C05S90 PERLIN ET AL BOTTOM EKMAN LAYERS C05S90, layer thickness is estimated as 0 4u f when u is computed from log profile using. and in turn influences velocity veering Pollard et al. Array of current meters 1 9 m and 50 m above the bottom Veering is registered. 1973 have argued that in the presence of stratification. The same as above plus ADCP Acoustic Doppler Current Profiler data Ekman. the height, p of the Ekman layer is governed not by u f but. Temperature conductivity and velocity data with 5 m vertical resolution to. Temperature conductivity and velocity data with 3 m vertical resolution to. Array of current meters Veering is registered only between current meters. by u Nf when N f where N is the stratification of the. layer adjacent to the mixed layer representing the ambient. stratification Observational evidence of the modification of. Measurements with current meters 5 and 20 m above the bottom. within 5 m from the bottom Estimation of friction velocity is. the Ekman layer in the presence of stratification can be found. elsewhere For example Price and Sundermeyer 1999, showed that the Ekman spiral in the surface boundary layer. was thinned by stratification and that the wind driven trans. Ekman layer is contained below the strong halocline. port was trapped mainly within the upper part of the Ekman. layer Weller and Plueddemann 1996 showed that the, Ekman transport was concentrated above the pycnocline. based on assumption of simple Ekman, between 1 and 9 m above the bottom. and was divided almost equally between the surface mixed. layer and a weakly stratified layer immediately below and. at 1 and 3 m above the bottom, that the diurnal cycle in mixed layer height affects the. within 3 m from the bottom, velocity structure inside the Ekman layer. layer momentum balance, 7 We have recently suggested a modification to the law. of the wall MLW that is intended to account for the. current meters data, suppression of turbulence by stratification away from the. boundary but within an unstratified boundary layer Perlin. et al 2005b We have concluded that the MLW predicts. significantly different velocity and turbulence dissipation. profiles than the law of the wall theory and agrees reason. ably well with the measured data in the lower 60 70 of. the bottom mixed layer versus 20 30 for the law of the. velocity and f is the Coriolis parameter, wall We have arrived at this conclusion by comparing the. 0 3 0 4 f where u is the friction, measured and modeled velocity and turbulence dissipation. rates profiles Here we extend this analysis to consider. Height of the Ekman Layer, rotation and apply the MLW in the form of eddy viscosity. formulation to investigate Ekman veering, 8 Specifically we demonstrate that in the presence of. stratification Ekman veering coincides with a clearly. defined turbulent layer Most of the Ekman transport. 20 to 100 m, occurs inside the well mixed layer but also extends into a. Up to 35 m, weakly stratified layer above Data from a broad relatively. flat region of the BBL on the Oregon Shelf are analyzed. The data discussed in section 3 include 3 months of high. resolution measurements of velocity to within 2 75 m of the. sea floor supplemented by 50 h of intensive turbulence and. density profiling measurements to within 2 cm of the sea. floor From these data we quantify the veering angle and the. veering layer height and evaluate dependence of these. Location and Duration of the Experiment, properties on the interior current velocity and the level of. turbulence in the BBL The veering rate change in veering. Oregon coast 1 and 2 months, angle veering layer height has been shown to be nearly. Arkona Basin Baltic Sea, Lake Michigan 4 months, Table 1 Observations of Bottom Ekman Layer. inversely proportional to the veering layer height so that the. Peruvian shelf 2 days, maximum veering angle has only a very weak dependence. two winter seasons, on interior flow velocity and thickness of the BBL Our. Straits of Florida, Lake Michigan, observations have been compared to solutions of the Ekman. Florida shelf, balance using both the law of the wall CRM and the. modified law of the wall Perlin et al 2005b paramete. rizations of eddy viscosity, 2 Definitions and Theory. 9 The BBL typically exhibits weaker stratification and. Lass and Mohrholz, Van Leer 1976, Saylor and Miller. Weatherly 1972, higher turbulence than the interior To characterize the state. Dickey and Van, Kundu 1976, Saylor 1994, Mercado and. of the BBL we define four length scales based on obser. vational criteria Figure 1 The bottom mixed layer D is. defined as the distance from the bottom over which the. potential density decreases by 6 10 4 kg m 3 from its. C05S90 PERLIN ET AL BOTTOM EKMAN LAYERS C05S90, Figure 1 Schematic diagram of different BBL definitions discussed in the text. value at the bottom To avoid the effects of local overturns equations 1 4 is solved given a specified Kv z v and. in the estimation of D we also require the density difference bottom stress. to remain below this threshold value for at least 1 m Above 11 We consider two possibilities for the specification of. the mixed layer there often lies a weakly stratified layer The Kv z First we consider Kv given by the law of the wall. combined mixed and weakly stratified layers is termed. the remnant layer Dr and its thickness is defined as the Kv u kz 5. distance from the bottom over which the potential density. decreased by 3 10 2 kg m 3 At least during upwelling where k is von Ka rma n s constant 0 4 and is a. conditions the top of the remnant layer marks the lower turbulence length scale which increases without bound as z. boundary of the pycnocline The turbulent bottom layer De goes to infinity The analytical solution of 1 5 is given. is defined as the height above the bottom at which the by CRM Second we use the modified law of the wall. turbulence dissipation rate decreases to 6 10 9 m2 s 3 where a stratified boundary layer has an outer length scale. For further details and discussion of mixed remnant and hd that limits the growth of The MLW eddy viscosity is. turbulent layer definitions see Perlin et al 2005a We given by. define the veering layer Dv as the layer that contains a. systematic counter clockwise rotation of the current vector Kv u kz 1 z hd 6. with depth see section 4, 10 Neglecting time dependence nonlinear accelerations for z hd and Kv 0 for z hd The value of hd is chosen to. and baroclinic pressure gradients the horizontal momentum be the largest value such that z o z at all depths. balances in the bottom Ekman layer are given by where the effect of stratification p limiting. the scale of, turbulence is represented by o e N 3 the Ozmidov. ue scale e is the turbulence dissipation rate and N is the. f ve v Kv 1, z z buoyancy frequency at the top of the mixed layer Perlin et. al 2005b Since o 1 within the mixed layer D the, value of hd is determined by the vertical profile of o just. ve above D Based on examination of many profiles on the. z z Oregon shelf we find hd D2 D 1 to be a good, approximation Perlin et al 2005b. where the interior geostrophic flow v is in the direction of. the y coordinate ue ve are velocity components inside the 3 Overview of the Data. Ekman layer the stress is parameterized by an eddy. viscosity Kv and z is the height above the bottom The 12 The observations used in this study come from a. boundary conditions are three month long mooring deployment and a 50 h vertical. profiling time series over the Oregon shelf during the. ue 0 ve v as z 1 3 summer upwelling season of 2001 as part of the Coastal. Ocean Advances in Shelf Transport COAST program, Barth and Wheeler 2005 The mooring was deployed in. ue 0 ve 0 at z z0 4 81 m of water 45 0 010 N 124 7 000 W directly offshore. west of Cascade Head Boyd et al 2002 Currents were. where z0 is a constant of integration frequently termed a observed with two acoustic Doppler profilers an upward. roughness length and is determined when the system of looking RDI 300 kHz ADCP 4 m above the bottom with 2 m. vertical resolution and a downward looking Nortek 2 MHz. C05S90 PERLIN ET AL BOTTOM EKMAN LAYERS C05S90, Figure 2 Time series from the mooring located at 45 0 010 N 124 7 000 W from 16 May to 28 Aug. 2001 which measured a wind stress b eastward velocity c northward velocity and d velocity. magnitude 20 m above the bottom Data have been smoothed by 1 day averages A 50 h Chameleon. profiler time series was started 8 August gray box Veering layer height is shown on b and c with. thick black line defined only when the speed exceeds 0 05 m s at 8 m above bottom and there are no. reversals of northward velocity during averaging period. Aquadopp profiler 9 m above the bottom with 0 5 m vertical 14 The turbulence profiler Chameleon was used to. resolution Due to side lobe interference and acoustic obtain a 50 h time series near the mooring measuring. spreading there are no reliable velocity data within 2 75 m turbulence dissipation rate temperature and conductivity. of the bottom A detailed description of Chameleon and the procedures. 13 The moored velocity data contain tidal and inertial used to process the data can be found in Moum et al. oscillations To isolate the low frequency characteristics 1995 Chameleon has been routinely run into the bottom. of the BBL daily averages of the 3 month data set were permitting profiles to within 2 cm of the seabed which is a. computed Figure 2 Daily averages do not differ necessary condition for estimating bottom stress Perlin et. significantly from the 25 h low passed filtered velocity al 2005b The time series starts during a period of high. Chebychev fourth order Filtered velocity gives very southward flow Figure 3d that has reversed 36 h into the. similar results if used for further analysis We opted to use observation The mixed layer D was thicker 20 m. daily averages for convenience The flow has been predo during the strong flow conditions thinning to less than 10 m. minantly southward upwelling favorable but with occa as the flow slowed Figure 3a The turbulence was also. sional relaxations and even a large reversal in late June larger during the high flow and the thickness of the. Figure 2c Data included in the analysis that follows come turbulent layer De roughly followed the mixed layer. from only those daily averages during which there were no thickness Figure 3b. alongshore flow reversals Since Ekman transport calcu 15 To relate the observations to the momentum balance. lations are sensitive to erratic veering angles at low speeds 1 4 two quantities are needed u and v u has been. all profiles with a speed smaller than 0 05 m s 1 at 8 m estimated directly from the profiles of turbulent dissipation. above the bottom have been excluded from the analysis e z using the dissipation method u h kzi1 3 This method. for computing the friction velocity is described by Dewey and. C05S90 PERLIN ET AL BOTTOM EKMAN LAYERS C05S90, Figure 3 Data from 50 h Chameleon time series collected near the mooring showing a 1 h averaged. density white lines mark mixed and remnant layer heights and b 1 h averaged turbulence dissipation. rate white line marks turbulent layer height Data from the mooring show c low passed second order. Butterworth 21h eastward velocity gray line marks veering layer height and d low passed second. order Butterworth 21h northward velocity white line marks veering layer height Vertical line marks the. time of the profile shown in Figure 6, Crawford 1988 and discussed by Perlin et al 2005b for is based on the quadratic drag approximation u 20. this same data set Direct estimates of u cannot be made CD U20 2 where U. 20 is the velocity measured 20 m above, from the mooring data however two indirect estimates can the bottom Perlin et al 2005b have found that for this shelf. be made based on the velocity time series The first method as a whole CD varies between 4 5 10 4 and 1 6 10 3. C05S90 PERLIN ET AL BOTTOM EKMAN LAYERS C05S90, definition was based on extensive analysis of the individual. veering angle profiles The threshold was defined to be. small enough to identify veering layers with smaller than. average rotation but large enough to exclude random. variation in direction of the velocity above the Ekman. layer Varying the threshold value from 1 h to 11 h deg. m leads to at most a 1 m root mean square RMS, difference in the height of the veering layer Figure 5. which is only a 20 difference for the thinnest veering. 18 An example of the veering of the velocity in a single. profile is shown in Figure 6a The interior current is slightly. above 0 2 m s 1 and flows 185 degrees clockwise from. north Counter clockwise veering starts approximately at. Dv 19 m and reaches 12 at 2 75 m above the bottom, below which we have no velocity measurements The. turbulence is high near the bottom Figure 6b and the. water is well mixed Figure 6c The veering in this, example starts at the depth at which the turbulence is high. Figure 4 Friction velocity computed from Ekman trans 19 It is only during the 50 h Chameleon time series that. port u t vs friction velocity computed from current velocity we can obtain estimates of D Dr and De During this. 20 m above the bottom u 20 Linear regression is shown by period the veering height Dv follows the turbulent layer. Organization of stratification turbulence and veering in bottom Ekman layers A Perlin 1 J N Moum 1 J M Klymak 1 2 M D Levine 1 T Boyd 1 and P M Kosro1 Received 3 August 2004 revised 17 November 2006 accepted 7 December 2006 published 24 May 2007 1 Detailed observations of the Ekman spiral in the stratified bottom boundary layer during a 3 month period in an upwelling season

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