the geostrophic wind is a good approximation for

Found inside – Page 25Moritz (1983, 1986) has shown that the NWS surface pressure analysis, incorporating Arctic buoy pressure data, provides good geostrophic winds. For barotropic PBLs, the surface pressures allow calculation of the geostrophic flow. Found inside – Page 480(5) We note also that a good approximation to the wind speed is the geostrophic wind V, which from equation (1) is given by =? f but the horizontal divergence must not be computed from this equation but from equation (4). Found inside – Page 128Ah ( 26 ) ra ( Vc ) 2 0.98 + fo Vcc = 1.59 g ( a 2 ) If an average geostrophic wind V , is defined as : g 4h , V , = fora ? equation ( 26 ) can be written as : Ira Vcx ? + fo Vcr = 1.6 fov , ( 27 ) 2 to a good approximation . So, if we assume that the geostrophic approximation is valid down to 23.8N, then identical 500mb geopotential height gradients yield markedly different geostrophic wind speeds at varying latitudes. 2) The geostrophic wind is a good approximation for (a) horizontal wind flow in upper atmosphere. %�� To good approximation, the Coriolis force is completely balanced by the pressure gradient, so at a latitude ‚ and with the rotation rate of the earth Ω. ��/\�91֥��v��pw8��/�� ؖHu��˦��8T}4mI6�"�{�́�nz$��G��!դ�0�kōk�e��^鑜�6�4�9�@K��n�6� rK(Nr�5X�|��%��ؕFT��y�I�~xx�|\��׼^f�)��ɛ;.�Q��Rf�4�r�/#�_/��)��q��=U��`I�K]�н�l��2ki�,uӍ�q��L�WY�Y1X��+/(��͈�A�f� 3) The Coriolis effect is an "apparent" force caused by. This is a question about the "geostrophic wind" which dominates the atmospheric circulation at heights exceeding about one kilometer above the ground. Are we missing a good definition for . In order to . �X��lY#��WƵ�japk��l��9�.��!c*O�7��q��Y��V�E|��ilwS�>��@y�Y��)N�� W�}{ɋg�VՍ��C��S��L��n��.A`;+-*>��I|�7�n�k� 8|��=< S;�C\��=82Az>��V�:��=��8"�J/'��&|/��]��BS��7�1&��w�OOq��n�&R�Ï�K�?�H��̟6�F��MM��k\�k��G��t��8�BM�Ge�|�C;��0B�t-�+#��_��6сC��;�.�O1��:��*$-�K��06��il�}�C 1y��e5b6��4d.�׸M�/��0d�j��5�~�3G�I�C* Ou�pI 8��9kY �*��S��2^ڱ=�C��kɧ�P �o��~#��4�pʫ�N��u�Z�%��fxy�w��h +-~��Ӯ��'mE�m�F@��B�P��Cxsq� Click here for the answer. For large scale flow in the upper atomosphere, the pressure gradient force and the coriolis force are the largest forces acting on the air, so the winds tend to be within about 10% of geostrophic balance. Quasi-Geostrophic Approximation Using the fact that the total wind can be divided into geo Found inside – Page 341... the Earth's surface, are similar to geostrophic ones. Among such motions are quasi-geostrophic motions. A quasi-geostrophic motion is an air motion, a real or a hypothetical one, a good approximation of which is a geostrophic wind. The Geostrophic Wind Equation. geostrophic balance. Found inside – Page 402 The geostrophic wind vg is horizontally divergent on pressure surfaces only to the extent that the latitude ... Thus ( g / f ) h is a good approximation to the vertical component of the vorticity of the geostrophic wind if L / a « 1 . The wind that blows because of thermals. Although ageostrophic terms are relatively small, they are essential for the time evolution of the flow and in particular are necessary for the growth and decay of storms. The balance that follows is not obtainable by a rigorous scale analysis as the geostrophic wind is, but it yields a useful conceptual wind model. of the geostrophic wind depending on the density. Gradient wind equation takes into account the centrifugal force due to the curvature of the trajectories, whereas the geostrophic wind tends to only account for the Coriolis parameter. 31 Geostrophic Wind • Geostrophic motion occurs when there is an exact balance between the . (a) horizontal wind flow in upper atmosphere. sure gradients are balanced by the coriolis force on the geostrophic wind so the term on the RHS is only involved in the highest order equation (i.e. Found inside – Page 319Therefore, we are interested in an acceptable approximation for the ageostrophic wind component as described by the ... wind vector by the geostrophic wind vector in the derivative with respect to time provides a good approximation ... Chapter 7 Quasi-Geostrophic Theory In the last chapter we deﬁned the potential vorticity in a number of contexts and showed that in the absence of heating and friction it is a quantity conserved by ﬂuid parcels. However, due to the nonlinearity of the inertial terms, it is always difficult to obtain the analytical solution of the boundary-layer model that retains the flow acceleration. 17. (b) Coriolis force This gives motions, however, the equations o 4 motion - f apo f po dt HWo' where ,!? One of the key assumptions we have made in deriving the QG equations is that the advective wind can be approximated by the geostrophic wind and that the actual vorticity is about equal to the geostrophic vorticity. 2‰Ωvsin‚ = jrpj; (1) geostrophic wind speed. (c) directed from low to high pressure. The temperature gradient in this region is light; however, the wind is directed from cold toward warm air, signifying cold air advection. 4)You are standing in the Northern Hemisphere in a field, facing north, with the wind at your back. Found inside – Page 194Like any approximation to reality, geostrophic balance is only as good as its assumptions. It's often a poor explanation of the winds near the equator because there the Coriolis force is nearly zero and does not balance the PGF by ... There is no friction. . 2.8 Geostrophic and Thermal Wind Balance 93 Fig. The warm wind that blows down the hül on the leeward side. Found inside – Page 35(2.38) ∇p = 1 acosφ ∂p∂λ ,a1 ∂φ∂p ∫ ∫ If we know the pressure, we are able to solve the geostrophic wind equation for vg. This is usually a good approximation to the flow pattern and helps us understand weather maps away from the ... ]��t��z��^'�U��L�� "t�o��P��'�'v T�Ԝϣ �+�b%��?ݷ�.KLeص�\�:x��$�wf�6��BM5d�,��>Pz�5��A��^2ek��R;�� on the ageostrophic wind, which in turn leads to an acceleration of the geostrophic flow perpendicular to the ageostrophic wind. geostrophic) components: V V V g a v v v = + (5) The geostrophic wind (Vg) is defined as: − V f k g o v v 1 (6) Here, fo is a constant Coriolis parameter (see Holton p. 148 for explanation). Found inside – Page 49... is a good assumption for all scales of motion larger than about 1000 km, except very near the equator, where f-0. (3.29) Retaining only the Coriolis and pressure gradient terms in (3.23a) and (3.23b), we obtain the geostrophic wind ... = dfldy, ug, vg are the components of the geostrophic wind, and 5, the geostrophic vorticity, at the equivalent-barotropic level. 8��b.��`�D0_�t8�·��3�� b��T��#�@4�>{5|r��.a��p�`m��v�}?w�,�Y�N:��=�)6~�켽x��(:5�+/[4�ݑr��(p7tثCI��Rz��+�-�m�H�sG�Y"��/��( �KjC��(G�>�g�k�\]��p3S]*B婂�B{\:넽�d[w��o��Q�,��. %�쏢 Found inside – Page 269In the stratosphere, to a good approximation, the geostrophic approximation may be applicable, and the geostrophic wind is related to the horizontal gradient of the thickness. The horizontal equation of motion is given by dv (. Found inside – Page 97At locations where the geostrophic wind provides a good approximation to the wind vector, a map of the geopotential height also provides useful qualitative information about the wind: since the gradient of a scalar field is a vector ... I've yet to come up with a good interpretation of the second term on the right hand side! The geostrophic wind is the natural response of midlatitudinalatmospheric . Found inside – Page 34Cressman ( 10 ) found in two different situations that lines of absolute vorticity lines of relative vorticity also , to a good approximation ) moved with the following percentages of the wind speed normal to the lines : speed of the ... Under this approximation, write out the expression for the geostrophic velocity. The Geostrophic wind is flow in a straight line in which the pressure gradient force balances the Coriolis force. All compared to the reference that is based on 3 wind speeds and 8 wind directions. (c) horizontal wind flow at the earth surface. Although ageostrophic terms are relatively small, they are essential for the time evolution of the flow and in particular are necessary for the growth and decay of storms. The geostrophic wind neglects frictional effects, which is usually a good approximation for the synoptic scale instantaneous flow in the midlatitude mid-troposphere. the gradient wind is a very good approximation of the actual wind •Friction,or turbulent drag, near theground slowsthewind and causes it to blow at an angle across isobars (height contours) from high towards low pressure •Near the surface the geostrophic and gradient wind is not a good approximation of the actual wind ��L��+��"��s7��s�"�M��pQ/��o:��ٓ� �!��]ʇ��{�^�!�g9R�p\�TU�Z�F�h�U.I��r�X��[�/�x��"_� �z�&��K+>��t!��̄[\C��DҸ�5ࢨ��7�H��5Ms� T'��*w�� -�Rm�� ):>�8�%a�&dC��1e@�X��}�O�1Cgۧ��L��d�9\%��~��H;��yx��B)�^� ��pyz�R�y�X��QfK%u�� 2 0 obj (d) West (to your left). The horizontal winds can be approximated by geostrophic winds in the momentum equations. (a) parallel to isobars. On a weather map where isobars are closely packed, the surface winds are likelyto be. At any rate, here's a stab at it. runs studying the influence of the geostrophic wind, calculations where made with 1, 2, 3 and 6 geostrophic wind speeds and with 4, 8, 16 and 32 wind directions. Found inside – Page 16If no winds were available , the geostrophic wind , computed from the pressure field , was used . ... the across - isobar accelerations would be small and the geostrophic wind a good approximation of the real wind , with one exception . Although ageostrophic terms are relatively small, they are essential for the time evolution of the flow and in particular are necessary for the growth and decay of storms. On a weather map where isobars are closely packed, the surface winds are likelyto be. Found inside – Page 6It represents an exact balance between the horizontal pressure gradient force and the horizontal component of the coriolis force . Geostrophic wind scales give a good approximation to the actual wind in the free atmosphere . • The friction force and centrifugal forces are negligible. Part B: The geostrophic vorticity approximation from Eta model grid files. (d) gravity. Found inside – Page 16Every map was considered as depicting the mean winds and pressures for a period of time centered on the time of the map ... would be small and the geostrophic wind a good approximation of the real wind , with one exception . Therefore radio sonde data have !e��'Bc��ݟ�@J{�4�1+��ڗa��V��^3�y��&}��e` ��E�f�>��l8�^��>/`��؎� �8�?_�C��nO��c��N�B�g=E5�MVh��S$!�h��k��|'��zY�K��)Щt��]g-�2[��[�\7ʸY^�n��C$`�+�_�0��QF��F�y8�s@VX�{�d�ӵU.Ǽ�)�g�y�(�1G�-ɄLI�LU��Wޛq{�s��B5y�:a(B M�. 5) Which of the following forces does not affect the horizontal wind? �+I� " qd��Ƥ"�I�_ߙY^�G� d^��ͽ3C�Ϸ��rǦo/��n��n��|Ohp��0��6n^�'��b�NV��x�m>��?6��. 4 0 obj Found insidefOCuS ON aN aDvaNCeD TOpIC 8.3 We know from an earlier discussion that the geostrophic wind gives us a good approximation of the real wind above the level of friction, about 500 to 1000 m above Earth's surface. Thus, students who embrace the concept of the geostrophic approximation "love" the 500 mb chart, because there the wind appears to flow parallel to the contours and in direct proportion to the pressure (or height) gradient. b. b. A less restrictive balance is one that includes the centripetal acceleration terms in the horizontal momentum equations. Trenberth shows that the advection of positive (cyclonic) vorticity by the thermal wind is a relatively good approximation to the sum of the PVA and temperature advection terms of the full omega equation. The results indicate that the numerical data and analytical method are in a good agreement with . The geostrophic wind neglects frictional effects, which is usually a good approximation for the synoptic scale instantaneous flow in the midlatitude mid-troposphere. Found inside – Page 197As mentioned in the preceding chapter, the geostrophic wind has many important uses. It is well known that the vorticity of the geostrophic wind is a rather good approximation to the vorticity of the actual wind, but the divergence of ... 1 0 obj x��ZYo�F~��dPQ܋G� Thus, the feedback of the ageostrophic circulation on the geostrophic flow is taken into account (derivation given in detail in Hoskins 1975 ). Then show that the vertical component of geostrophic vorticity (ζg can be written purely as a function of geopotential height (Φ) Question: The Coriolis parameter is taken as a constant when it appears in the expression for geostrophic wind. . 17. It is also nearly parallel to the 850 hPa height contours, suggesting that the full wind is a good proxy for the geostrophic wind. Vertical wind shear can occur on smaller scales that is not in thermal wind balance, if the flow is highly . AT 351 Lab 8 Air Pressure, Forces, and Upper Level Winds - Geostrophic Wind. The gradient wind is similar to the geostrophic wind but also includes centrifugal force (or centripetal acceleration). ]�|}\�z��,��;�NO��"]1 To a very good approximation, the dominant balance in the atmosphere at large scales is between the pressure gradient force and the Coriolis force. to a good approximation the scale height His approximately constant and has a value of . view of the parameter space in which a balanced model is a good approximation of the full system. Definition of geostrophic wind in the Definitions.net dictionary. You'll notice that, in most places, the ageostrophic component of the wind is relatively light, thus proving that geostrophic balance is a good approximation at 300 mb! Found inside – Page 208In the absence of exact values, AFOAT-1 had to guess, and the only approximation they could make was a bad ... It is well known that the geostrophic wind is at times a poor approximation to the actual wind, giving results as much as 25% ... Why geostrophic balance is a good approximation to the observed wind? Found inside – Page 2801 9.3 Pressure gradients and winds Having reviewed the four forces acting on a parcel of air in the Earth's ... the Coriolis force approaches zero , the geostrophic wind speed is a good approximation to the measured wind velocity . For any identical, 500mb zonal height gradient, the windspeed at Dhaka would be (sin45/sin23.8) 1.75 times greater than at Minneapolis. Found inside – Page 604The second term on the right depends upon the horizontal component of the radius of curvature for zonal flow. Since the absolute vorticity ... In many cases the geostrophic wind gives a sufficiently good approximation to the real wind. • Balance between pressure gradient and Coriolis force → geostrophic balance • The geostrophic wind is a horizontal wind. �e�� 5��. In other words, given the actual wind ($\mathbf v$) and the geostrophic wind ($\mathbf v_g$), the ageostrophic wind ($\mathbf v_a$) is the vector difference between them. stream Remember, the wind barbs here only show the ageostrophic component of the wind, NOT the full wind! • Geostrophic wind: wind on the turning earth: Geo ( Greek) Earth, strophe (Greek) ^turning. The differences between the gradient and geostrophic (or cyclostrophic) winds at r Au are V G - V g 5 (f 21 2 1)V g 5 [(f 2 1 . Science; Earth Sciences; Earth Sciences questions and answers; 1. (b) vertical wind flow in upper atmosphere. This information is presented as a good faith service to the scientific community, the public in general and to our colleagues and friends. 2‰Ωvsin‚ = jrpj; (1) Thermal wind is a special case of wind shear, that, on the synoptic scale, under the assumption of geostrophic balance, is due to horizontal temperature gradients, and is defined as the vertical shear of the *geostrophic* wind. 9/28/10 4 Split the total horizontal velocity into geostrophic and ageostrophic components (ug, v g) → geostrophic → portion of the total wind in geostrophic balance (ua, v a) → ageostrophic → portion of the total wind NOT in geostrophic balance • Recall the horizontal equations of motion (isobaric coordinates): where 994 mb 996 mb 998 mb Lower Pressure Higher Pressure Note: Geostrophic flow is often a good approximation away from the Earth's surface. The gradient wind is an excellent approximation to the actual wind observed above the Earth's surface, especially at the middle latitudes. 6 0 obj ˺\;��ow�7�'�?2��gd ��?��w��$:��z QtIi�@�H�ur�/?�JyJ�I{@M�=��|)urS�"\D��[b�'�hz��tn8��A��Z��tA��Y��ˠ9��2��}wEN�y^�,5%R[�D�۞-2�NA\8��,�4�V� y��2{(�X��(e��LI+ɲMa8`��fQ䆤FP�Ģ��b�!c +��-�B��cNoQ�)�Ne��]�UVNg�%�x��Ȭ��x��6��0k\w��:�7#��q��X1�4�;WD�ho�{�C�P��R2�dS�ʨ�Ph�e��FP��Pa"� Կ۲�=��)#��g`�L�&�� H5=��LĈ��,Z��%rd�Ӓ��M�-mH�t@��+O�]�$CS��8��dWn9��%�K�W��$�H�[z�2�԰M�;J��I��f�O~�l+�U��{{- �k��5�zg�[�]��&��H�e4. a horizontal, even, and straight movement of air with no force of friction and with balance in the gradient of pressure and the deflecting force of the earth's rotation; the simplest theoretical scheme of air movement of the rotating earth. Found inside – Page 157Thus , from qualitative inspection , the geostrophic relation for the rotational wind approximation is a useful tool for geopotential analysis on isobaric surfaces . The geostrophic approximation ( 3.17 ) is approximately satisfied at o ... The geostrophic wind neglects frictional effects, which is usually a good approximation for the synoptic scale instantaneous flow in the midlatitude mid-troposphere. In which direction is the lowest pressure? It is the wind that blows parallel to the curved isobars under the balance of Pr Grad Force, Coriolis Force & Centripetal Force. (b) vertical wind flow in upper atmosphere. <> The warm wind that blows down the hül on the leeward side. The information, views and opinions herein provided should not be viewed as . (a) Pressure Gradient Force The thermal wind relation will give you the vertical gradients of the geostrophic field in terms of horizontal density gradients: (rho*f*u)_z = + g*rho_y (rho*f*v)_z = - g*rho_x Here, rho is the density of the fluid, f is the Coriolis parameter and g is gravity. This is a question about the "geostrophic wind" which dominates the atmospheric circulation at heights exceeding about one kilometer above the ground. (d) gravity. • It displays a good approximation of the horizontal wind . Found inside – Page 91The UM zonal wind at an altitude of 4km is illustrated. The geotriptic wind is a good approximation to the model wind, but is somewhat stronger. This is because of the cyclonic curvature, which makes the geostrophic wind an overestimate ... geostrophic assumption is invalid and air motion will be at right angles to isobars. (d) vertical wind flow at the earth surface. Traditionally, the accuracy of geostrophic or gradient-wind balance approximation has been studied generally by scaling analysis of the primitive equation system (Gent and McWillams, 1983b), which is a (c) Friction Vertical shear of geostrophic wind is a vector which lies parallel to the isotherm on level surface with low temperature on its left in the northern hemisphere. Of course, Va can be found by subtracting the geostrophic wind from the total wind. %PDF-1.7 Found inside – Page 18the observed winds will be assumed to be a good approximation to the geostrophic wind as expressed for our purpose by fv, X k = gWah, (1.3) where f = 2\o sin p is the Coriolis parameter, o is earth's angular velocity, p is latitude, ... At the equator there is no Coriolis force, thus there cannot be a geostrophic wind. where ∂z/∂n is the slope of the isobaric surface normal to the contour lines to the left of the direction of motion in the Northern Hemisphere and to the right in the Southern Hemisphere. Equation (10) is commonly called the Gradient Wind Equation. �N�O)%�R��f�r <>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Equation (10) can be solved for Vgr, the gradient wind: 2 1 2 2 2 4 ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ gr =− ± + fRVg fR f R V (11) where Vg is the geostrophic wind . Found inside – Page 133... and it was indicated that the geostrophic wind, as given by the orientation and spacing of the isobars, is a good approximation to the actual wind above the levels at which friction is of importance. The pressure gradient itself, ... (2) based on the dz assumption that zonal wind is in geostrophic balance. It can be shown that the main terms in horizontal equations are Coriolis force and pressure gradient terms; therefore, one can use geostrophic approximation. Geostrophic Wind winds balanced by the Coriolis and Pressure Gradient forces An air parcel initially at rest will move from high pressure to low pressure because of the pressure gradient force (PGF).. geostrophic wind theoretical wind which results from the equilibrium between horizontal components of the pressure gradient force and the coriolis force (deviating force) above the friction layer . Found inside – Page 86Z - axis vertically upward , and the X - axis in the direction of the geostrophic wind . ... 5 , an exponential profile is a good approximation for the profile of geostrophic wind in the jetstream region : Ug ( z ) = ( ilm- u , ) e ( 6 ) ... ): @u @t = 1 . c. The horizontal advection is approximated by geostrophic of the geostrophic wind depending on the density. The geostrophic wind is defined at every point except along the equator.The validity of this approximation in dynamic theory depends upon the particular context. Good luck. If the vertical shear of geostrophic wind is known, we dT can calculate - using Eq. Geostrophic Flow¶ Away from the boundaries, Friction is weak, and the flow is, to a good approximation geostrophic. Geostrophic flow in air or water is a zero-frequency inertial wave. %PDF-1.2 In other terms, the wind is such that the Coriolis force associated to this wind opposes the pressure gradient. The equations for the Ekman flow are a2u f - + K (u - U#O - t+z) = 0 dZ2 g -; (IJ - ugo - urz) = 0 The geostrophic wind neglects frictional effects, which is usually a good approximation for the synoptic scale instantaneous flow in the midlatitude mid-troposphere. Found inside – Page 364.4, because of frictional effect the wind is not parallel to the isobar, but it blows toward the low pressure with an angle O. In general, however, the geostrophic wind is a good approximation. 4.3.2 Gradient Flow Since isobars are ... The Gradient Approximation to the Wind Speed is defined as a horizontal wind having the same direction as the geostrophic wind but with a magnitude consistent with a balance of three forces: the pressure gradient force, the Coriolis force, and the centrifugal force arising from the curvature of a parcel trajectory and is represented as U gr = (A * B *(p n-p c)* exp (-A / r ^ B)/(D * r ^ B)+((r . Location C exhibits non-geostrophic flow probably due to non-geostrophic effects caused by the nearby jet core (where contours are packed together). <>/Metadata 280 0 R/ViewerPreferences 281 0 R>> This balance is called the geostrophic balance and the motion required to acheive that balance is called the geostrophic wind. 2.5 Schematic of geostrophic ﬂow with a positive value of the Coriolis parameter f. Flow is parallel to the lines of constant pressure (isobars). This is called geostrophic balance. The geostrophic wind must have vertical shear if the slopes of isobars vary with height. Why is Gradient Wind Often a Better Approximation Than Geostrophic Wind to the Actual Wind? 3 0 obj (d) always greater than friction. a Perpendicular to heights, lower heights lie to the left of an observer with his back to the wind, no friction. the equation for geostrophic balance). stream Geostrophic Wind. Hydrostatic Approximation (pressure coordinate form) *Φ *1 =− GH 1 Continuity Equation *0 *6 + *2 *7 + */ *1 =0 Which can . 1. Which of the following best describes geostrophic winds in the Northern Hemisphere? (c) East (to your right) The geostrophic wind will be assumed to vary according to the formula ve = v#J + vg-2 (2.1) where vgo is the geostrophic wind at the lower boundary, vr the geostrophic thermal wind, and z is height. Found inside – Page 29Table 1 CORRECTION TO GEOSTROPHIC WIND FOR SEA SURFACE - AIR TEMPERATURE DIFFERENCE Ts - Ta * ( ° F ) Ts - Ta * ( ° C ) ... the curvature of the path is negligible and the geostrophic wind speed is a good approximation of the wind speed ... Found inside – Page 86Z - axis vertically upward , and the X - axis in the direction of the geostrophic wind . ... 5 , an exponential profile is a good approximation for the profile of geostrophic wind in the jetstream region : Ug ( z ) = ( il.m — u ... By replacing the advected momentum with the geostrophic wind, the effect of the flow acceleration is partially considered and the original nonlinear partial differential equation set is converted to . (a) friction. Although ageostrophic terms are relatively small, they are essential for the time evolution of the flow and in particular are necessary for the growth and decay of storms. Geostrophic flow: terms (2) & (4) Under the action of the body force, particles will move at right angles to the force, to the right in the N. hemisphere (left in S. Hemisphere). The geostrophic wind neglects frictional effects, which is usually a good approximation for the synoptic scale instantaneous flow in the midlatitude mid-troposphere. The geostrophic model does not apply very well to near-surface winds due to the presence of terrain friction that slows the wind. The model has earlier been used without any thermal wind influence. . Found inside – Page 125Surface geostrophic velocities are usually good approximations for velocities immediately above boundary layers. ... to ascertain wind stress exactly there should be Ua À u instead of Ua, but since Ua ) u the approximation used is good.

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