1. Mixed-layer processes A short course on: Modeling IO processes and phenomena INCOIS Hyderabad, India November 16−27, 2015 Thanks to P. N. Vinaychandran for advice on this talk.

2. Questions How do atmospheric momentum (wind stress) and buoyancy (heat and rainfall) fluxes enter the ocean across the ocean surface? surface mixed layer What is the annual cycle of mixed-layer thickness in the Arabian Sea? in some locations from 5 m to more than ~100 m What is the diurnal variability of mixed-layer thickness in the Arabian Sea? in some locations from 5 m to more than ~100 m What processes cause mixing in the surface mixed layer? wind stirring, convective overturning, and KH instability How is the mixed layer represented in ocean models? Kraus/Turner, Philander/Pacanowski, Price/Weller/Pinkel (PWP), Mellor/Yamada, KPP

3. References 1)Turner, J.S. and E.B. Kraus, 1967: A one-dimensional model of the seasonal thermocline I. A laboratory experiment and its interpretation. Tellus, 18, 937−946. 2)Kraus, E.B. and J.S. Turner, 1967: A one-dimensional model of the seasonal thermocline II. The general theory and its consequences. Tellus, 18, 98−106. 3)Denman, K.L., 1973: A time-dependent model of the upper ocean. J. Phys. Oceanogr., 3, 173−184. 4)J.F. Price, R.A. Weller, and R. Pinkel, 1986: Diurnal cycling: observations and models of the upper ocean response to diurnal heating, cooling, and wind forcing. J. Geophys. Res., 91, 8411−8427.

4. Introduction 1)Arabian-Sea mixed layer 2)Kraus-Turner ML model 3)Other ML models 4)Arabian-Sea ML model

5. Arabian-Sea mixed layer

6. Mixed-layer variability (Arabian Sea) Arabian Sea biology and upper-ocean physics were intensively studied from 1994 to 1996. As part of that effort, a mooring was deployed in the central Arabian Sea at 15.5°N, 61.5°E by WHOI. Among other things, it measured near-surface temperatures, heat and buoyancy fluxes, and contained optical sensors from which phytoplankton biomass could be estimated.

7. Wind stress over the Arabian Sea varies strongly during the year, reversing from the winter to the summer. In addition, there is a strong surface cooling during the winter, when cool, dry air blows over the AS from the surrounding continent. These large changes in wind strength and Q lead to a prominent annual cycle in the AS mixed-layer thickness. Mixed-layer variability (Arabian Sea)

8. WHOI mooring At the mooring site, the mixed layer exhibited a prominent annual cycle. It deepened during the monsoon periods, most strongly during the NEM. It was thin during the intermonsoon periods. It also exhibited a striking diurnal cycle, gradually thickening during the night and rapidly thinning during the day.

9. Kraus-Turner ML model

10. KT mixed-layer model Turner and Kraus (1967) described the tank experiment of Rouse and Dodu (1955) as follows: “They expected that such stirring would smear out the interfacial gradients, but discovered to their surprise that the interface in fact became sharper, with a transfer of material always from the nonturbulent into the turbulent fluid, where it quickly became well mixed [i.e., entrainment].” Observations and tank models show that surface turbulence leads to the formation of a mixed layer.

11. KT mixed-layer model To model these processes with equations, Kraus and Turner (1967) parameterized surface turbulence P r by Observations and tank models show that surface turbulence leads to the formation of a mixed layer. where and τ > 0 is wind speed. Forcing u* (wind “friction velocity) measures the strength of mixing by wind stirring, and m is an arbitrary factor. Forcing Q (surface heat flux) causes mixing when Q < 0. KT argued that the factor ϕ ≈ 1.

12. KT mixed-layer model KT assumed that when P r > 0, so that turbulence is produced in the mixed layer, there is entrainment into the mixed layer at the rate Note that if Q > 0, P r can become negative, which is not physically sensible. So, KT assumed that if P r in (1) ever tried to become less than zero, the system immediately adjusts h m to a value that sets P r = 0, the “Monin-Obhukov” depth.

13. KT mixed-layer model Solution to a modified KT model forced only by u* (Q = 0), showing T(z) profiles every 3 hours. Denman (1973) As time passes, the mixed layer thickens. In addition, T(0) cools as cool subsurface water is entrained into the mixed layer. Further, the entrainment rate decreases because ½gh m ∆ρ increases.

14. KT mixed-layer model Q = R + B Solution to a modified KT model forced by weak u* and Q = R + B, where R = incoming solar radiation and B = back radiation. The T(z) profiles are plotted every 2 hours. There is no evaporative cooling! During the day, P r = 0 because Q > 0 and dominates wind stirring (mu* 3 ). As a result, h m thins as it continually adjusts to a thinner h mo. The mixed layer warms due to the heating. During the afternoon, Q weakens and eventually mu* 3 dominates P r. So, P r > 0 and h m begins to thicken. The mixed layer continues to warm. During the night, R = 0 so that Q = B < 0. So, both wind stirring and convective overturning contribute to P r and h m thickens faster. The mixed layer cools due to Q < 0. Finally, during the second morning, a new thin mixed layer forms.

15. Other mixed-layer models

16. Other mixed-layer models are conceptually similar to KT, but have different parameterizations of P r. Mellor/Yamada actually include additional equations to determine the turbulence that generates mixing of heat and momentum in the mixed layer. Other schemes (Philander/Pacanowski, Price/Weller/Pinkel, KPP) recognize the importance of Kelvin-Helmholtz instability in turbulence generation. They assume that P r is large only if Ri is small, say, less than a constant of the order of ¼.

17. Arabian-Sea ML model

18. Mixed-layer variability (Arabian Sea) WHOI mooring

19. Mixed-layer variability (Arabian Sea) Model The Kraus-Turner (1967) mixed-layer model is able to simulate the seasonal and diurnal variability at the mooring site reasonably well, except for the thinning of h m due to the passage of two eddies during Nov/Dec 1994 and Aug 1995.

20. Mixed-layer variability (Arabian Sea) …but not well enough! In a later study, we found that, when our mixed- layer model used the parameters that give this MLT, our biophysical model was not able to simulate biological activity very well in the Arabian Sea. So, we modified parameter ϕ in Q to allowing the strength of convective mixing (Q < 0) to be varied. Then, we adjusted m and n until the h m represented throughout the AS (at the WHOI mooring site and elsewhere) as well as possible.