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Circulation- Coupling With a Wave Parameterization For the Idealized Coastal Region

Le Ly and Curt Collins Dept. of Naval Postgraduate School Monterey, CA 93043

1. Introduction atmospheric model), POM (Princeton Momentum and energy transfers across the air- Model; Blumberg and Mellor, 1987), and WAM interface under realistic ocean conditions are wave model (Wilczak et al., 1999), and an important not only in theoretical studies, but also atmosphere-POM-WAM for the Mediterranean in many applications including marine region (Lionello et al., 1999). atmospheric and oceanic forecasts and climate Based on a new concept of oceanic turbulence modeling on all scales. Surface breaking and a wave breaking condition of the linear wave are believed to be an important supplier of theory, a parameterization is turbulent energy besides shear production of the developed and presented. This wave classical turbulence theory. Waves contain a parameterization with wave-dependent roughness considerable amount of momentum and energy, is tested against available data on wave- and they redistribute these quantities over great dependent turbulence dissipation, roughness distances. waves supply energy for length, coefficient, and momentum turbulence due to breaking. Ocean waves strongly using a coupled air-wave-sea model. We also effect the air-sea system on all scale. A part of the present a circulation-wave coupling study using a energy and momentum is transferred directly wave dependent roughness (Ly and Garwood, from the atmosphere to ocean currents while 2000) and taking the wind-wave-turbulence- another part is transferred to surface waves. The relationship into account. The NAval influence of surface waves on the air-sea system postgraduate school ocean Model (NAM, POM- has been studied experimentally and numerically based model) includes a new turbulence closure by many investigators. with the wave parameterization is presented. The Despite the importance of surface wave effects wave parameterization in the model is able to on the air-sea system, air-wave-sea coupling in relate model variables to wave parameters such as general, and circulation-wave coupling in , age, phase speed, period, and length. particular, has received little attention. There are The NAM box model (idealized California some air-wave-sea systems developed by various coastal regions) is used in a circulation-wave investigators including Doyle, 1995; Lionello et coupling study with idealized wave height and al., 1996, 1999; Welsh et al., 1999; Wilczak et al., wave age fields. This study is focused on the 1999. The investigators limited their studies on sensitivity of the current field to the surface the surface roughness effects on the air-sea waves. This study also demonstrates the system using Charnock’s (1955) and Janssen’s capability of the NAM model in reproducing an (1989) formulas. observed feature for the idealized The same approach has been used by Welsh et California coastal region. al. (1999), Wilczak et al. (1999), and Lionello et al. (1999) in their coupled hydrodynamic and 2. Circulation-Wave Coupling With a Surface WAM wave models for Lake Michigan (Welsh et Wave Parameterization al., 1999), regional coupled MM5 (mesoscale-

a. The Model with Coupling Physics height (h), period (T), and phase speed at the In addition to traditional shear production in the spectral peak (Cp ). The NAM box model with a air-sea system, a new turbulence concept wave parameterization has been used in a considers surface waves to be an important circulation-wave coupling with idealized wave supplement of turbulent energy. A turbulence height and wave age fields. The NAM ocean closure with a surface-wave parameterization is model is used in a case-study which shows the developed and tested again all available wave- model capability in reproducing observed dependent observed data of ocean turbulent upwelling off the California . dissipation (H) distribution, wave-dependent The equations for momentum, and roughness length ( z0a ), drag coefficient (Cd ) and salinity contain the vertical turbulent exchange momentum fluxes. Simulations show that waves coefficients that are determined by a turbulence have an important role in causing H to differ from closure scheme (Ly, 1991, 1995; Ly and the classical wall-layer theory and z0a , with a Garwood, 2000) with a surface wave value of 0.30 for the empirical constant. The parameterization (Ly and Garwood, 2001). This model-predicted H, and wave-dependent z0a , Cd scheme consists of equations for the turbulent and Cgd agree well with data. Fig. 1 shows the kinetic energy (TKE), E, for the turbulent H model H-distribution in the ocean is in dissipation, , and for turbulent exchange comparison with observed data of all sources and coefficient, Km, and wind-wave-turbulence- the classical theory prediction. current relationship equations. The equation for TKE can be& written as follows 2 ˜E/˜t + U .’ E + W wE/wz = D1Km [(w U/wz) + 2 (w V/wz) - D3 g/D1 U0 wU/wz] + D4 w/wz (Km w E/wz) 2 - D2 E /Km + Fe  (1) H The equation& for has the form 2 ˜H /˜t + U .’ H + W w H /wz = 1Km [(w U/wz) + 2 (w V/wz) - 3J1 U0 wU/wz] + 4 w/wz (Km w H /wz) 2 - 2 H /E + F , (2) Fe in equation (1) and F in equation (2) are the horizontal mixing terms, which are similar to F in equations for temperature and salinity. The first two terms on the right-hand side (RHS) in Figure 1. Nondimensional 0 as function of depth z. The vertical line show the classical wall-layer (1) and (2) represent shear production. The next turbulence prediction. The three curves show the terms are the and vertical model prediction with a new wave parameterization terms. The next terms on the RHS represent for various wave breaking status. Data points of dissipation. The turbulent exchange coefficient various sources are adapted from Agrawal et al. for momentum is expressed in terms of TKE and (1992). (Adapted from Ly and Garwood, 2001). energy-dissipation using the Kolmogorov The NAval postgraduate school ocean Model equation (NAM) is a POM-based model, which uses a new 2 Km = .H E /H , (3) turbulence closure with the wave where .H = .2 = 0.046 is a universal coefficient. parameterization and wave-dependent roughness In ocean and atmosphere modeling practices, .H length, which takes the wind-wave-turbulence- and .2 may be varied to provide a realistic current relationship into account. The model can relationship between turbulent and thermo- relate the model variables to typical wave dynamical structures. The set of constants . and  parameters, such as wave age (Cw ), length (O),

link the exchange coefficients for buoyancy and 1986; Ly and Garwood, 2000; Ly and Benilov, transport with Km as follows 2001). Kh = .3 Km ; KK = 3 Km , Ke = .4 Km ; K = The following wave-dependent roughness 4 Km (4) length (Ly and Garwood, 2000) .   2 The constants and have the following values z0a 0.30 u *a / gcw (5) . . . . (Ly, 1991): 1 = 1.0; 2 = 0.046; 3 = 1.0; 4 = This roughness length has been used in the 1-D     0.73 and 1 = 1.43; 2 = 1.97; 3 = 1.45; 4 = 0.73 air-wave-sea coupled model and tested against available data. The comparison shows an b. Wind-Wave-Turbulence-Current Relationship agreement with observed data of all sources (Ly The , heat, and salinity fluxes are and Garwood, 2000). For the developed waves prescribed at the . Heat and salinity with wave age cw = 20-30 the roughness length fluxes are assumed zero at the bottom. All fluxes reduces to Charnock's (1955) formulation with are assumed zero at the lateral boundaries the Charnock's constant of between 0.01-0.015. (Blumberg and Mellor, 1987). In the ocean mixed The surface boundary conditions of the NAM layer, surface wave breaking is an important ocean model include wind stress, heat and source of turbulent energy, supplementing shear salinity fluxes. The bottom boundary conditions production. Wave breaking plays an important for TKE and H, heat and salinity fluxes all role in enhancing TKE and dissipation in the approach zero. There are also conditions for upper ocean layer. The 1-D air-wave-sea coupled bottom stress, which is determined by matching model results have been compared against all velocities with the log law of the wall (Blumberg available observed data and used in the and Mellor, 1987). circulation-wave coupling study. The new version of the parameterization is based on results of both c. Circulation-Waves Coupling experimental and numerical studies, which show The NAM box model (idealized California that breaking waves strongly enhance not only coastal regions) is used in a circulation-wave TKE dissipation, but also TKE. The new version coupling study with idealized wave height and of the parameterization is also modified to wave age fields. The study is focused on the incorporate a boundary condition for velocity sensitivity of the current field to the surface across the interface (Ly and Benilov, 2001). waves and on demonstration the capability of the Hereafter, subscript "a" is used for marine NAM model in reproducing an observed atmosphere characteristics, and subscript "s" for upwelling feature for the idealized California the oceanic ones. Based on conservation of coastal region. A stratified ocean with a specified energy and similarity theory (Ly, 1986), breaking initial temperature distribution is used in the wave effects can be incorporated in an equation experiment. This distribution is similar to for the TKE . Using a wave breaking observations off California. The initial salinity is condition from the linear wave theory, the assumed constant at 35.0 psu. Both initial oceanic TKE at the interface can be written in temperature and salinity fields are horizontally terms of wind stress and wave parameters (Ly, homogeneous. The basin is 100 km wide and 500 1995; Ly and Garwood, 2000; Ly and Benilov, km long. The depth approximates the bottom 2001). A similar equation can be written for the topography of the California Pacific coast. The TKE dissipation. The current-wave relationship basin covers a region with an ocean depth of can be obtained from the equation for the energy 2000m, a -slope and a narrow fluxes. In the above equations, if h = 0 (no shelf of depth less than 100m. A horizontally waves), we have traditional conditions for TKE, homogeneous upwelling-favorable (northernly) H, and velocity at the interface (the wave layer wind stress of 2 dyne cm-2 was imposed in a band becomes an interface surface in this case) (Ly, 300-km long and 60-km wide in the south-eastern

part of the basin. No wind stress curl and no Lionello, P., P. Malguzzi, and A. Buzzi, 1998. surface heat flux are imposed. The temperature Coupling between the field of the 10-day simulation shows evidence of and the ocean wave field: an idealized case. J. coastal upwelling along the , which is Phys. Oceanogr., 28, 161-177. typical for the California coastal region in Lionello, P., P. Malguzzi, E. Elvini, A. Sanna, M. summer. Coastal upwelling is an observed and G. Villani, 1999. Progress in coupled meteo- important physical phenomenon, which this oceanic predictions in the Mediterranean region. numerical model can reproduce. Third Conf. on Coast. Atmosph. & Oceanic Pred. & Proc. New Orleans, LA, 3-5 Nov. 247-252. 3. Conclusions Ly, L. N. 1986. Modeling the interaction between A new turbulence closure with the wave atmospheric and oceanic boundary layers, parameterization and wave-dependent roughness including a surface wave layer. J. Phys. length is used for coupled model developing and Oceanogr., 16, 1430-1443. testing against available data. The wave Ly, L. N. 1991. An application of the E-0 parameterization in the model is able to relate varepsilon turbulence model to studying coupled model parameters to wave parameters, which are air-sea boundary layer structure. Boundary-Layer standard outputs of wave prediction models. The Meteorol., 54, 327-346. NAM includes a new turbulence closure with the Ly, L. N. 1995. A numerical coupled model for wave parameterization. The NAM box model studying air-sea-wave interaction. Phys. Fluids, (idealized California coastal regions) is used in a 7(10), 2396-406. circulation-wave coupling study with idealized Ly, L. N. and R. W. Garwood, Jr. 2000. wave height and wave age fields. The study Numerical modeling of wave-enhanced turbule shows a strong sensitivity of the current field to nce in the oceanic upper layer. J. Oceanogr., 56, the surface waves. The simulations show the 373-383. capability of the NAM model in reproducing an Ly, L. N. and A. Yu. Benilov (2001). Air-Sea observed upwelling feature for the idealized Interaction: Surface Waves. Encyclopedia of California coastal region. Atmospheric Sciences. Ed. by J. Holton, J. Pyle REFERENCES and J. Curry. Academic Press. (Submitted). Agrawal, Y.C., E. A. Terray, M. A. Donelan, P. Ly, L. N. and R. W. Garwood, Jr. 2001. An ocean A. Hwang, A. J. Williams, W. Drennan, K. K. circulation model with surface wave Kahma, and S. A. Kitaigorodskii, 1992. parameterization. Applied Num. Math. (To be Enhanced dissipation of kinetic energy beneath appeared). breaking waves. Nature, 359, 219-220. Welsh, D. J. S., R. Wang, P. Sadayappan, and K. Blumberg, A. F. and Mellor, G. L. 1987. A W. Bedfort, 1999. Parallel coupling of description of a three-dimensional coastal ocean hydrodynamic and wind-wave models. Third circulation model. Three-Dimensional Coastal Conf. on Coast. Atmosph. & Oceanic Pred. & Ocean Models, N. S. Heaps (Ed.), 1-16. Proc. New Orleans, LA, 3-5 Nov., 111-112. Charnock, H. 1955. Wind stress on a Wilczak, J., J. W. Bao, L. Kantha, and J. K. Choi, surface. Quart. J. Roy. Meteorol. Soc. 81, 639- 1999. A regional. coupled atmosphere-ocean- 640. wave modeling system. Third Conf. on Coast. Doyle, J. D., 1995. Coupled ocean Atmosph. & Oceanic Pred. & Proc. New wave/atmosphere mesoscale model simulations Orlearns, LA, 3-5 Nov., 124-129. of cyclogenesis. Tellus, 47!, 766-778. Wittmann, P., M. Clancy and T.Mettlach,1995. Janssen, P. A. E. M. 1989. Wave-induced stress Operational wave forecasting at FNMOC. Fourth and the drag of air flow over sea waves. J. Phys. Inter. Workshop on Wave Hindcasting, Oceanogr. 19, 745-754. Downsview, On., Canada, 335-342