal hydraulic jump develops over the bank slope. This disturbance propagates on bank during the reverse phase of the tide, evolving into two internal solitonlike features that impinge upon the frontal zone separating stratified bank-edge water from the homogeneous water on bank. Thermistor chain data from the bank edge show that two internal wave packets per tidal cycle are characteristic of the region during this time of year. The available potential energy plus kinetic energy of the internal disturbances, estimated using the Batfish and thermistor chain data, is found to be 35 J m^{âˆ’3} in a plug of fluid 60 m deep and 4 km long (cross bank). A simple model of bank-edge energetics indicates that the wave packets are potentially significant in frontal evolution and in the supply of inorganic nutrients to primary production in the frontal zone.

## Abstract

This paper discusses the energetics of the internal waves generated by the tide on the northern edge of Georges Bank in the outer Gulf of Maineâ€“-a region of strong tidal flow, a density/temperature front, and abrupt topography. A series of bank-edge cross sections in early July 1988, using the towed vertically profiling Batfish, shows that during off-bank flow a large internal hydraulic jump develops over the bank slope. This disturbance propagates on bank during the reverse phase of the tide, evolving into two internal solitonlike features that impinge upon the frontal zone separating stratified bank-edge water from the homogeneous water on bank. Thermistor chain data from the bank edge show that two internal wave packets per tidal cycle are characteristic of the region during this time of year. The available potential energy plus kinetic energy of the internal disturbances, estimated using the Batfish and thermistor chain data, is found to be 35 J m^{âˆ’3} in a plug of fluid 60 m deep and 4 km long (cross bank). A simple model of bank-edge energetics indicates that the wave packets are potentially significant in frontal evolution and in the supply of inorganic nutrients to primary production in the frontal zone.

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## Abstract

A low-order, basin-averaged, coupled atmosphereâ€“ocean paleoclimate model is developed and the results from a 3.2-Myr model paleointegration described. A three-basin version of the Wrightâ€“Stocker ocean model is used to compute the thermohaline circulation component of the climate system, with a six-basin energy balance atmosphere coupled to the ocean and land surfaces.

As expected, amplitude spectra of the paleo-integration results show that the annually averaged global air temperature (*T*
_{atm}) closely follows the net radiation (*Q*
_{
N
}), with power in the obliquity (40 kyr) and eccentricity bands (100 kyr and 400 kyr). However, there are also some unexpected results: the globally and annually averaged ocean temperature (*T*
_{ocean}) is negatively correlated with *T*
_{atm} in the obliquity band, *T*
_{ocean} shows significant energy in the precessional band (20 kyr), and the response of *T*
_{ocean} to *Q*
_{
N
} variations is suppressed in the eccentricity band.

Physical explanations for the above results are presented and supported by a simple box climate model. This model helps to isolate and clarify the mechanism by which the ocean temperature varies significantly at precessional periods while the atmospheric temperature does not. The same model also illustrates the cause of the 40 kyr atmosphereâ€“ocean temperature anticorrelation. Model integrations and analysis confirm that convection serves to rectify the zero annual-mean precessional forcing, resulting in 20 kyr energy in the ocean, which shows up only weakly in the atmosphere. The 40 kyr anticorrelation is the result of the latitudinal distribution of net radiation at obliquity periods, and thus can be reproduced only by a climate model with horizontal resolution. Ocean convection plays a critical role in determining both the 20 kyr and 40 kyr responses.

The suppressed response of the ocean in the eccentricity band is attributed to a combination of two effects. First, the larger albedo at high latitudes results in reduced variation of the airâ€“sea heat flux at high latitudes so that variations in convection, and hence in deep water temperatures, are also reduced. Second, the nonlinearity of the equation of state for seawater contributes latitudinal variations in ocean densities, which result in changes in the overturning circulation, which further suppress the ocean temperature variations in the eccentricity band.

The implications of the authorsâ€™ results for interpretations of the paleoclimate record are discussed.

## Abstract

A low-order, basin-averaged, coupled atmosphereâ€“ocean paleoclimate model is developed and the results from a 3.2-Myr model paleointegration described. A three-basin version of the Wrightâ€“Stocker ocean model is used to compute the thermohaline circulation component of the climate system, with a six-basin energy balance atmosphere coupled to the ocean and land surfaces.

As expected, amplitude spectra of the paleo-integration results show that the annually averaged global air temperature (*T*
_{atm}) closely follows the net radiation (*Q*
_{
N
}), with power in the obliquity (40 kyr) and eccentricity bands (100 kyr and 400 kyr). However, there are also some unexpected results: the globally and annually averaged ocean temperature (*T*
_{ocean}) is negatively correlated with *T*
_{atm} in the obliquity band, *T*
_{ocean} shows significant energy in the precessional band (20 kyr), and the response of *T*
_{ocean} to *Q*
_{
N
} variations is suppressed in the eccentricity band.

Physical explanations for the above results are presented and supported by a simple box climate model. This model helps to isolate and clarify the mechanism by which the ocean temperature varies significantly at precessional periods while the atmospheric temperature does not. The same model also illustrates the cause of the 40 kyr atmosphereâ€“ocean temperature anticorrelation. Model integrations and analysis confirm that convection serves to rectify the zero annual-mean precessional forcing, resulting in 20 kyr energy in the ocean, which shows up only weakly in the atmosphere. The 40 kyr anticorrelation is the result of the latitudinal distribution of net radiation at obliquity periods, and thus can be reproduced only by a climate model with horizontal resolution. Ocean convection plays a critical role in determining both the 20 kyr and 40 kyr responses.

The suppressed response of the ocean in the eccentricity band is attributed to a combination of two effects. First, the larger albedo at high latitudes results in reduced variation of the airâ€“sea heat flux at high latitudes so that variations in convection, and hence in deep water temperatures, are also reduced. Second, the nonlinearity of the equation of state for seawater contributes latitudinal variations in ocean densities, which result in changes in the overturning circulation, which further suppress the ocean temperature variations in the eccentricity band.

The implications of the authorsâ€™ results for interpretations of the paleoclimate record are discussed.

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## Abstract

A three-dimensional, *z*-level, primitive-equation ocean circulation model (DieCAST) is modified to include a free-surface and partial cells. The updating of free-surface elevation is implicit in time so that the extra computational cost is minimal compared with the original DieCAST code, which uses the rigid-lid approximation. The addition of partial cells allows the bottom cell of the model to have variable thickness, hence improving the ability to accurately represent topographic variations. The modified model is tested by solving a two-dimensional, linearized problem of internal tide generation over topography. method is modified to more cleanly separate the internal tide from the full solution. The model results compare favorably with the semianalytic solution of . In particular, the model reproduces the predicted variation of internal tide energy flux as a function of the ratio of bottom slope to characteristic slope.

## Abstract

A three-dimensional, *z*-level, primitive-equation ocean circulation model (DieCAST) is modified to include a free-surface and partial cells. The updating of free-surface elevation is implicit in time so that the extra computational cost is minimal compared with the original DieCAST code, which uses the rigid-lid approximation. The addition of partial cells allows the bottom cell of the model to have variable thickness, hence improving the ability to accurately represent topographic variations. The modified model is tested by solving a two-dimensional, linearized problem of internal tide generation over topography. method is modified to more cleanly separate the internal tide from the full solution. The model results compare favorably with the semianalytic solution of . In particular, the model reproduces the predicted variation of internal tide energy flux as a function of the ratio of bottom slope to characteristic slope.