The Influence of Wind Direction upon Flow along the West Coast of Britain and in the North Channel of the Irish Sea

JANUARY 2003 DAVIES AND XING 57 The Influence of Wind Direction upon Flow along the West Coast of Britain and in the North Channel of the Irish Sea ALAN M. DAVIES AND JIUXING XING Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead, Merseyside, United Kingdom (Manuscript received 31 October 2000, in final form 3 July 2001) ABSTRACT This paper briefly describes the development of a three-dimensional nonlinear hydrodynamic model of the sea region off the west coast of Scotland, the North Channel, and the Irish Sea. The model uses a sigma coordinate in the vertical, and subgrid-scale mixing of momentum is parameterized by a vertical eddy viscosity computed using a turbulence energy submodel. Numerical calculations illustrate the importance of wind direction and topography in determining flow pathways along the west coast of Scotland, through the North Channel, and within the Irish Sea. The role of a northward flow into the Irish Sea through St. George s Channel, arising from wind events over the Celtic Sea, in controlling the flow in the North Channel and deep regions of the Irish Sea is also considered. The series of calculations presented here helps to explain the spatial and temporal variability of the observed flows (from both direct measurements and tracer studies) found off the west cost of Scotland and in the North Channel and the Irish Sea. 1. Introduction Although three-dimensional models of the European Continental Shelf are now well established and have been used to examine tidal currents (e.g., Lardner 1990; Davies et al. 1997c; Davies et al. 1997a,b, and references therein) and wind-driven flows (Davies et al. 2000) in some detail, the grid resolution of these models (of order 12 km) has been insufficient to accurately resolve the spatial variability of the flow along the west coast of Scotland, through the North Channel, and in the Irish Sea (Figs. 1a,b). A detailed study of the wind and open boundary forced response of the Irish Sea in isolation using a high-resolution model (of order 3 km) was performed by Davies and Lawrence (1994). A similar study of the region off the west coast of Scotland was made by Xing and Davies (1996a). Although models of these regions in isolation yielded insight into the role of wind direction, bottom topography, and open boundary forcing in determining the dominant flow paths in the regions, they could not examine the spatial variability of the flow in the North Channel, which connects the two regions and the interactions between the two sea areas. Initial measurements of transport in the North Chan- Corresponding author address: Dr. Alan M. Davies, Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead, Merseyside CH43 7RA, United Kingdom. E-mail: amd@pol.ac.uk nel were made by Prandle (1976). Subsequently, detailed measurement of currents across the North Channel (Howarth 1982; Brown and Gmitrowicz 1995; Knight and Howarth 1999) have shown that there is significant horizontal variability in the North Channel, which can only be resolved in a numerical model if the grid is sufficiently fine in this region. Measurements in the channel suggest that there is a long-term persistent southerly flow on the western side of the channel that can transport Atlantic water into the Irish Sea on this western side (Edwards et al. 1986). Also, measurements within the Irish Sea suggest an intermittent southward flow in the western Irish Sea; but whether this is coherent with the southerly flow through the North Channel remains unanswered. On the eastern side of the North Channel, measurements suggest that there is a long-term persistent northerly flow that transports material out of the Irish Sea. This northward flow is clearly shown from the monitoring of the Caesium 137 isotope which is discharged into the northern Irish Sea from a nuclear reprocessing plant at Sellafield, United Kingdom (Fig. 1b), from tracer studies (McKay et al. 1986) and measurements (Hill and Simpson 1986). This Irish Sea water is transported northward along the Scottish coast in the shallow (depth 100 m) inner shelf region. Measurements made by Howarth (1982), both in the North Channel and off the north coast of Ireland, suggest that the eastward flow along the north coast of Ireland can bifurcate with some 2003 American Meteorological Society

58 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 33 flow going southward into the North Channel, with a part moving northward along the Scottish coast. This northward movement is confirmed by tracer studies in the area. By correlating current measurements in the North Channel area and along the west coast of Scotland with wind forcing, the magnitude and direction of the wind has been shown to be important in determining the flow through the North Channel with the maximum flow in the area corresponding to winds aligned with the channel (Howarth 1982; Brown and Gmitrowicz 1995). In this paper we use a high-resolution 1 20 north south and 1 15 west east three-dimensional model of the Irish Sea, the region off the west coast of Scotland, and the adjacent shelf edge area (Fig. 1a). Examined are the influence of local wind direction (i.e., winds over the region of the model) and far-field influence, namely, flow from the Celtic Sea into the Irish Sea upon flow through the North Channel, within the Irish Sea, and along the west coast of Scotland. The three-dimensional model is fully nonlinear and assumes a homogeneous sea region (a valid approximation during major wind events). Vertical eddy viscosity in the model is computed using a two-equation turbulence energy closure method (Blumberg and Mellor 1987). The model can be forced with tidal input through the open boundaries, and external flow at the southern end of the Irish Sea. In the calculations described subsequently, in addition to open boundary forcing, motion was induced by the wind. By this means, processes controlling flow in the region can be determined. The model covers a range of water depth, from oceanic (of order 1000 m) to shallow eastern Irish Sea (water depths below 25 m). Water depths in the North Channel change rapidly from shallow (of order 50 m) near coast to depths of up to 280 m in the center of the North Channel (Figs. 1b, 2). In the next section, a brief overview of the hydrodynamic model, and the numerical solution of the equations, is given. Subsequent parts of the paper consider wind-induced flows in the area and far-field effects. A final concluding section summarizes the main points from the calculations. 2. The three-dimensional model FIG. 1. (a) Three-dimensional grid of the numerical model with marked positions indicating where the current profile is examined in detail. (b) Geographical location of various regions named in the text. a. Hydrodynamic equations and turbulence energy model The three-dimensional equations for a homogeneous sea region expressed in transport form using a sigma coordinate, [ (z )/H ], in the vertical are given by

JANUARY 2003 DAVIES AND XING 59 FIG. 2. Bottom topography in the area covered by the model showing the 25-, 50-, 100-, 120-, 200-, 600-, 1000-, 1400-, and 1800-m contours. Hu Hu (HuV) fh t 1 Hu gh K m (1) 2 x H H H (H V) fhu t 1 H gh K m (2) 2 y H 0 (HV) d 0. (3) t 1 In these equations, V (u, ) and (u,, ) are the velocity components corresponding to the (x, y, ) coordinates; H h is the total water depth; is the elevation of the sea surface above the undisturbed level; z is the vertical coordinate increasing vertically upward, with z the free surface and z h the sea bed; f is the Coriolis parameter; g is the gravitational acceleration; t is time; and K m is the vertical eddy viscosity coefficient. The two-equation model given by Blumberg and Mellor (1987), which involves prognostic equations for the turbulence energy and mixing length, is used to determine the vertical eddy viscosity. FIG. 3. Computed major and minor axis of M 2 surface current ellipse at every second grid point. b. Boundary conditions At land boundaries a condition of zero flow normal to the coastline is assumed, with a zero flux of q 2 (turbulence energy) and q 2 l (with l being mixing length) at both land and open boundaries. Tidal energy enters the region through the open sea boundary where a radiation condition involving both elevations and depth mean currents is applied. This radiation condition is such that an external flow V f can be specified at an inflow boundary to examine how this influences the solution. At outflow boundaries water can leave the region through the radiation condition. Such a boundary condition proved stable with little or no reflection of energy. [Details of the radiation condition can be found in Davies and Lawrence (1994), with an overview of the numerical problems associated with open boundary conditions in the review articles of Davies et al. (1997a,b); further details will not be given here.] A slip condition is applied at the seabed at a reference height z h above the seabed, and the bed stress components F B and G B are related to the bottom currents u h and h using a quadratic condition, namely, 2 2 1/2 FB k u h(uh h ), (4) 2 2 1/2 GB k h(uh h), with being density of sea water, and k a drag coefficient given by K 0 2 k, (5) lnz /z h 0

60 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 33 FIG. 4. Currents at every second grid point at (a) sea surface, (b) depth mean, (c) depth mean (expanded), and (d) residual elevation computed with a southeast wind stress of 0.2 N m 2. In the case of the depth mean currents, an expanded version of the flow in the North Channel and Irish Sea is presented, with current vectors at every grid point. where K 0 is von Kármán s constant and z 0 the bed roughness. In the turbulence energy submodel a boundary condition, including the balance of the turbulence production, dissipation, and diffusion formulated by Xing and Davies (1996b), is used at the bed to compute the vertical derivative of the turbulence energy. [Details are given in Xing and Davies (1996b) and will not be re-

JANUARY 2003 DAVIES AND XING 61 TABLE 1. Summary of various parameters used in the calculations. Calculation 1 2 3 4 5 Wind direction Southeast Southwest No Southeast Southwest Inflow to south of Irish Sea No No Yes Yes Yes peated here.] The mixing length l tends to z 0 at the seabed and a roughness length z s at the sea surface in the case of wind forcing. For wind-driven flow the surface stress in the model equals the external wind stress and there is a source of surface turbulence related to the surface wind friction velocity (Davies et al. 2001a,b). In the absence of wind forcing, the surface boundary condition is one of zero surface stress and zero derivative of turbulence energy. c. Numerical solution The numerical solution of the three-dimensional hydrodynamic equations was accomplished using a staggered finite difference grid in the horizontal, with a nonuniform grid (having enhanced resolution in the surface and bed layers) in the vertical. A time-split integration method was used, with an implicit solution for the vertical diffusion term. Implicit methods were also used in the turbulence energy equations. Since extensive details of the numerical solution of these equations can be found in Davies et al. (1997a,b) and Davies et al. (1995), they will not be repeated here. 3. Wind-forced motion a. Overview In the calculations presented here the model was forced by a wind stress of 0.2 N m 2, approximating a monthly mean stress due to a moderate wind. Two orthogonal components of the wind direction were taken, namely, a wind aligned with the North Channel (taken here as a wind from the southeast, calculation 1) and one in the cross-channel direction (taken as a southwest wind, calculation 2), in order to relate steady-state model flow fields obtained with uniform winds to the flow fields measured by Brown and Gmitrowicz (1995), Howarth (1982), and their conclusions concerning alongand across-channel winds. It is not the intention here to simulate the observations of Brown and Gmitrowicz (1995) or Howarth (1982), but rather to understand the factors, namely, how the wind direction, resulting elevation gradients, bottom topography, and flow from the Celtic Sea, influence the currents in the North Channel, within the Irish Sea, and along the west coast of Scotland. Since the tidal elevations and currents are significant in the region, with M 2 tidal elevations as large as 2.7 m (Davies et al. 1997c), and tidal currents are up to2ms 1 (Fig. 3), the tidal input was included in the model in order to determine the correct level of background friction. The residual wind-driven flow was then obtained by subtracting a harmonically analyzed tideonly solution from one forced by tide and wind. By this means, tidal and wind-driven residuals can be separated. To avoid exciting inertial oscillations the model was started from a state of rest with the wind stress increased gradually over three inertial periods. A near steady-state wind-driven circulation occurred after about 10 days from which the wind driven residual was obtained. b. Wind from the southeast The computed surface current (Fig. 4a; current vectors are shown at every second grid point) induced by a southeasterly wind (calculation 1, Table 1) shows a uniform flow field in essence in the direction of the wind. Away from the surface layer the depth mean [Fig. 4b; current vectors every second grid point], expanded version [Fig. 4c; current vectors every grid point], and bottom currents (not presented) show a northward flow across the whole width of the North Channel with no evidence of the flow going to the south in the deep Irish Sea region. A detailed comparison of depth mean and bottom currents (not presented) showed that the main features of the flow fields were comparable. However, bottom currents had a reduced magnitude from the depth mean currents due to frictional effects. In all subsequent calculations only the depth mean current will be presented. Along the west coast of Scotland, at depth, a northward flow is evident [Fig. 4b]. In the sea region off the west coast of Scotland some flow passes northward through the Minch channel. Topographic effects in the Sea of the Hebrides (Fig. 1b) cause a weak southward flow along the eastern side of the Hebrides, which subsequently flows westward, and then northward in the vicinity of the shelf edge, with a small circular gyre located to the southwest of the Hebrides. Observational evidence (Hill 1993) and results from radioactive tracer studies (McKay et al. 1986) exist to support the main features of the flow field found in the model and the location of the gyres in this region. Contours of surface elevation (Fig. 4d) show a small increase of the order of 2 cm along the Scottish coast, with a decrease of the order of 8 cm in Liverpool Bay. In essence, the primary effect of along-channel wind is to drive water through the North Channel. This flow pattern is particularly interesting in that it relates to the transport of material discharged in the Sellafield area through the North Channel. From the figure and a detailed analysis of results, currents were in the same direction at all depths. Consequently, any pollutants discharged into the coastal region in the area of Sellafield will be transported northward leaving the Irish Sea through the North Channel, under southeast wind conditions. This, however, is not true for all wind directions. Calculations (not presented) showed that for all wind

62 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 33 FIG. 5. As in Fig. 4 but for a southwesterly wind stress. cases in deep water, the surface current in essence followed the wind direction. However, in shallow water, bottom friction influences the direction of surface current. Also in regions where there was an onshore wind, with an associated coastal setup, the bottom current was often in the opposite direction to the surface current. (See, e.g., the Sellafield region with a wind from the southwest, presented later.) Under such conditions the depth at which a pollutant is discharged into the water column has a significant influence upon its transport

JANUARY 2003 DAVIES AND XING 63 not give rise to significant elevation gradients. However, in the region of the north coast of Wales and Liverpool Bay, the wind direction is such as to produce an offshore flow at the surface (Fig. 4a), with a compensating flow at the bed (not shown) forced by the local elevation gradient, which is shown in Fig. 4d. c. Wind from the southwest Surface currents computed with a southwesterly wind (calculation 2, Table 1) are, in essence, aligned with the wind direction in deep water (Fig. 5a) where surface elevation gradients (Fig. 5d) are negligible and bottom frictional effects are small. In regions such as the Irish Sea where there is a buildup of elevation gradients against the coast of England (Fig. 5d) and bottom frictional effects have an influence, the surface currents in certain regions (e.g., to the west of the Isle of Man) are not aligned with the wind direction but are deflected to the right (Fig. 5a) by the southerly, pressure-driven depth mean current (Fig. 5b). Depth mean and bottom currents (not presented) show significant spatial variability (Fig. 5b) with a strong flow (stronger than for the previous wind direction) going northward toward the Scottish coast from the north of Ireland, with the typical recirculation pattern in the Sea of the Hebrides, and a northward flow through the Minch. Flow through the North Channel [Figs. 5b,c], both depth mean and bed, is very small, with a southward flow in the center of the Channel. Consequently, pollutants from the Sellafield region are less likely to leave the Irish Sea through the North Channel under these wind conditions. Although there are significant east west elevation gradients off the west coast of Scotland and in the eastern Irish Sea that drive the strong (of order 20 cm s 1 ) current shown in Fig. 5b, there is only a small north south elevation gradient across the North Channel, with a corresponding small flow in the region. Within the Irish Sea itself, a northward flow is evident along the English coast, subsequently flowing to the west to the north of the Isle of Man, but then flowing southward to the west of the Isle of Man. FIG. 6. (a) Depth mean currents and (b) residual surface elevation gradients induced by a flow V f 0.1 m s 1 in the radiation condition at the southern end of St. George s Channel. pathway. This is examined later in connection with surface and bottom boundary layers. The alignment of this wind with respect to the coast is such that in many regions it is approximately parallel to the coast and does d. Summary These model results help to explain the findings of Brown and Gmitrowicz (1995), Howarth (1982), Knight and Howarth (1999), namely, that the maximum outflow from the Irish Sea through the North Channel occurs in response to wind aligned with the direction of the channel. Such winds not only drive water in the surface layer from the Irish Sea through the North Channel, but also give rise to significant depth mean northward flows. In the case of the cross-channel winds, there is only a small amount of along-channel flow in the direct surface winddriven layer, and no significant elevation pressure gradient is set up in the region of the channel (Fig. 5d). The pressure gradients that are set up (Fig. 5d) in the

64 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 33 FIG. 7. Currents at (a) sea surface, (b) depth mean, and (c) residual elevation induced by a flow V f 0.1 m s 1 through the radiation condition at the southern end of St. George s Channel and a southeasterly wind stress. Irish Sea, although driving a westward transport to the north of the Isle of Man, effectively prevent the northward movement of this water through the North Channel. Similarly, there is no significant northward flow into the North Channel in the area of the Firth of Clyde. In essence, there is a small southward flow in the deep areas of the North Channel. This series of calculations has clearly shown that the direction of the wind fields and the resulting elevation pressure gradients have a significant influence on the

JANUARY 2003 DAVIES AND XING 65 FIG. 8. As in Fig. 7 but with a southwesterly wind stress. magnitude and spatial variability of flow in the area of the North Channel, with the direction of the flow at depth being related to topographic features. However, in this series of calculations no effects of the inflow at the southern end of the Irish Sea through St. George s Channel have been considered, although Davies and Lawrence (1994) demonstrated the importance of this upon the circulation of the Irish Sea. Such inflows can arise due to shelf-wide wind effects (Davies et al. 2001a,b; 2000).

66 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 33 4. Flow through St. George s Channel West coast storm surge calculations (e.g., Davies and Jones 1992) have shown that major wind events over the Celtic Sea region can drive water northward into the Irish Sea. Also, more idealized calculations (Davies and Lawrence 1994) using a limited area Irish Sea model have shown the importance of an inflow through St. George s channel upon the circulation of the Irish Sea. To examine what influence this has upon the flow through the North Channel, it is instructive to repeat some of the previous calculations with an inflow V f of the order of 0.1 m s 1 at the southern end of the Irish Sea (calculation 3, Table 1). Currents produced by forcing the model with an input (V f 0.1ms 1 ) to the radiation open boundary condition at the southern end of the Irish Sea [in a similar manner to that described in Davies and Lawrence (1994)] exhibited identical horizontal variations at all depths. Since these currents did not show a high degree of vertical variation (except for frictional retardation in the near bed region), only the depth mean current (Fig. 6a) is given here to illustrate the spatial variations. A region of northward flow is clearly evident (Fig. 6a) following the deep channel (Fig. 2) in the western Irish Sea, with little flow entering the eastern Irish Sea, where water is shallower and frictional effects are larger due to the strong tidal currents in the area (Fig. 3). A strong northward flow is evident off the west coast of the Isle of Man and through the North Channel, although this flow does not appear, unlike in the wind driven cases, to produce a circulation within the Clyde Sea. However, the flow pathway along the west coast of Scotland is not significantly different from that found with the southeast wind [Fig. 4b], with part of the flow continuing northward through the Minch, with a southward flow along the eastern side of the Hebrides in the region of the Sea of the Hebrides, and a subsequent northward flow to the west of the Hebrides (Fig. 6a). The associated residual elevations (Fig. 6b), show a significant elevation gradient in the region of the North Channel with elevations decreasing from 12 cm to the northwest of the Isle of Man, to the order of 4 6 cm in the region off the north of Ireland and west of Scotland. An elevation gradient of the order of 4 cm is evident across the region of the deep channel in the western Irish Sea, with no evidence of an elevation gradient in the eastern Irish Sea. The presence or absence of these elevation gradients explains why strong or weak currents exist in certain regions due to the northward flow into the Irish Sea, which would arise from wind events over the Celtic Sea area. To consider the interaction of this externally forced flow with local wind-driven flows, and in particular how this influences the flow in the North Channel, two further calculations were performed. In an initial calculation (calculation 4, Table 1) the circulation produced by the addition of a southeast wind was examined. Surface currents (Fig. 7a) in the deep ocean region and in the eastern Irish Sea were not significantly different from those found previously with southeast winds alone (Fig. 4a). However, in the deep water regions of the Irish Sea, in the North Channel, and along the west coast of Scotland the surface current is enhanced (Fig. 7a) by the flow entering through St. George s channel, which is to first order aligned with the wind-driven flows in these regions. Surface elevation gradients (Fig. 7c) are to first order a linear combination of those produced by wind forcing (Fig. 4d) and external flow (Fig. 6b). However, in shallow water regions such as the eastern Irish Sea, additional flow in this area produced by the wind (cf. Fig. 7b with Fig. 6a) changes the spatial distribution of bed stress over the Irish Sea, and this affects the local elevation gradients with resulting changes in bottom (not shown) and depth mean currents [cf. Fig. 7b with Fig. 4b]. Although the nonlinear form of bottom friction means that strictly the two flow fields cannot be linearly combined to give the flows shown in Fig. 7b, it is evident that these flows can be interpreted to first order as a combination of Figs. 4b and 6a. Comparing Fig. 7b with Fig. 4b, it is evident that the northward winddriven flow through the North Channel and along the west coast of Scotland is enhanced by the northward flow through St. Georges Channel. However, the circulation of the eastern Irish Sea is largely unaffected by the St. Georges Channel flow. This suggests that under these conditions, flow in the eastern Irish Sea can be simulated without taking account of flow from the Celtic Sea, although in any simulation of measured currents in the North Channel at times of strong northward flow in the area it will be necessary to account for wind effects over the Celtic Sea and the flow they drive northward into the Irish Sea. In a subsequent calculation (calculation 5, Table 1), a southwesterly (cross channel) wind stress was applied. As previously, surface currents in the deep ocean (Fig. 8a) are not affected by the northward flow through St. George s Channel. However, in the western Irish Sea the west east alignment of the surface current found previously (Fig. 5a) in deep water is replaced by a surface current aligned with the wind direction (Fig. 8a). However, there is no difference in the surface current in the eastern Irish Sea. The reason for these changes can be understood as a linear combination of the external FIG. 9. Computed u and current profiles, and time series of turbulence and viscosity at four points (Fig. 1) computed (a) with only tidal forcing and (b) with tidal and a southerly wind forcing.

JANUARY 2003 DAVIES AND XING 67

68 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 33 FIG. 9.(Continued)

JANUARY 2003 DAVIES AND XING 69 FIG. 9.(Continued)

70 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 33 FIG. 9.(Continued)

JANUARY 2003 DAVIES AND XING 71 flow shown in Fig. 6a, which when added to the surface current shown in Fig. 5a changes the orientation of the currents in the deeper parts of the western Irish Sea, through the North Channel, and along the west coast of Scotland. Within the eastern Irish Sea the external winddriven flow is negligible (Fig. 6a) and does not affect the wind-driven flows. The southward depth mean and bottom currents (not shown) found in the deep parts of the western Irish Sea without an inflow from the Celtic Sea (Fig. 5b) are imposed by the inflow, giving rise to a weak (of order 5cms 1 ) spatially variable northward flow (Fig. 8b) in this area when the flow into the Irish Sea from the Celtic Sea through St. George s Channel is included. This input increases the northward flow through the North Channel and along the west coast of Scotland and through the Minch at all water depths (cf. Fig. 8b with 5b). In the region just to the north of Ireland, the wind-driven flow along the west coast of Ireland (Fig. 5b) is enhanced by the flow through the North Channel (Fig. 8b) producing a flow to the north in this region. Calculations with other wind directions (not presented) showed that the flow field in this region was a balance between the coastal flow from the west of Ireland and the flow through the North Channel. Wind direction, coastal setup, together with inflows through St. George s Channel had a major effect upon the flow paths to the north of Ireland. The strong southwestward flow in the Sea of the Hebrides off the east coast of the Hebrides opposes the direct northeastward wind-driven flow in this region producing a region of reduced surface currents (Fig. 8a) in the western half of the Sea of the Hebrides and to the southwest. As in the previous calculation, the flow fields and residual elevation distributions (Fig. 8c) can be regarded to first order as a linear combination of those due to an external flow (Fig. 7c) and the windinduced response (Fig. 5d). This calculation, together with the previous one, clearly illustrates that the magnitude of the flow through the North Channel not only depends upon the alignment of the local winds with the channel and the associated elevation gradients, but is influenced by the inflow into the Irish Sea from the Celtic Sea, which will be affected by wind events in this region. In the previous sections we have been mainly concerned with circulation in the horizontal, as a means of moving water masses from one region to another. However, as shown by the near horizontal uniformity of the surface currents, and their higher velocities, material in the surface layer is not constrained by topographic effects. If the surface layer is thick enough and vertical mixing is significant, then material can be advected from one region to another by direct wind-driven surface advection, with vertical mixing diffusing it down from the surface layer. To gain some insight as to the thickness of the surface layer, and the intensity of wind-driven mixing, in the next section we will examine current profiles and time series at four locations. 5. Mixing intensities and thickness of the surface and bed boundary layer Profiles of the u and components of current, and time series of turbulence energy and viscosity over two tidal cycles at a number of positions 1 4 (Fig. 1) computed with tidal forcing only are shown in Fig. 9a. These points span a range of water depths from h 372 m (position 1) located to the west of the shelf break, with position 2 located to the northwest of Ireland in a water depth h 42 m. Two other points, position 3 in a water depth h 155 m, in the North Channel, and position 4 with h 43 m, are located in areas of strong tidal currents (Fig. 3). Profiles of the u and components of velocity at positions 1 and 3 in deep water show a region of nearly constant tidal current above a thin (of order 10 m) bottom boundary layer where the tidal current magnitude is decreased by frictional effects. At position 1 in deep water the tidal current strength is small (less than 10 cm s 1 ) and, hence, the shear production of turbulent energy is small and concentrated in the bottom boundary layer, with maximum turbulence occurring at times of maximum flow. The product of mixing length [which is small in the surface and bed regions although larger at middepth (Xing and Davies 1996a,b)] with the turbulence energy produces the time variation of viscosity and the maximum viscosity near midwater (Fig. 9a). The shear production of turbulence at the seabed is a maximum near the time of maximum flow, with turbulence diffusing away from this region, producing a maximum higher in the water column at a later time (Fig. 9a). At positions 2 and 4 located off the west coast of Ireland and in the Irish Sea, the water depth is much shallower and the u component of current dominates. At these locations turbulence energy in the upper part of the water column is much larger than in the deep water sites, since in shallow water the surface is much closer to the turbulence production region. The nonlinear terms in the hydrodynamic equations produce a tidal residual flow at these locations (see later). The magnitude of the tidal residual is larger at the surface than the bed and gives rise to the mean flow, which can be clearly seen in the profiles of the velocity at these locations. The addition of a wind from the south increases the magnitude of the northward component of flow in the surface layer at all locations. At position 1 in deep water, a northward flow occurs at all depths (Fig. 9b) with the north component of current increasing in the surface layer. An increase in the u component due to rotational effects is also evident with surface turbulence energy increasing significantly due to surface shear production of turbulence, and a surface source depending upon wind friction velocity. The mixing length in the surface layer, however, remains small, and this prevents any significant change in surface eddy viscosity.

72 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 33 6. Tidal residuals FIG. 10. Spatial distribution of the depth mean tidal residuals. At position 3 in the North Channel an increase in near-surface turbulence and velocity is clearly evident (cf. Fig. 9b with 9a) although it is restricted to the surface layer. In shallow water regions (positions 2 and 4), the southward tidal residual flow in the surface layer particularly at position 2 is opposed by the northward wind-driven flow; although as in the deep water locations, this effect is limited to the top 10 15 m, with turbulence energy and viscosity increasing in these regions. These calculations suggest that at the wind speeds considered here the direct wind-driven surface layer and associated turbulence mixing layer is confined to a region of 10 15 m. In shallow water (of order 40 m) material moving in this layer represents a significant fraction of the total transport. Also, the increased turbulence in this region allows for enhanced diffusion of material into this region, suggesting that it is not just the flow paths followed by the depth mean current that will influence the movement of material in shallow water, but that the direct wind-driven surface layer will be important, particularly at higher wind speeds where its thickness will increase. In the previous sections we have examined the windinduced residual in the region of the North Channel and how it would advect material from the eastern Irish Sea northward. Besides the long-term movement of material by the wind-induced residual, it is instructive to examine the tidal residual in the region. From a comparison of surface, bed, and depth mean tidal residuals, it is apparent that there is no significant change in the direction of flow, with tidal residuals at the sea bed being smaller than those above the bottom boundary layer due to frictional effects. Here we will concentrate on the depth mean flow (Fig. 10), since this is representative of flow in the majority of the water column. It is evident from Fig. 10 that there is a strong (of order 10 cm s 1 northward residual along the Irish Coast, north of 54 N, although to the south of 54 35 N the flow is to the south. A southward flow along the English coast in the southern part of the eastern Irish Sea connecting to a westward flow along the Welsh coast is evident in the Liverpool Bay region with two gyres to the northwest of Anglesey, United Kingdom, arising from the large advective terms in this region. A counter-clockwise gyre exists in Morecambe Bay of a similar magnitude and extent to that found by Davies and Jones (1995) using a 1-km grid of the eastern Irish Sea. To the north of Morecambe Bay there is a weak (of order 5 cm s 1 ) northward residual flow, although farther offshore this is to the south. Again, this is in agreement with results from the 1-km models, although these higher resolution models predicted a stronger near-shore northward flow. A complex gyre system is evident in the region to the north of the Isle of Man, associated with the corners in the finite difference grid used to represent the coastal boundary in this area. Due to this problem and the lack of resolution in this region, it is difficult to attribute a great deal of physical significance to this flow field. As shown by Davies and Jones (1996) using a high-resolution (1-km grid) model of the eastern Irish Sea, grid resolution is particularly important in the near-coastal region in order to accurately resolve the near-shore region. In this area the tidal residual is largest and influenced by the finite difference representation of the coastal boundary. Also, within the North Channel itself there does not appear to be a coherent pattern in the tidal residuals, with large, up to 0.3 m s 1, tidal residuals occurring in the North Channel at 55.2 N, associated with the strong tidal currents in these regions. However, the grid resolution and representation of the coastline is poor in this region, suggesting that there may be major inaccuracies in the model in this area. These numerical problems suggest that a significantly finer grid than the one used here is required to accurately resolve the tidal residual in this region. Also, the inclusion of a horizontal viscous term is required (at present not included) to control the buildup of grid-scale energy due to the nonlinear terms.

JANUARY 2003 DAVIES AND XING 73 7. Concluding remarks In the initial part of this paper we have briefly described the three-dimensional numerical model and turbulence energy submodel used to examine the windinduced flow in the region off the west coast of Scotland and the Irish Sea. By using a model with a high horizontal resolution covering both areas, rather than a separate model of the west coast (Xing and Davies 1996a) or the Irish Sea (Davies and Lawrence 1994; Xing and Davies 1996b), the effects of flow in one region upon the other can be studied in detail. Also, this high-resolution model enables the spatial variability of the flow in the North Channel that connects the two areas to be considered in detail. To first order, major features of the model can be related to simple analytical models: in particular the separation of wind-forced flow, into a direct local wind component (in essence, the wind drift current) having its greatest influence on surface currents, and far-field winds, which set up elevation gradients against coastlines. These gradients force a uniform flow in the vertical, with bottom friction and the associated bottom Ekman layer together with the surface Ekman layer determining the vertical profile. Although a coarse grid model can represent the gross features of the influence of coastline and topography upon the flow, the fine grid model presented here is essential to resolve such features as the North Channel, and the area of the Minch, et cetera, which are essential together with the small-scale topography in determining the flow pathways. Also, by using a wind field aligned with the North Channel and its orthogonal component, the importance of wind direct and far-field flows through St. George s Channel upon the west coast flow region as a whole can be determined to a degree that is not possible with a limited set of observations (Howarth 1982; Brown and Gmitrowicz 1995; Hill and Simpson 1986; Knight and Howarth 1999). The high spatial variability of the flows emphasize the need for accurate topography and a comprehensive deployment of current meters over a large area for model validation. Initial calculations with uniform wind fields have shown that wind direction, the resulting elevation pressure gradients, and the effects of topographic steering determine the flow paths off the west coast of Scotland, within the Irish Sea, and through the North Channel. The complexity of the horizontal variability found with the model even in the steady state with a uniform wind forcing explains the difficulties found by experimentalists (Howarth 1982; Hill and Simpson 1986; Brown and Gmitrowicz 1995) in trying to determine the flow pathways in the region from a limited set of observations. The fact that the flow direction along the west coast of Scotland and within the Irish Sea is significantly influenced by topography helps to explain the success of the model in determining the location of the gyres reported by Hill (1993) and the features of the flow fields inferred from tracer studies and other measurements in the region (McKay et al. 1986; Ellett 1979; Edwards et al. 1986). Of particular interest is the importance of a northward flow entering the Irish Sea through St. George s Channel, as a result of wind events over the Celtic Sea region. The model results clearly show that this can block the southward flow through the North Channel. Also, the interaction of this flow with the surface wind-driven flows shows that in some regions it can modify the direction of the flow in the surface layer and, hence, change the transport pathways of material in this layer. In terms of the long-term flow of material from the Irish Sea through the North Channel, it is clear that the tidal residuals are important and must be accurately reproduced in this region. Also, from the detailed study of the wind-induced flow in the region of the North Channel, in particular in the area between the Isle of Man and the North Channel, it is clear that there is significant spatial variability in the wind-induced flow fields in this region that must be accurately resolved in order to correctly advect material from the eastern Irish Sea through the North Channel. The more uniform nature of the wind-induced flow in the area between the North Channel and the western Irish Sea suggests that model resolution will not be so crucial in this area. The spatial and temporal complexity of the flow found in the North Channel measurements (Howarth 1982; Brown and Gmitrowicz 1995) can be readily understood in terms of the magnitude and direction of the wind over the region covered by the model, and far-field events such as the magnitude of the current into the Irish Sea from the Celtic Sea region. These results suggest that in order to accurately model the spatial distribution and magnitude of the flows through the North Channel, a high-resolution model (of order 1 km) of the area is required. Recently, such a model has been developed (Davies et al. 2001a) with boundary conditions supplied by a model having a grid resolution comparable to that given here, nested within a shelf-wide model. Calculations showed that the accuracy of the meteorological forcing both magnitude, direction, and temporal change is crucial in determining the correct balance between forcing over the Malin Shelf and the Celtic Sea Irish Sea region. Any inaccuracies in this balance give rise to errors in the pressure gradients across the North Channel and, hence, the flow in the channel. The present calculations have concentrated upon the wintertime when the region is well mixed, although a recent modeling study with a baroclinic model of the Irish Sea (Xing and Davies 2001) showed that stratification effects are important in summer. Acknowledgments. The authors are indebted to Mr. R. A. Smith with help in preparing diagrams and Mrs. L. Ravera and Mrs. L. Parry for typing the text.

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