ITIN PGEForm Approve v/d AD-A254 396 TION PAGEft. O70-0 Pu 1h oWF fS"POt , trG thu time OFr eviS tg iWMt lCII l.S C la stg dala sourcesg.a t" ard ,Ibt. Sanooffn wetts rV tbh urdanoranyothwaspaaffttohdi mcso klftTatlon.bI cIdkg uggestions rntin Opnratlona and Reports. 1215 Jefferson Davis Highway. Sule 1204. Ailt*gon. VA 2222-4302. and to ,he 9). Washington, DC 20503. 1. ... . . . I. t1n9e9p2or t Us. 3. FRienpaol r-t JToyupren aanl dA rDtiactlees Covered. 4. Title and Subtitle. 5. Funding Numbers. Turbulent Transport from an Arctic Lead: A Large-Eddy Simulation Contract Program Element No. 0601153N Prect No. 03103 6.A uthor(s). John W. Glendening and Stephen D. Burk Task NO. 380 Accession No. DN251030 Wok Unt No. 14411A 7.P erforming Organization Name(s) and Address(es). 8.P erforming Organization Naval Oceanographic and Atmospheric Research Laboratory Report Number. Atmospheric Directorate JA 442:016:91 Stennis Space Center, MS 39529-5004 9. Sponsoring/MonitorIng Agency Name(s) and Address(es). 10. Sponsoring!Monitoring Agency Naval Oceanographic and Atmospheric Research Laboratory Report Number. Basic Research Management Office Stennis Space Center, MS 39529-5004 JA 442:016:91 11. Supplementary Notes. Published in Boundary-Layer Meteorology Department of Meteorology, Naval Postgraduate School, Monterey, CA AL aV9 12a. Distribution/Availability Statement. C Approved for public release; distribution is unlimited. 13. Abstract (Maximum 200 words). The upward transfer of heat from ocean to atmosphere is examined for an Arctic "lead," a break in the Arctic ice which allows contact between the cold atmosphere and the relatively warm ocean. We employ a large-eddy modelto compute explicitly the three- dimensional turbulent response of the atmosphere to a lead of 200 m width. The surface heat flux creates a turbulent "plume" of individual quasi-random eddies, not a continuous updraft, which penetrate into the stable atmosphere and transport heat upward. Maximum updraft velocities and turbulence occur downwind of the lead rather than over the lead itself, because the development time of an individual thermal eddy is longer than its transit time across the lead. The affected vertical region, while shallow over the lead itself, grows to a height of 65 m at 600 m downwind of the lead; beyond that, the depth of the turbulent region decreases as the eddies weaken. The maximum vertical turbulent heat flux occurs at the downwind edge of the lead, beyond which a relative maximum extends upward into the plume. Negative surface heat flux immediately downwind of the lead creates a growing stable layer, but above that internal boundary layer the turbulent heat flux is still positive. Updraft maxima are typically 28 cm/s, but compensating downdrafts result in time-averaged verticalvelocities of lessthan 1 cm/s in the plume. Conditional sampling separates the updraft and downdraft contributions. Formulas for the horizontal eddy development distance and for the vertical plume penetration height are presented. The relative importance of mean and turbulent transport is compared for both vertical and horizontal heat transfer; turbulence dominates the vertical heat transport whereas mean advection dominates the horizontal transport, these offsetting transports producing a quasi-stationary state. 14. Subject Terms. 15. Number of Pages. Arctic leads, boundary layer, mesoscale 24 16. Price Code. 17. Security Classification 16. Security Classification 19. Security Classification 20. Umltallon of Abstract. of Report. of This Page. of Abstract. Unclassified Unclassified Unclassified SAR NSN 7540-01-280-5500 Standard Form 296 (Rey 2-89) PrescrIedby AtNSI Std. Z9-1 6 29580- 2 Acegsiong For NT1: J--,fti ~at i qr_ DTIC QUALITY INSPECTED 5 Av~llsibiity Cod," ~A ai d/or TURBULENT TRANSPORT FROM AN ARCTIC LEAD: DIst Sp ocial \ A LARGE-EDDY SIMULATION JOHN W. GLENDENING' and STEPHEN D. BURK. tDepartmento f Meteorology. Naval Postgraduate School. Monreres. Califorma. U.S.A.. .Vaal Oceano- graphic and Atmospheric Research Laboratory, Atmospheric Directorate. Monterey. California. U-S-i (Received in final form -1O ctober. 1991) Abstract. The upward transfer of heat from ocean to atmosphere is examined for an Arctic -lead". a break in the Arctic ice which allows contact between the cold atmosphere and the relatively warm ocean. We employ a large-eddy model to compute explicitly the three-dimensional turbulent response of the atmosphere to a lead of 200 m width. The surface heat flux creates a turbulent "plume" of individual quasi-random eddies. not a continuous updraft, which penetrate into the stable atmosphere and transport heat upward. Maximum updraft velocities and turbulence occur downwind of the lead rather than over the lead itself, because the development time of an individual thermal eddy is longer than its transit rime across the lead. The affected vertical region. while shallow over the lead itself, grows to a height of 65 m at 600 m downwind of the lead; beyond that. the depth of the turbulent region decreases as the eddies weaken. The maximum vertical turbulent hear flux occurs at the downwind edge of the lead. beyond which a relative maximum extends upward into the plume. Negative surface heat flux immediately' downwind of the lead creates a growing stable layer, but above that internal boundary layer the turbulent heat fl[' is still positive. Updraft maxima are typically 28 cm/s. but compensating downdrafts result in time-averaged vertical velocities of less than I cm/s in the plume. Conditional sampling Sseparates the updraft and downdraft contributions. Formulas for the horizontal eddy development distance and for the vertical plume penetration height are presented. The relative importance of mean and turbulent transport is compared for both vertical and horizontal heat transfer: turbulence dominates the vertical heat transport whereas mean advection dominates the horizontal transport. these offsetting transports producing a quasi-stationary state. (V 1. Introduction During the Arctic winter, pack ice separates the cold Arctic atmosphere from the relatively warm Arctic ocean. Breaks in the pack ice allow air-ocean contact. generating large upward fluxes of heat and moisture. The term "lead" usually refers to a transient break resulting from local ice stress divergence, whereas •p olynya" usually refers to a semi-permanent break - typically much larger than a lead - associated with a specific location. Leads are approximately linear, with widths ranging from 1 m to 1 km and lengths from 1 km to 100km. Air-ocean temperature differences are typically 20-40°C. creating heat fluxes up to two orders of magnitude larger than those over the pack ice. Consequently the total heat input into the atmosphere from leads can be larger than that from the surrounding ice, despite the relatively small area coverage of the leads (Mavkut. 1978). This heat release makes Arctic winters less frigid. at sea level, than those of the Antarctic (Smith et at., 1990). The influence of sea ice on the large-scale polar climate has been a subject of Boundary-Layer Meteorology 59: 315-339. 1992. © 1992 Kluwer Acad nic Publishers. Printed in the .Vetherlands. 92 8 24 035 316 JOHN W. GLENDENING AND STEPHEN D. BLRK many modeling studies. Large-scale models have included a sea ice effect in different ways: with a specified surface boundary condition (North and Coakley. 1979), with parameterized sea ice in an ocean model (Wetherald and Manabe. 1981), and with a one-layer thermodynamic model (Washington and Meehl. 1984). Ledley (1988) specifically separated out the effect of leads in a coupled climate- sea ice model, finding a lead-temperature feedback that increased the annual zonally-averaged surface air temperature in the north polar region by 1.0 K when the winter lead fraction was increased from 1.1 to 4.3%. Since leads are small- scale features. their effects must be parameterized in large-scale models. The small-scale physics of pack ice and leads has been reviewed by Untersteiner (1986). Smith et al. (1990) summarized several lead observational experiments. which primarily investigated the region over the lead itself. For example. Andreas et al. (1979) described heat flux variations with fetch over several leads and Smith et al. (1983) investigated larger polynyas for which the heat flux was not fetch- limited. Heat and momentum transfer coefficients for leads/polynyas have resulted (e.g., Andreas and Murphy. 1986). Aircraft observations have found plumes from Arctic leads extending up to 4 km vertically (Schnell et al.. 1989), indicating that such plumes can penetrate the Arctic inversion and transport heat into the lower troposphere. Previous small-scale modeling of lead effects has been relatively limited and has considered only the response above the lead itself. Shreffler's (1975) two- dimensional model employed eddy diffusivity closure and a molecular surface sublayer to predict surface fluxes and vertical growth of the internal boundary layer (IBL) created over a 20 m wide lead. Lo (1986) employed a two-dimensional model with a ttlfbulent kinetic energy (TKE) closure to predict profile variations as a function of do.. wind distance over a polynya. This investigation primarily discusses the r.gion of turbulence and upward heat flux which occurs downwind of the lead, rather than the region immediately above the lead. because the strongest turbulent response occurs in the downwind region. Also, this investigation considers lead effects in a strongly stratified upstream environment, as is typical of the Arctic, whereas both previous numerical models assumed the upstream environment to be neutrally stratified. Our approach is embodied in Figure 1, an observed downwind growth of individual eddies over a lead. We use a large-eddy (LE) model to simulate the thermal eddies created by a lead and thereby determine their integrated effect. We find that the strongest vertical turbulence and deepest upward heat transfer occurs downwind of the lead. rather than immediately above it. because an individual eddy's travel time over the lead is smaller - for our chosen lead width of 200 m - than its development time. The eddies therefore continue to grow downwind of the lead itself, creating an extensive turbulent "plume" with significant upward heat flux. (We shall use the term "plume" to refer to the region of time-averaged upward heat flux created by the lead as a result of individual eddy transports.) A major field program to study Arctic leads and enhance understanding of TURBULENT TRANSPORT FROAI AN ARCTIC LEAD 317 20 ! WiNO 0 20 40 60 80 X (mi Fig. 1. Growth of eddies over a lead: stippling indicates indivtdual thermals as interpreted from smoke plume photographs by Smith eta l. (1983). coupled atmosphere/ice/ocean dynamics, called LEADEX. will be conducted dur- ing Spring 1992. The effect of both single and multiple leads upon atmospheric and oceanic properties will be investigated. One motivation for the present study is to assist planning for instrumentation deployment around a lead. 2. Large-Eddy Model The large-eddy (LE) model we employ is fundamentally that described by Moeng (1984), which uses a Deardorff K-theory parameterization for the sub-eddy scale closure. The inhomogeneous forcing created by the lead does require several model changes. since the existing coding assumed the surface forcing to be horizon- tally homogeneous. Surface values of temperature, temperature flux, and stress are allowed to-vary in the x direction and the predicted mean variables become functions of x. In addition. the distinct differences between directions perpendicu- lar and transverse to the lead require a rectangular grid to provide a long downwind domain. The simulation must treat strongly stratified regions close to the surface ad- equately. though such is not the fundamental purpose of an LE model since no large eddies exist in such regions. To accomplish this. we modify the subgrid parameterization. First, the surface layer is allowed to be stable, using Monin- Obukhov similarity theory with relationships between surface profiles and fluxes given by Businger et al. (1971). Second. the subgrid mixing length scale I is not allowed to exceed the similarity value kz/lb, in the surface layer (i.e.. for Z < ILl) where k is the von Karman constant. 6,,, is the dimensionless wind shear. and L is the Monin-Obukhov length. Third, to retain congruence between the mixing coefficient parameterized in the model - i.e.. K,, = cle". where e is the subgrid TKE and c is an empirical proportionality constant of 0.1 - and that of surface- layer similarity -i.e.. K,,, = kzuI,,/ b,,, where u,,i s the surface friction velocity - the subgrid TKE is set to (uic)2 at the lowest grid point. Our subgrid parameterization assumes, for stable stratification in the surface layer, that vertical mixing dominates horizontal mixing and that the vertical mixing length is smaller than that set by the grid spacing. 318 IOHN. W. GLENDE.NING AND STEPHEN 0. BURK Z 120 m 200m ICE 2304 m 0 1200 m LEAD Fig. 2. Lead (water) and ice regions within the model domain. A hydrostatic radiation boundary condition (Klemp and Durran. 1983) is em- ployed at the model top. This condition does not eliminate reflections from the model top. since the model is non-hydrostatic. but it does reduce them: in one test generating a strong impulsive gravity wave, this radiation condition reduced vertical velocities resulting from trapped modes by 2/3. Lateral boundary con- ditions (BC) are cyclical, as the model is spectral. Cyclic BC are entirely appropri- ate in the lead-parallel direction. Cyclic BC in the lead-perpendicular direction would simulate a series of leads, rather than a single lead, if the model were to be run for a sufficiently long period, our simulation. however, is terminated before lead-induced effets can propagate through the domain and so represents a single lead. The model equations do not introduce artificial horizontal diffusion. but wavelengths smaller than 3.\x are filtered at every time step to control non-linear instability. To reduce storage space requirements. the model is run without the complexities of water vapor, cloud formation. or radiative transfer. At cold Arctic tempera- tures. with small saturation vapor pressures. the latent heat flux from an open lead is typically 25% of the total heat flux (Andreas et al., 1979); such latent heat fluxes can be significant if condensation occurs. Satellite observations have found both clear and cloudy regions extending downwind from leads (R. W. Fett. per- sonal communication). The latent heat flux ceases when the lead freezes over, but the sensible heat flux through thin ice can still be significant. 3. Simulation Parameters We simulate a single idealized lead in an Arctic ice pack. Our linear lead is 200 m wide and infinitely long, with a surface temperature of -2 'C. Figure 2 indicates the lead location within the model domain, The ice temperature is -29 °C. giving a surface temperature difference of 27°C between water and ice. For our base- state atmosphere. constant throughout the domain, we choose a strongly stable rtIRBLt.eNr TRANSPORT FROM AN AW.TIC LEAD 319 stratification a0/oz = 10 K/km with 9 = -27 'C at the surface. The geostrophic wind is perpendicular to the lead at 2.5 m/s. The ice is slightly rougher (z.= 0.1 cm) than the water in the lead (z,, = 0.01 cm). The Coriolis parameter repre- sents a latitude of 79' N. The scales of interest in this simulation are small by typical convective large- eddy standards. Our 'grid spacing is 4 m vertically and 8 m horizontally. The domain extends 2304 m perpendicu lar to the lead (in the x direction). 200 m transversely and 120 m vertically. The lead-perpendicular domain must be exten- sive to avoid cyclic BC interference: array size maxima therefore force a limited lead-parallel domain, but the latter is large enough to allow vortex roll formation. An empirically-determined time step of 0.5 s is required for numerical stability with the small grid spacing employed. The model is initialized in a horizontally homogeneous state, the initial tempera- ture being that of the base state. The initial wind is the model's one-dimensional equilibrium solution over the ice surface. so the flow would be quasi-stationary if no lead were present. Due to the stable stratification. initially all TKE is subgrid and no large eddies exist except for specified random velocity perturbations of 0.01 m/s in the lowest layer. This initialization creates a transient, since effectively the lead "opens" instantaneously rather than over several hours. The initialization procedure was largely dictated by computer time constraints: it eliminates the time scale associated with the lead opening. Since turbulent fields are simulated, the results must be averaged. Unless other- wise indicated, all mean results presented are spatially averaged in the lead- parallel direction and time averaged over a period from 576 s to 702 s after model initialization, when the region from the upwind lead edge to 800 m down vind of the lead has achieved quasi-stationarity. Each average represents 6048 individual values. 4. Simulation Results 4.a. QUASI-STATIONARITY The instantaneous opening of the lead creates an initial transient. as heat is released into the air above the lead. which increases in depth and strength until advection of cold air balances the heat transfer. After the transient propagates downwind, a quasi-stationary state is approached. Figure 3 depicts passage of the initial transient for x = 500 m and x = 1000 m. rhe indicated values are for a height of 32 m. averaged over 36 s and in the v direction. At a given location, the transient first appears as a negative vertical velocity (w). with the subsequent positive velocity relaxing towards a mean vertical velocity typically less than I cm/s. Simul- taneously, potential temperature (0) increases rapidly from its initial state and then relaxes toward a quasi-stationary solution. Based upon analysis of the temporal adjustment of w and 0.a nd mean w contours given in the next section, we consider 320 JOHN W. (GLENDENIN,( AND STEPHEN D. BURK .-. .14 -11.4 .|. A% 7111.5- 7 -I1 t " II too 2;0 300 400 500 S00 700 Time (s) Fig. 3. Potential temperature (solid) and vertica! velocity (dashed) changes as a function of ime at x = 500m (heavyl and x = 1000m (thin). x = 1000 m to be the downwind limit of quasi-.itationarity for our chosen time- averaging period. This does mean that large changes are occurring for x > 1000 m: near the center transient, at x = 140U in over the Nimulation period 576 to 702 s, the maximum aelar is only 1 x 10-' K/s. Heat transfer essentially occurs within x < 1000 m for both the transient and the quasi-stationary events. 4.b. INDIVIDUAL EDDY STRUCTURE We first examine the individual eddy structure. Since eddies continually grow and decay. the variables at any given point continually change with time. Near the upwind edge of the lead. the turbulent scales are too small to be resolved by the finite grid. but the eddies become resolved as they grow downwind. Maximum turbulence occurs downwind of the lead itself, as discussed in Section 5b. Figure 4 depicts instantaneous vertical velocities over the region of maximum eddy growth at 648 s after model initialization, the middle of the averaging period. Two levels are shown: for clarity, only a partial domain is displayed. At the lower level (z = 24 m), upward velocities are largest nearer the lead. where they exhibit linear features parallel to the wind - suggesti, of roll vortex formation - with an along- wind/cross-wind aspect ratio greater than one: farther downwind the eddies are rLR LENT TRANSPORT FROM AN %RCTIC LEAD 4GO Soo0 C 0 X Im (a) 40 000 ~M0S) 900 00 .. .. o - • - (b; 00 Soo0 600 00 Soo 900 1000 .- X (m) Fig. 1. Instantaneous vertical velocity at t 648s for (a 5 m. ib) = 4 m. Contours of 10cm/s. shading indicates downward motion. less intense, lose their linear structure. and eventually decay due to the lack of upward surface heat flux. At the upper level (z = 56 m), upward velocities are negligible close to the lead because the eddies have not yet penetrated to that depth, the first eddies to do so being hot columns with large upward velocities and small lateral extent: farther downwind, the eddies become larger in extent with smaller upward velocities. Figure 5 illustrates the tendency for the eddies to orient themselves in an along- wind direction. i.e.. to have an aspect ratio greater than one. Vertical velocities in the along-wind and cross-wind directions at aheight of 40 m have been averaged based upon their relative distance from the local updraft maxima: thus Figure 5 represents perpendicular slices through a "'typical" updraft. Averaged over the entire domain, the along-wind extent is double the cross-wind extent: Figure -4 indicates that this aspect ratio is actually a decreasing function of downwind distance. Since the transverse width of a typical updraft is significantly smaller than half the transverse domain, the lateral cyclic boundary conditions do not artificially limit the eddy size. 322 JOHN W. GLENDENING AND STEPHEN D. BURK L 0S - 0 - - - - - -- -- --- - - - ---- tO30 40 50 60 Distance (m) Fig. 5. Vertical velocity as function of distance from the local updraft maximum in along-wind Isolid) and cross-wind (dotted) directions at z= 40 m and r = 648 s. .C.. MEAN VERTICAL VELOCITIES Figure 6 depicts meanriertical velocities over the entire model domain. The initial transient created by the instantaneous lead opening is apparent for x > 1000 m (parcels initially over the lead have advected to between x = 1600-1800 m at the middle of the averaging period). The vertical velocity contours tilt with height near the upper boundary due to the radiation BC applied there, iftr apped modes were prominent, these contours would be vertically oriented. In the quasi-stationary region, from x = 0 to x = 1000 m. mean vertical velocities are small - typically less than I cm/s - because the large upward velocities of the individual eddy updrafts - with typical maxima of 28 cm/s - are compensated by eddy downdrafts. These smdll mean vertical velocities are a consequence of the small eddy travel time over the lead. significantly larger mean vertical velocities would be expected over much wider leads or for winds more parallel to the lead. The downward velocity near x = 50 m reflects the near-surface speedup of the lead-perpendiculcr component of the wind, which is created by downward mixing of higher momentum air and by the smaller Z,)of the water. 4.d. MEAN TURBULENCE Near the surface, turbulent length scales are smaller than the model resolution so all turbulent kinetic energy (TKE) is subgrid. Figure 7a depicts this subgrid energy. which increases in magnitude and vertical extent with distance over the lead as TURBULENT TRANSPORT FROM AN ARCTIC LEAD 323 12 0 . . . . I , , so. 5 00 t a S0 z2O0 0 Fig. 6. Mean vertical velocity (in cm/s). 1 0 ..' " ...".. . ... oi Menrsle oi onttuar bulence 70- soo 20- 10- 0z 100 20 0 400 6 00 goo [coo Fig. 7, (a) Mean subFrid turbulent kinetic energyi b) Mean resolved vertical turbulence (): (c) Meanreslvedhorzonal trbuenc (it - ): d) Mean total turbulent kinetic energy (in m:/s).