Djoko Wirosoetisno
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Djoko Wirosoetisno has a total of 24 co-authors. Here are the top co-authors by number of shared publications:
- Michael S. Jolly
Indiana Univ, Dept Math, Bloomington, IN 47405 USA
6 shared publications - Roger Temam
Department of Mathematics and Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, USA
6 shared publications - Xiaoming Wang
School of Mathematical Sciences Eastern Institute of Technology Ningbo China
4 shared publications - Florentina Tone
Department Mathematics and Statistics, University of West Florida, Pensacola, FL 32514, USA
3 shared publications - Jacques Vanneste
University of Edinburgh
3 shared publications Theodore G. Shepherd
3 shared publications
Latest Publications
- Open Access
- 13 June 2024
- Published by IOP Publishing in Nonlinearity
- Vol. 37 (7) , 075025
The Batchelor–Howells–Townsend spectrum: large velocity case
We consider the behaviour of a passive tracer θ governed by ∂ t θ + u ⋅ ∇ θ = Δ θ + g in two space dimensions with prescribed smooth random incompressible velocity u ( x , t ) and source g(x). In 1959, Batchelor et al (J. Fluid Mech. 5 113) predicted that the tracer (power) spectrum should scale as | θ k | 2 ∝ | k | − 4 | u k | 2 for | k | above some κ ¯ ( u ) , with different behaviour for | k | ≲ κ ¯ ( u ) predicted earlier by Obukhov and Corrsin. In this paper, we prove that the BHT scaling does indeed hold probabilistically for sufficiently large | k | , asymptotically up to controlled remainders, using only bounds on the smaller | k | component.
- 13 June 2024
- Published by IOP Publishing in Nonlinearity
- Vol. 37 (7) , 075025
Open AccessThe Batchelor–Howells–Townsend spectrum: large velocity case
We consider the behaviour of a passive tracer θ governed by ∂ t θ + u ⋅ ∇ θ = Δ θ + g in two space dimensions with prescribed smooth random incompressible velocity u ( x , t ) and source g(x). In 1959, Batchelor et al (J. Fluid Mech. 5 113) predicted that the tracer (power) spectrum should scale as | θ k | 2 ∝ | k | − 4 | u k | 2 for | k | above some κ ¯ ( u ) , with different behaviour for | k | ≲ κ ¯ ( u ) predicted earlier by Obukhov and Corrsin. In this paper, we prove that the BHT scaling does indeed hold probabilistically for sufficiently large | k | , asymptotically up to controlled remainders, using only bounds on the smaller | k | component.
- Open Access
The Batchelor-Howells-Townsend spectrum: large velocity case
We consider the behaviour of a passive tracer $θ$ governed by $\partial_tθ+ u\cdot\nablaθ= Δθ+ g$ in two space dimensions with prescribed smooth random incompressible velocity $u(x,t)$ and source $g(x)$. In 1959, Batchelor, Howells and Townsend (J.\ Fluid Mech.\ 5:113) predicted that the tracer (power) spectrum should then scale as $|θ_k|^2\propto|k|^{-4}|u_k|^2$ for $|k|$ large depending on the velocity $u$. For smaller $|k|$, Obukhov and Corrsin earlier predicted a different spectral scaling. In this paper, we prove that the BHT scaling does indeed hold probabilistically for sufficiently large $|k|$, asymptotically up to controlled remainders, using only bounds on the smaller $|k|$ component.Open AccessThe Batchelor-Howells-Townsend spectrum: large velocity case
We consider the behaviour of a passive tracer $θ$ governed by $\partial_tθ+ u\cdot\nablaθ= Δθ+ g$ in two space dimensions with prescribed smooth random incompressible velocity $u(x,t)$ and source $g(x)$. In 1959, Batchelor, Howells and Townsend (J.\ Fluid Mech.\ 5:113) predicted that the tracer (power) spectrum should then scale as $|θ_k|^2\propto|k|^{-4}|u_k|^2$ for $|k|$ large depending on the velocity $u$. For smaller $|k|$, Obukhov and Corrsin earlier predicted a different spectral scaling. In this paper, we prove that the BHT scaling does indeed hold probabilistically for sufficiently large $|k|$, asymptotically up to controlled remainders, using only bounds on the smaller $|k|$ component. - 13 December 2022
- Published by Elsevier in Physica D: Nonlinear Phenomena
- Vol. 445
The Batchelor–Howells–Townsend spectrum: Three-dimensional case
- 13 December 2022
- Published by Elsevier in Physica D: Nonlinear Phenomena
- Vol. 445
The Batchelor–Howells–Townsend spectrum: Three-dimensional case
- 24 February 2020
- Published by Springer Nature in Journal of Mathematical Fluid Mechanics
- Vol. 22 (2) , 1-14
Tracer Turbulence: The Batchelor–Howells–Townsend Spectrum Revisited
- 24 February 2020
- Published by Springer Nature in Journal of Mathematical Fluid Mechanics
- Vol. 22 (2) , 1-14
Tracer Turbulence: The Batchelor–Howells–Townsend Spectrum Revisited
- Open Access
- 1 January 2019
- Published by Elsevier in Physica D: Nonlinear Phenomena
- Vol. 386-387, 31-37
Navier–Stokes equations on the -plane: Determining modes and nodes- 1 January 2019
- Published by Elsevier in Physica D: Nonlinear Phenomena
- Vol. 386-387, 31-37
Open AccessNavier–Stokes equations on the -plane: Determining modes and nodes - 1 July 2018
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 59 (7) , 073104
Energy spectra and passive tracer cascades in turbulent flows
We study the influence of the energy spectrum on the extent of the cascade range of a passive tracer in turbulent flows. The interesting cases are when there are two different spectra over the potential range of the tracer cascade (in 2D when the tracer source is in the inverse energy cascade range and in 3D when the Schmidt number Sc is large). The extent of the tracer cascade range is then limited by the width of the range for the shallower of the two energy spectra. Nevertheless, we show that in dimension d = 2, 3, the tracer cascade range extends (up to a logarithm) to , where κdD is the wavenumber beyond which diffusion should dominate and p is arbitrarily close to 1, provided Sc is larger than a certain power (depending on p) of the Grashof number. We also derive estimates which suggest that in 2D, for Sc ∼ 1, a wide tracer cascade can coexist with a significant inverse energy cascade at Grashof numbers large enough to produce a turbulent flow.- 1 July 2018
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 59 (7) , 073104
Energy spectra and passive tracer cascades in turbulent flows
We study the influence of the energy spectrum on the extent of the cascade range of a passive tracer in turbulent flows. The interesting cases are when there are two different spectra over the potential range of the tracer cascade (in 2D when the tracer source is in the inverse energy cascade range and in 3D when the Schmidt number Sc is large). The extent of the tracer cascade range is then limited by the width of the range for the shallower of the two energy spectra. Nevertheless, we show that in dimension d = 2, 3, the tracer cascade range extends (up to a logarithm) to , where κdD is the wavenumber beyond which diffusion should dominate and p is arbitrarily close to 1, provided Sc is larger than a certain power (depending on p) of the Grashof number. We also derive estimates which suggest that in 2D, for Sc ∼ 1, a wide tracer cascade can coexist with a significant inverse energy cascade at Grashof numbers large enough to produce a turbulent flow.- Open Access
Navier--Stokes equations on the $β$-plane: determining modes and nodes
We revisit the 2d Navier--Stokes equations on the periodic $\beta$-plane, with the Coriolis parameter varying as $\beta y$, and obtain bounds on the number of determining modes and nodes of the flow. The number of modes {and nodes} scale as $cG_0^{1/2} + c'(M/\beta)^{1/2}$ and $cG_0^{2/3} + c'(M/\beta)^{1/2}$ respectively, where the Grashof number $G_0=|f_v|_{L^2}^{}/(\mu^2\kappa_0^2)$ and $M$ involves higher derivatives of the forcing $f_v$. For large $\beta$ (strong rotation), this results in fewer degrees of freedom than the classical (non-rotating) bound that scales as $cG_0$.Open AccessNavier--Stokes equations on the $β$-plane: determining modes and nodes
We revisit the 2d Navier--Stokes equations on the periodic $\beta$-plane, with the Coriolis parameter varying as $\beta y$, and obtain bounds on the number of determining modes and nodes of the flow. The number of modes {and nodes} scale as $cG_0^{1/2} + c'(M/\beta)^{1/2}$ and $cG_0^{2/3} + c'(M/\beta)^{1/2}$ respectively, where the Grashof number $G_0=|f_v|_{L^2}^{}/(\mu^2\kappa_0^2)$ and $M$ involves higher derivatives of the forcing $f_v$. For large $\beta$ (strong rotation), this results in fewer degrees of freedom than the classical (non-rotating) bound that scales as $cG_0$. - Open Access
Energy spectra and passive tracer cascades in turbulent flows
We study the influence of the energy spectrum on the extent of the cascade range of a passive tracer in turbulent flows. The interesting cases are when there are two different spectra over the potential range of the tracer cascade (in 2D when the tracer forcing is in the inverse energy cascade range, and in 3D when the Schmidt number Sc is large). The extent of the tracer cascade range is then limited by the width of the range for the shallower of the two energy spectra. Nevertheless, we show that in dimension $d=2,3$ the tracer cascade range extends (up to a logarithm) to $\kappa_{d\text{D}}^{p}$, where $\kappa_{d\text{D}}$ is the wavenumber beyond which diffusion should dominate and $p$ is arbitrarily close to 1, provided Sc is larger than a certain power (depending on $p$) of the Grashof number. We also derive estimates which suggest that in 2D, for Sc${}\sim1$ a wide tracer cascade can coexist with a significant inverse energy cascade at Grashof numbers large enough to produce a turbulent flow.Open AccessEnergy spectra and passive tracer cascades in turbulent flows
We study the influence of the energy spectrum on the extent of the cascade range of a passive tracer in turbulent flows. The interesting cases are when there are two different spectra over the potential range of the tracer cascade (in 2D when the tracer forcing is in the inverse energy cascade range, and in 3D when the Schmidt number Sc is large). The extent of the tracer cascade range is then limited by the width of the range for the shallower of the two energy spectra. Nevertheless, we show that in dimension $d=2,3$ the tracer cascade range extends (up to a logarithm) to $\kappa_{d\text{D}}^{p}$, where $\kappa_{d\text{D}}$ is the wavenumber beyond which diffusion should dominate and $p$ is arbitrarily close to 1, provided Sc is larger than a certain power (depending on $p$) of the Grashof number. We also derive estimates which suggest that in 2D, for Sc${}\sim1$ a wide tracer cascade can coexist with a significant inverse energy cascade at Grashof numbers large enough to produce a turbulent flow. - Open Access
- 1 January 2016
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 36 (10) , 5681-5707
Averaging method applied to the three-dimensional primitive equations
In this article we study the small Rossby number asymptotics for the three-dimensional primitive equations of the oceans and of the atmosphere. The fast oscillations present in the exact solution are eliminated using an averaging method, the so-called renormalisation group method.
- 1 January 2016
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 36 (10) , 5681-5707
Open AccessAveraging method applied to the three-dimensional primitive equations
In this article we study the small Rossby number asymptotics for the three-dimensional primitive equations of the oceans and of the atmosphere. The fast oscillations present in the exact solution are eliminated using an averaging method, the so-called renormalisation group method.
- Open Access
- 1 February 2015
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems-Series B
- Vol. 20 (4) , 1263-1271
Navier--Stokes equations on a rapidly rotating sphere
- 1 February 2015
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems-Series B
- Vol. 20 (4) , 1263-1271
Open AccessNavier--Stokes equations on a rapidly rotating sphere