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James R. Baker and Thomas F. Jordan

Abstract

The elements of an eigenfunction expansion for time-dependent currents as a function of depth are worked out for viscosity that is given as a parabolic function of depth that goes to zero at both the bottom and top of the water. This yields currents with logarithmic behavior characteristic of turbulent boundary layers at both the bottom and top. Also, solutions are obtained for the two viscosity functions that are half a parabola, going to zero at either the bottom or top but not both. In all cases the solutions are Legendre functions. In some cases the eigenfunctions are Legendre polynomials.

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James R. Baker and Thomas F. Jordan

Abstract

A previously developed eigenfunction expansion, that describes horizontal current as a function of depth and time, is extended to include any eddy viscosity given as a product of a function of depth and a function of time.

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Thomas F. Jordan and James R. Baker

Abstract

Solutions of a linear hydrodynamic equation of motion with linear boundary conditions are obtained to describe the horizontal current, as a function of depth and time, determined by a given history of the wind force and pressure gradient up to that time, at a fixed point in the horizontal plane, in well-mixed water of finite depth. The bottom friction is assumed to be proportional to the bottom current, with zero bottom current and zero bottom friction considered as limiting cases. The general solution is established as an eigenfunction expansion when the eddy viscosity is given as a positive function of depth. Explicit formulas are worked out for viscosity functions that are constant, exponential, or varying as a power of the height from somewhere below the bottom or above the top of the water. For the latter the limit as the viscosity goes to zero at the bottom or top is considered. Numerical results are presented for viscosities that are constant, exponential, linear, or varying as the 3/4 power.

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David H. Bromwich, Kirstin Werner, Barbara Casati, Jordan G. Powers, Irina V. Gorodetskaya, François Massonnet, Vito Vitale, Victoria J. Heinrich, Daniela Liggett, Stefanie Arndt, Boris Barja, Eric Bazile, Scott Carpentier, Jorge F. Carrasco, Taejin Choi, Yonghan Choi, Steven R. Colwell, Raul R. Cordero, Massimo Gervasi, Thomas Haiden, Naohiko Hirasawa, Jun Inoue, Thomas Jung, Heike Kalesse, Seong-Joong Kim, Matthew A. Lazzara, Kevin W. Manning, Kimberley Norris, Sang-Jong Park, Phillip Reid, Ignatius Rigor, Penny M. Rowe, Holger Schmithüsen, Patric Seifert, Qizhen Sun, Taneil Uttal, Mario Zannoni, and Xun Zou

Abstract

The Year of Polar Prediction in the Southern Hemisphere (YOPP-SH) had a special observing period (SOP) that ran from 16 November 2018 to 15 February 2019, a period chosen to span the austral warm season months of greatest operational activity in the Antarctic. Some 2,200 additional radiosondes were launched during the 3-month SOP, roughly doubling the routine program, and the network of drifting buoys in the Southern Ocean was enhanced. An evaluation of global model forecasts during the SOP and using its data has confirmed that extratropical Southern Hemisphere forecast skill lags behind that in the Northern Hemisphere with the contrast being greatest between the southern and northern polar regions. Reflecting the application of the SOP data, early results from observing system experiments show that the additional radiosondes yield the greatest forecast improvement for deep cyclones near the Antarctic coast. The SOP data have been applied to provide insights on an atmospheric river event during the YOPP-SH SOP that presented a challenging forecast and that impacted southern South America and the Antarctic Peninsula. YOPP-SH data have also been applied in determinations that seasonal predictions by coupled atmosphere–ocean–sea ice models struggle to capture the spatial and temporal characteristics of the Antarctic sea ice minimum. Education, outreach, and communication activities have supported the YOPP-SH SOP efforts. Based on the success of this Antarctic summer YOPP-SH SOP, a winter YOPP-SH SOP is being organized to support explorations of Antarctic atmospheric predictability in the austral cold season when the southern sea ice cover is rapidly expanding.

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