Q. J . R. Meteorol. SOC. (1989), 115, pp. 29-44 551.510.522:551.526.6:551.584.33:551.465.5

Dynamical analyses of marine atmospheric boundary layer structure near the Gulf Stream oceanic front

By MICKEY MAN-KUI WAI and STEVEN A. STAGE Department of Meteorology, Florida State University, Tallahassee, U.S.A.

(Received 21 March 1988, revised 17 August 1988)

SUMMARY The effects of the sea surface temperature (s.s.t.) front at the edge of the Gulf Stream on the marine

atmospheric boundary layer (MABL) are investigated using a numerical model to study the modification effects of an oceanic front on the MABL structure. The situation simulated is flow from over cold shelf water to over the warm water of the Gulf Stream. The initial temperature and humidity profiles of the air are specified to be near neutral over the cold water and are therefore typical of undisturbed conditions. The differential in s.s.t. across the oceanic front creates a horizontal variation in the surface perturbation pressure and the stability. The surface perturbation pressure and turbulent fluxes modulate the flow and produce horizontal variations in horizontal wind components with associated vertical motions. A thermally direct cell is produced as a result of the s.s.t. difference across the front. The isotherms slope upward towards the warm water. Entrainment of inversion layer air and upward vertical motion over the warm water cause the MABL to be deeper there. A layer of cloud forms over warm water and is associated with mixed layer deepening rather than lowering of the condensation level. Turbulent fluxes in the MABL show considerable spatial variation. Surface stress is much larger over the front and over the warm water than over the cold water. This is mostly caused by wind speed changes associated with the front. Changes in the drag coefficient due to changes in surface roughness and stability are much less important.

Mean budgets for temperature and total water indicate that there is a balance between horizontal advection and turbulent flux divergence. The U momentum budget shows that once the geostrophic balance terms are subtracted, the balance is mainly between the pressure gradient force associated with the induced temperature field and turbulent friction, with horizontal advection and the Coriolis force acting on the geostrophic departure playing minor roles. The V momentum budget shows a balance between horizontal advection, Coriolis force and friction.

Although there are few data for comparison, the results are in qualitative agreement with observations in the area. This study shows that the s.s.t. front at the Gulf Stream edge produces marked local changes in the nearby atmospheric surface layer.

1. INTRODUCTION

Warm currents such as the Gulf Stream in the western Atlantic and the Kuroshio in the western Pacific bring warm water northward near continental coasts. These currents are 10 degC or more warmer than surrounding waters. The associated large horizontal temperature differentials at the edges of the currents produce significant atmospheric and oceanic changes which have often been noted by observers crossing an oceanic front such as the Gulf Stream edge. In the cold water region, fog and haze with poor visibility are the typical conditions. On the warm side of the oceanic front, convective phenomena with improved visibility are the persistent features. An increase in the horizontal wind and changes in the wind direction are also found when the air moves across the s.s.t. front from the cold water. Associated with the horizontal variation in the wind speed, the sea state changes from calm sea over the cold water to rougher seas over the warm water. Although these atmospheric and oceanic differences in the vicinity of the oceanic front have been reported by Sweet et al. (1981), little discussion was given to what dynamical processes produce them.

In this paper we consider the structure of the MABL in the vicinity of the Gulf Stream s.s.t. front during undisturbed conditions in which air nearly in equilibrium with non-Gulf-Stream cold shelf water flows over the much warmer Gulf Stream water. In these cases, surfaces fluxes and atmospheric mixing would be small in the absence of the Gulf Stream. Surface fluxes are much smaller both over the near-shore waters and over the Gulf Stream in these undisturbed conditions than in the more dramatic case of a cold air outbreak; however, we shall see that a large horizontal air temperature difference

29

30 M. M.-K. WAI and S. A. STAGE

induced by the s.s.t. gradient at the Gulf Stream front produces strong modification of the MABL and significant secondary circulation.

There have been several numerical studies on the modification of the atmospheric boundary layer by air-water interaction effects. The effects of a small isolated pond or lake on the atmospheric boundary layer were studied by Yamada (1979) and Beniston (1985). Asai and Nakamura (1978) reported their numerical study of the developing MABL in AMTEX (Air Mass Transformation Experiment). The evolution of a sub- tropical MABL structure was described by Moeng and Arakawa (1980). More recently, Wai (1988) discussed the effects of a cold spot on the MABL structure and cloud properties off the California coast. Stage and Businger (1981) used a slab model to study modification of the MABL over Lake Ontario during cold air outbreaks. Chow and Atlas (1982), Atlas et al. (1983) and Stage (1983) have discussed surface heat and vapour fluxes associated with cold air outbreak episodes. No studies have yet considered an s.s;t. front in the model domain and its effects on the MABL circulation and on the thermal, moisture and velocity fields.

This absence of numerical studies has probably been partly due to limited availability of detailed MABL measurements with which to support modelling. The Mesoscale Air- Sea Interaction Experiment (MASEX, see Chou et al. 1986) in 1983 and the Genesis of Atlantic Lows Experiment (Dirks et al. 1988; SethuRaman and Riordan 1988) are two recent experiments which have gathered data relevant to the determination of MABL structure near the Gulf Stream front. However, both of these experiments gathered data during post-frontal cold air outbreak episodes and therefore do not provide data for the situation to be studied in this paper. The Frontal Air-Sea Interaction Experiment (FASINEX, see Stage and Weller 1985, 1986) measured the effects of the subtropical oceanic front on the MABL. Although FASINEX made measurements during undis- turbed conditions, the subtropical front (strength typically 2 degC in FASINEX) is much weaker than the Gulf Stream front, thus FASINEX results cannot be directly compared with the results of this paper. We are currently using the model from this paper to study the FASINEX data. Those results will appear in another paper.

We begin by discussing the model in section 2. Boundary and initial conditions are discussed in section 3. Section 4 discusses the model results, first for the mean MABL circulation induced by the front, then the horizontal variation of the turbulence in the region. Finally in section 5 , budget studies are used to investigate the importance of various physical properties in determining MABL structure.

2. MODELLING DETAILS

(a) Description of the model The model used in this present study is based on Wai (1988), which includes a

boundary layer module, a level-4 second-order turbulence transfer module, and a long- wave radiative transfer module. The boundary layer module consists of primitive equations of all three wind components U, V, W, the liquid water static energy, H; the total moisture, R; and the continuity equation. The atmospheric pressure is given by p = P + R, wherep is the total pressure, P is a background pressure, which is hydrostatic and whose horizontal gradient is determined by the synoptically imposed geostrophic wind, and n is the deviation of the actual pressure from the background pressure. The turbulence transfer module, which contains prognostic equations for all second moments, allows water vapour condensation. The effects of cloud top bumpiness are neglected. A detailed discussion of this turbtllence transfer module has been given in Wai (1987).

BOUNDARY LAYER STRUCTURE NEAR THE GULF STREAM 31

To simplify the model computation, fog formation and precipitation processes are not considered in the study. When clouds form, the radiative effect is expected to have a significant influence on the dynamics of the clouds. Long-wave radiative cooling from the cloud top can produce strong cooling which tends to destabilize the clouds, generate turbulent mixing, and produce entrainment. Thus radiative cooling is an important mechanism in the break-up of stratus. In his study of cloud streets in the MABL, Mason (1985) reported that the entrainment rate is only slightly reduced with no cloud top cooling but the overall dynamics remains the same as with the cloud top cooling. In this paper we do not intend to study the details of the cloud dynamics and its properties and therefore we inactivate the long-wave radiative transfer module; radiation computations require considerable time and it is not yet known if the radiation processes are important in the MABL at the Gulf Stream edge.

(b ) Numerical technique A staggered grid system described by Harlow and Welch (1965) and Williams (1969)

is used. Values of mean vertical velocity W are located at the horizontal mid-points between U grid points, and values of V, H, R, and n are located at vertical mid-points between the mean velocity U grid points. Then, the continuity equation can be expressed at each pressure point. Second-moment terms are hence computed at the intermediate level between the mean variables. The model has 60 vertical levels with a grid size of 50 m. In the horizontal, there are 64 grid points with a horizontal grid size of 25 km.

Equations for the momentum, the liquid water static energy, and the total mixing ratio are finite differenced with a leap-frog scheme. The second-moment terms are advanced by forward steps. Advective terms are put into the momentum and the energy conservation form of Piacsek and Williams (1970). The pressure is determined by the Poisson equation and is solved by the block-cyclic reduction method.

3. INITIAL AND BOUNDARY CONDITIONS

The intensity of the modification of the boundary layer structure near an oceanic front partly depends on the strength and the width of the oceanic front. In the present study, the temporal and spatial variations of the frontal axis with latitude are not considered. Sweet et al. (1981) reported a 2 degC change in s.s.t. across the north wall of the Gulf Stream in December off Cape Hatteras (35"N). The width and the temperature difference across the Gulf Stream were not reported. Hsu (1984) used these data to obtain his estimate of the strength of MABL secondary circulation induced by the Gulf Stream front which had a mean width of 150 km (Stommel 1966). Instead of using a mean width of 150 km and arbitrarily assigning a s.s.t. difference across the front, we decided to use a five-day-mean s.s.t. analysis for January provided by the U.S. National Weather Service. Based on this 5-day-mean s.s.t. analysis off the east coast of the United States in January 1984, the s.s.t. is prescribed with a constant s.s.t. of 6°C from the upwind boundary to 475 km, a linear increase in the front from 6°C at 475 km to 19°C at 825 km, and constant at 19°C beyond 825 km. The orientation of the s.s.t. front is between north-south and north-east-south-west, depending on latitude. The x axis of the model is aligned perpendicular to the front, and our results are stated in this coordinate system as upwind and downwind of the front so that the results can be generalized to various frontal directions.

The initial potential temperature profile is well mixed with 6°C up to an inversion base at 850 m. The humidity is well mixed up to the inversion and has a value such that the relative humidity at the inversion base is just saturated. This is the most moist upwind

32 M. M.-K. WAI and S . A. STAGE

sounding which does not contain a cloud. The inversion, which has a thickness of 300 m, consists of a jump increase in temperature of 10 degC and a jump decrease in the total mixing ratio of 3 g kg-'. The air above has a temperature lapse rate of 3 degC km-', and the vertical gradient of the total mixing ratio is zero. Profiles of horizontal wind com- ponents are obtained with an Ekman spiral with a specified geostrophic wind speed of 10 m s-l crossing the front at an angle of 45" and corresponding to winds from the south- west or west depending on the orientation of the front.

These profiles are used to initialize the two-dimensional model. Therefore the initial fields above the sea surface are horizontally homogeneous. In order to satisfy the equation of continuity, the vertical velocity component is set initially to zero. Clouds do not exist at first.

The lower horizontal boundary is a rigid surface. Values for the liquid water static energy and total mixing ratio are specified at the surface (Dirichlet conditions, see Roache 1972). The surface fluxes are computed with similarity relations (Businger et al. 1971) between the surface and the lowest level. The surface roughness is specified according to Charnock's relationship,

Z, = 0*016~2*/g, (1) (Wu 1969). At the model top, the vertical derivatives of U and V are set to zero, and the liquid water static energy and the total mixing ratio have specified lapse rates (Neumann boundary conditions, see Roache 1972). The upper boundary conditions for the vertical velocity and second moments are zero. For the lateral boundary conditions, the original model has been modified to use the Sommerfeld radiation condition. A detailed discussion on this formulation of open lateral boundary conditions can be found in Orlanski (1976) and Clark (1977), among others.

To prevent time-splitting as a result of using a leap-frog scheme, a time filter of Asselin (1972) is used. This time filter considerably reduces the computational modes affecting the mean variables calculated with the leap-frog scheme. As a means of removing short waves, a fourth-order horizontal filter is used in the model interior. In small buffer regions near both lateral boundaries, a second-order horizontal filter is used.

4. RESULTS

The numerical integration is carried out to eight physical hours, at which time the MABL is in a nearly steady state. All the results presented here refer to this time. A series of contour maps of some mean and turbulent fields are displayed to give a general view of the MABL structure. Discussions of the secondary flow induced by the oceanic front and changes in the sea state across the front are also given. Each diagram is oriented to have cold water to the left (upwind) and warm water to the right (downwind). The solutions near the boundaries are not shown. The location of the s.s.t. front is indicated at the bottom of the diagrams.

(a) Mean Jielu3 The contour map of the virtual dry static energy in Fig. 1, at 1 K intervals, exhibits

the thermal structure of the MABL. In the boundary layer, the air temperature increases towards the warm water. The largest horizontal temperature gradient is found across the oceanic front. The air downstream is warmer than the air upstream by six degrees. The change in s.s.t. across the front is 13 degrees, thus the air-sea temperature difference increases and the surface heat flux is larger over the Gulf Stream water than upwind. At

275.0 350.0 425.0 500.0 575.0 650.0 725.0 800.0 875.0 350.0 1025.0 1100.0 1175.0

Figure 1. Contours of virtual dry static energy in 1 K intervals.

1100 m the horizontal temperature gradient across the oceanic front is about 0.003 K km-'. Above the mixed layer top, the horizontal change in the temperature is small. At a given point, the temperature within the MABL is vertically well mixed. The top of the mixed layer slopes upward from the specified depth of 850m over the cold water to around 1200 m over the warm water. The growth in MABL depth is the result of the combined effects of upward vertical motion of the secondary flow over the warm water (see below) and of vertical mixing. Examination of the increase in elevation of the isotherms at the lower inversion level indicates that a little more than 100 m of the MABL growth was caused by the vertical motion of the flow induced by MABL convergence, leaving nearly 250 m of growth by mixing. In a slab model such as was used by Stage and Businger (1981), this vertical mixing across the MABL top would be parametrized as entrainment. Using that interpretation we see that entrainment produces most of the MABL growth but that a slab model would need to include vertical motions to give accurate prediction of MABL depth.

2000.0.

1500.0 - E 1000.0 u u

50040

080 I I I I ,-- I , , I I I I I I - B m T C l O N T - ". 1 L . u

275.0 350.0 425.0 500.0 575.0 650.0 725.0 800.0 875.0 950.0 1025.0 1100.0 1175.0

X(km)

Figure 2. Contours of total mixing ratio in 1 g kg-' intervals.

Figure 2 displays a contour map of the total mixing ratio at 1 g kg-' intervals. Over the cold water, the horizontal change in the total mixing ratio is small. As the air moves across the front, the total mixing ratio in the air at 75 m increases rapidly from 4.5 g kg-' over the cold water to about 6 g kg-' over the warm side of the front. Beyond the front, the total mixing ratio increases only slightly. Above the boundary layer, the total mixing ratio varies little horizontally. The sloping boundary layer top seen in the temperature field is also visible here.

34 M. M.-K. WAI and S. A. STAGE

2000 a 0

1500.0

t

t 500*0 L

c SST C I O N T - 0.0 275.0 350.0 425.0 500.0 575.0 650.0 725.0 800.0 875.0 950.0 1025.0l100.0 1175.0

X ( k m )

Figure 3. Contours of liquid water mixing ratio in 0.1 g kg- ' intervals.

At hour eight, a layer of cloud is found downstream, with top near 1100 m and base at 800m. The cloud deck is shallow near the oceanic front and thickens downstream. The upwind air has a lifting condensation level (1.c.I.) of 850m. The warming and moistening of MABL air very nearly exactly offset each other to produce a constant 1.c.l. The presence of the cloud is therefore due to the increase in MABL depth. The distribution of liquid water mixing ratio in Fig. 3 shows considerable spatial variation inside the cloud. The maximum liquid water content is about 0.3 g kg-'. Since this model was run using a 25 km horizontal grid spacing, it cannot resolve convection in individual cumulus clouds, and the model is not capable of differentiating between a stratus deck and a layer of cumulus clouds.

The positive s.s.t. anomaly induces a local perturbation low pressure centre near the sea surface south of the oceanic front (Fig. 4). Higher perturbation pressure is found over the cold water. The strongest horizontal perturbation pressure gradient is found low in the boundary layer upwind of the front. Downwind of the front the slope of the isobars rapidly decreases and the perturbation pressure gradient becomes small. Near 800m, the isobars show little horizontal variation as the air moves across the front. Between 800 m and the inversion base, the horizontal perturbation pattern reverses from that found in the lower levels. Such a pattern comes naturally in order to satisfy the conservation of mass and is associated with the return branch of the secondary circulation cell discussed below. The horizontal pressure gradient near the inversion base is much weaker than that low in the MABL and produces lower secondary flow speeds near the inversion base than near the surface.

The pattern of the perturbation pressure in the boundary layer has some effect on the horizontal flow. In areas upwind of the front, we may expect that the horizontal

2000.0

1500.0

E 1000.0 Y

N

500.0

c SST FlONT - 0.0 275.0 350.0 425.0 500.0 575.0 650.0 725.0 800.0 875.0 950.0 1025.0 1100.0 1175.0

X [ k m l

Figure 4. Contours of perturbation pressure in 0.1 mb intervals.

BOUNDARY LAYER STRUCTURE NEAR THE GULF STREAM 35

2000.0 L I I 1 I I I I 1 I I I I I I I I I I I I I I I I I 1 I I I 1 I I I I I 4

1500.0 - E 1000.0 e N

500.0

0.0 275.0 350.0 425.0 500.0 575.0 650.0 725.0 800.0 875.0 950.0 1025.0 1100.0 1175.0

X ( hm)

Figure 5. Contours of wind speed in 0.25 m s-' intervals.

perturbation pressure gradient force acts to accelerate the flow as the air moves across the front. When the air leaves the south wall of the oceanic front, the flow is gradually decelerated because the horizontal perturbation pressure gradient force gradually decreases. Similarly, the upper-level horizontal perturbation pressure gradient force acts to decelerate the flow in areas upwind of the front while it acts to speed up the flow downwind of the front.

The distribution of the horizontal wind speed at hour eight is displayed in Fig. 5 . In the boundary layer, the horizontal wind speed at a given location increases with height towards the inversion base. Above the inversion base, the horizontal wind speed tends to blow geostrophically . The wind speed exhibits considerable horizontal variation. In the mixed layer north of the oceanic front, the low-level wind speed remains relatively constant at about 8 m s-'. Approaching the oceanic front, the wind begins to accelerate and reaches a maximum of 10 m s-' near the middle of the front. At increasing fetch, the wind speed decreases only slightly. In the upper level of the boundary layer, the wind speed decreases from 10.5 m s-l in areas north of the front to about 10 m s-l over the oceanic front. As the air continues to move downstream, the wind speed decreases to 9.5 ms-I. The mean wind direction is essentially constant with less than 4 degrees variation over the model domain.

Associated with the spatial variation in the horizontal wind speed is a system of vertical motions induced by the oceanic front. In the boundary layer there are two broad regions of vertical motion (Fig. 6). The descending branch is located over the cold water and a part of the oceanic front. The centre of the maximum sinking motion, with a magnitude of 0.14 cm s-', is located near 600 m just north of the oceanic front. The maximum rising motion near 800 m just south of the oceanic front is 0.12 cm s-'. It is of

2000. b

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500.0

0.0 275.0 350.0 425.0 500.0 575.0 650.0 725.0 800.0 875.0 950.0 1025.IJ IlOO.0 1175.0

X ( km)

Figure 6. Contours of the vertical velocity in 0.02 cm s-' intervals.

36 M. M.-K. WAI and S. A. STAGE

interest to note that due to strong convection over the warm water the centre of ascending motion is higher than the centre of descending motion.

( b ) Secondary f20 w Further information about the effects of the s.s.t. front on the MABL can be

obtained by examining the secondary flow. For this purpose, let the perturbation field or secondary flow be defined as the difference between the value of a quantity at a particular point and the horizontal mean of that quantity averaged over the model domain. There is a certain amount of arbitrariness in this definition since the model domain could be changed without changing the physics of the MABL. However, the computed secondary flow is not too sensitive to such changes.

The secondary flow induced by the oceanic front is depicted by the perturbation streamlines (Fig. 7). Here the perturbation streamlines are calculated by integrating the perturbation U and W speeds. A big, asymmetric, thermally direct cell is found over the oceanic front with rising motion over the warm water and sinking motion over the cold water and having return flow aloft. The cell centre is found at a height of 700m over the oceanic front. The horizontal extent of the cell is about 500 km. The ascending branch is deeper than the descending branch by about 200 m. It is of interest to note that the branch of return flow slopes downward towards the cold water and that return flow is present both in the upper MABL and in the inversion layer. Comparison of Figs. 6 and 7 shows that the s.s.t. gradient produces a thermally direct secondary circulation cell whose width is comparable to the frontal width and with cores of vertical motion over the edges of the region of s.s.t. gradient.

Figure 7. Contours of perturbation streamfunction in units of 50 m2 s-I.

(c) Turbulence fields For the turbulence fields, only virtual heat flux, the total water flux, and momentum

fluxes are shown. In Fig. 8, the maximum positive heat flux is found at the sea surface. In the cloud-free regions, heat flux decreases linearly with height and changes to a negative maximum near the mixed layer top. The ratio between the heat flux at the inversion and the surface heat flux is about -0.21. In the sub-cloud layer, low heat flux is located over the cold water. As the air moves across the front, the heat flux increases rapidly horizontally and reaches a maximum just south of the front. For instance, at a level of 75 m the turbulent heat flux increases from 6 W m-' upwind to 100 W m-' near the south wall of the front. As s.s.t. ceases to increase, the heat flux is nearly constant showing a slight, gradual decrease as the air temperature slowly approaches the s.s.t.

BOUNDARY LAYER STRUCTURE NEAR THE GULF STREAM 37

2006. tl

1500.0

x (hm)

Figure 8. Contours of the buoyancy flux in 25 W m-* intervals.

The cloud layer is associated with a number of features in the heat and moisture fluxes. At cloud formation, latent heat release causes an increase in turbulent mixing and an increase in MABL-top entrainment. The dry air being entrained means that the vertical gradient of moisture flux is much less under the cloud than in the clear MABL. The heat flux decreases vertically to a minimum, which is sometimes negative, near cloud base, rapidly increases to a maximum low in the cloud, then gradually decreases to a negative maximum near the cloud top. The maximum turbulent heat flux is about 50 W m-2 near cloud base, and the minimum is about -45 W m-2 near cloud top.

The total water flux in Fig. 9 shows a similar horizontal variation to that of the turbulence heat flux. At the 75 m level, it increases from 30 W mP2 upstream to about 200 W m-2 downstream. The total water flux displays a similar adjustment near the south wall of the oceanic front. Over the front the total water flux is maximum at the surface, and linearly decreases to a minimum at the boundary layer top. When clouds develop, a small secondary maximum is found inside the cloud layer. Inside the cloud layer, the maximum total water flux is about 150 W m-2. The heat flux and the total water flux show considerable spatial variation inside the cloud layer. This may be due to cumulus convection at scales large enough to be resolved by the model even though the grid spacing is too large to resolve the most energetic scales of convection. It would then seem that the model can indicate the existence of cumulus convection without resolving the details. Caution is needed on this point, however, because the smallest wavelengths in the model are influenced by the filtering due to removing computational noise.

The surface fluxes of 100 W m-2 in sensible heat and of 200 W m-2 in latent heat are a large fraction of the daily average insolation and indicate that even in cases which are not cold air outbreaks, heat transfer to the air is an important term in the heat energy budget of Gulf Stream water.

2000.0 1 1 ~ 1 1 ~ 1 1 ~ 1 1 1 l I ~ I I I I 1 1 1 l I I J l 1 1 1 1 ~ 1 ' ~

1 L500.0

1 * E LOOO.0 c

500,o

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mmT CUONT - e

0 425.0 500.0 575.0 650.0 725.0 800.0 875.0 350.0 1025.0 1100.0 1175.0 ~~

0 425.0 500.0 575.0 650.0 725

X k m l

Figure 9. Contours of the total water flux in 25 W m-* intervals.

38 M. M.-K. WAI and S . A. STAGE

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1500.0 - E 1000.0 ” N

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0.0 2

c mmT FUONT - 75.0 350.0 425.0 500.0 575.0 650.0 725.0 800.0 875.0 350.0 1075.0 1100.0 1175.0

X ( h m l

- Figure 10. Contours of the u’w‘ momentum flux in 1 x m2se2.

- - The momentum fluxes, u’w’ and u‘w‘ , are shown in Figs. 10 and 11. The surface

stress is smallest over the cold water, increases across the front, and then very gradually decreases over the warm water. The maximum surface stress is about 66% larger over the front than over the cold water and remains about 36% larger at the downwind edge of the model than over the cold water. In order to gain understanding of the importance of various physical processes to this stress change we write the surface stress as

t = pui = pCDM2

= p C D N ( C D / C D N ) M 2 (2) where M is the wind speed, CD is the drag coefficient, and C D N is the neutral drag coefficient. Using the diabatic profiles (Businger 1973) we can write

CD = k2{ln(z/z,) - v , } - ~ (3)

cDN = k2{In(z/zo)}-2. (4)

where q!~, is the diabatic profile function and depends on z /L . We define

Here we use z = 75 m so that M, CD, and CD, are relative to the lowest model level.

TABLE 1. FACTORS CONTRIBUTING TO SURFACE STRESS CHANGES

125 km 1150 km

20 66 36 CDN 9 5 cD/cDN 16 17 CD 26 23 Wind speed, M 15 5 M2 32 10 Surface stress 66 36

The table shows percentage increases in various parameters when compared with values over the cold water.

Table 1 shows how these various parameters contribute to the stress changes. Numbers in the table show the percentage increase in each parameter at the point of maximum stress (near 725 km) compared with over the cold water and at the downwind edge of the model (1150 km) compared with over the cold water. From (1) and (2)

Z, = 0.016 t/gp ( 5 )

BOUNDARY LAYER STRUCTURE NEAR THE GULF STREAM 39

X ( k m )

- Figure 11. Contours of the u'w' momentum flux in lx10-2m-2s-2.

and we see that surface roughness changes in proportion to surface stress. According to Table 1 both of these increase by 66% over the front. This produces only a 9% increase in CDN. The effects of stability on the stress are seen in the ratio CD/CDN which increases by 16%. The net result of changes in surface roughness and stability is thus a 26% increase in CD. The square of the wind speed increases by 32%. These results show that there is a large increase in the surface stress associated with the front and that most of this increase is due to the changes in the wind speed induced by pressure gradients generated by the front. The direct contribution of changes in surface layer stability to the stress increase is smaller. Changes in the neutral drag coefficient and surface roughness (CDN and 2,) have only a minor effect on the surface stress. Note, however, that the large increase in the surface roughness produced by the surface stress increase is in agreement with the observation that the sea state changes from calm over the cold water to rougher over the warm water (Sweet et al. 1981). The surface stress decreases from over the front to the downwind edge of the model but remains 36% higher than over the cold water. Table 1 reveals that the factors contributing to the increased stress at 1150 km have similar importance to those at 775 km and that the wind speed remains the dominant factor. Nearly all of the decrease in surface stress between these two locations is due to a decrease in wind speed. The secondary circulation cell perpendicular to the front produces a region of increased stress near the front and is thus important to the air-sea momentum transfer. The circulation cell does not extend to the downwind edge of the model, but the baroclinic effects of the front accelerate the flow over the warm water and increase the stress there.

There is a centre of positive u'w' in the upper mixed layer over the centre of the front at the same position as the centre of the low-perturbation streamfunction. Exam- ination of the vertical derivative of u'w' shows that this stress component tends to act as a frictional - drag opposing the secondary flow. There is a region of large vertical gradient of u'w' and therefore of large frictional force over the front. Comparing the regions over the warm and cold water, we see that even though the surface stress is 36% larger over the warm water (see Table l), the deeper mixed layer causes the vertical derivative of stress and the frictional force to be smaller there than over the cold water.

As near-surface air flows across the front, it is accelerated by the pressure gradient associated with the frontal warming. The acceleration is partly opposed by an increase in the vertical derivative of the turbulent stress. Over the warm water the pressure gradient force and the vertical derivative of stress both decrease, but the change in the pressure gradient is larger causing the air to slow slightly. Further support of this analysis will be given below in the discussion of the momentum balance.

-

40 M. M.-K. WAI and S. A. STAGE

5 . MEAN BUDGETS

Further insight into the physical processes at work in the MABL can be gained by examining the terms in the budget equations for the mean quantities. We have examined budgets for four heights: 75, 375, 575 and 775m. Comments will focus on the near- surface (75 m) budgets with mention of other levels when they exhibit interesting features.

In all budgets and at all levels vertical advection is very small. Near the top and bottom of the MABL, the vertical velocities are small (Fig. 6). In the mid-MABL the vertical velocity is larger, but the vertical gradients of mean quantities are small.

The simplest budgets are those for the liquid water static energy and the total moisture (Fig. 12). Horizontal advection and the turbulent flux gradient terms dominate these budgets indicating the fundamental importance of horizontal changes in surface fluxes. Cold, dry air is advected from over the cold water and gives rise to increased surface fluxes over the region of s.s.t. gradient. The turbulent flux term decreases over the warm water because the surface fluxes are slowly dropping off and because the mixed layer is deepest there. These budgets have very similar shapes at all levels except near the top of the mixed layer. Near the MABL top the turbulent heat flux produces cooling associated with entrainment as is frequently seen in the tops of convective mixed layers. In horizontally homogeneous mixed layer tops there is a balance between the turbulent cooling and local time-rate change of temperature. In the Gulf Stream front region the balance is between turbulent cooling and warming by horizontal advection. This advection is the result of the fact that the slope of the mixed layer top results in warm inversion base air being horizontally advected into locations near the top of the MABL.

The budget for U momentum is dominated by the synoptic pressure gradient force and the Coriolis force which are nearly in balance. We therefore choose to present the

Figure 12. Budgets for (a): liquid water static energy at 75 m in lxlO-'Ks-'; (b): total water mixing ratio in 2 . 4 5 ~ 1 0 - ~ J kg-k'. Key: H = horizontal advection; V = vertical advection; F = turbulent flux divergence.

BOUNDARY LAYER STRUCTURE NEAR THE GULF STREAM

n 0)

0.2

E ? 0.0 z

-0.2

-0.4

41

- a 75 m - -

//- 1 -

74- - & - L j . q q - - L&qq--qiI & 1 *---- =i---- - -

- 1 1 1 l I I I I I I I I I I I I

-

0.10

0.05 VI E

go.00 c

-0.05

-0.10 t I 1 I I 1 I 1 I I I 1 I I I 1 I I I I I I I I 1 I I I I I I I I I I I 1 275.0 350.0 425.0 500.0 575.0 650.0 725.0 800.0 875.0 950.0 1025.0 1100.0 1175.0

Figure 13. Budgets for (a): U momentum at 75 m in l x 1O-h s-*; and (b): mean V momentum. Key: P = horizontal perturbation pressure gradient force; C-SP = the difference between the Coriolis and synoptic pressure gradient forces (equivalent to the Coriolis force acting on the geostrophic departure); A = advection;

and F = turbulent flux divergence.

budget as shown in Fig. 13. The synoptic pressure gradient force has been subtracted from the Coriolis force to produce a term which is the Coriolis force acting on the geostrophic departure. In this representation of the budget the dominant balance is between the pressure gradient force associated with the temperature difference induced in the MABL by the s.s.t. front and the turbulent stress term. The Coriolis force acting on the geostrophic departure is much smaller and advection is very small.

Because homogeneity is assumed in the y direction, there is no frontally induced pressure gradient in the V budget. The turbulent flux divergence, horizontal advection, and the Coriolis force acting on the geostrophic departure all have similar magnitudes.

These momentum budgets support the behaviour that we have seen in our modelling studies of flow in the vicinity of the subtropical oceanic s.s.t. front. In those studies (to be published separately) we found that the circulation perpendicular to the front (U component in this case) can be explained qualitatively by beginning with the unmodified MABL then noting the temperature changes induced by the front and the resulting pressure gradient force. The circulations perpendicular to the front are thermally direct. The circulations parallel to the front are much more difficult to explain. Sometimes the V circulation is in the direction of the Coriolis force acting on the perturbations in U, and at other times it is in the oppostie direction. As Fig. 13 shows, the V flow is the result of the competing influences of advection, Coriolis force, and turbulent flux divergence and cannot be as readily explained as the U momentum budget.

The U and V momentum budgets near the top of the MABL (775 m) (Fig. 14) are opposites of those near the surface. Each term in the 775 m budget has similar shape to that at 75 m but a smaller magnitude and opposite sign. At the low levels the induced pressure gradient tends to accelerate the U component toward the warm water and friction opposes it. As previously noted, the pressure field high in the h4ABL is the

42 M. M.-K. WAI and S . A. STAGE

0.2 1 1 ~ 1 1 ~ 1 1 ~ 1 1 ~ 1 1 ~ 1 1 ( 1 1 ~ 1 1 ~ 1 1 ~ 1 1 ~ 1 1 ( 1 l -

- I 775 m 0.1 - -

n - 'I -C-SP - - - - E - - - - -R- - - - - -

- ' P \ - -- a - -F 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

-0.1 . - - -

0.10

0.05 n 8

; 0.00 5! -0.05

-0.10 275.0 350.0 425.0 500.0 575.0 650.0 725.0 800.0 875.0 950.0 1025.0 1100.0 1175.0

Figure 14. As Fig. 13 except at a height of 775 m.

opposite of that at low levels and tends to accelerate U towards the cold water. Turbulent friction also opposes this. It is striking that the terms in the V momentum budget at 775 m are also the opposites of those at 75 m. In this particular case the V component can be understood as being forced by the Coriolis force acting on the U component with friction opposing the motion. Advection aloft has the opposite sign from below because the U and V wind fields have opposite signs. We hasten to add that in our earlier discussion of the MABL near a subtropical oceanic front the V field shows forcing by changes in the turbulent stress rather than the simpler Coriolis forcing shown here. We therefore expect that symmetry between the surface and high MABL seen in Figs. 13 and 14 will only hold in a few selected situations.

6. SUMMARY AND CONCLUSIONS

This study has examined the behaviour of the MABL in the vicinity of the Gulf Stream s.s.t. front during conditions in which the air temperature is close to that of the shelf water. Even though surface heat and vapour fluxes are much smaller in these situations than during cold air outbreaks, the surface sensible and latent heat fluxes become as large as 100 and 200 W m-' respectively. There is a pronounced secondary circulation induced by the Gulf Stream and there are strong horizontal gradients in temperature and humidity. Vertical motions associated with the secondary circulation and inversion base entrainment both contribute to produce a much deeper mixed layer over the warm water than over the cold. A cloud layer is formed in the mixed layer. At least for the combination of parameters chosen for this study, warming and moistening approximately balance to keep the lifting condensation level of the MABL nearly constant and the formation of clouds is attributed to mixed layer deepening.

The surface stress has a maximum over the front and remains increased over the warm water. This stress increase is mostly due to the wind field baroclinically induced

BOUNDARY LAYER STRUCTURE NEAR THE GULF STREAM 43

by the front. Changes in the drag coefficient due to stability changes contribute much less, and changes in neutral drag coefficient have minor importance to the stress. The increased stress produces increased surface roughness.

Our results are consistent with the fact that Sweet et al. (1981) found changes in visibility, convective activity, and sea surface roughness near the oceanic front. Our results also support the expectation that there is local cloudiness associated with the Gulf Stream s.s.t. front. There is, however, a shortage of quantitative data with which to compare these results.

In recent years there has been an increase in awareness of the importance of non- homogeneous s.s.t. on the atmospheric boundary layer (Stage and Weller 1985). There are many additional aspects of the MABL in the vicinity of the Gulf Stream front which can be studied. This paper shows that the Gulf Stream s.s.t. front produces significant effects in the nearby MABL even in the absence of cold air outbreaks or other strong atmospheric forcing. This situation has been ignored in past field studies and data are needed to test the conclusions of this paper.

ACKNOWLEDGMENTS

This work was supported by a grant from the Marine Meteorology Program of the Office of Naval Research of the United States. Additional support was provided by the Florida State University through time granted on its Cyber 205 supercomputer.

Asai, T. and Nakamura, K.

Asselin, R.

Atlas, D., Chow, S.-H. and

Beniston, M. Byerly, W. P.

Businger, J. A.

Businger, J. A., Wyngaard, J . C., Izumi Y. and Bradley, E. F.

Chow, S.-H. and Atlas, D.

Chou, S.-H., Atlas, D. and

Clark, T. L.

Dirks, R. A,, Kuettner, J. P. and

Harlow. F. H. and Welch J . E.

Yeh E.-N.

Moore, J. A.

Hsu, S. A.

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